particles and the universe: proceedings of the eighteenth lake louise winter institute lake louise,...

Proceedings of the Eighteenth Lake Louise Winter Institute

PARTICLES AND THE UNIVERSE

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Proceedings of the Eighteenth Lake Louise Winter Institute

PARTICLES AND THE UNIVERSE

lake Louise, Alberta, Canada; 16 - 22 February 2003

Editors

A Astbury B A Campbell F C Khanna M G Vincter

K World Scientific N E W J E R S E Y L O N D O N S I N G A P O R E * S H A N G H A I - H O N G K O N G * T A I P E I - C H E N N A I

Published by

World Scientific Publishing Co. Re. Ltd. 5 Toh Tuck Link, Singapore 596224 USA ofice: Suite 202, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library

PARTICLES AND THE UNIVERSE Proceedings of the 18th Lake Louise Winter Institute

Copyright 0 2004 by World Scientific Publishing Co. Re. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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ISBN 981-238-810-9

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PREFACE

The eighteeth annual Lake Louise Winter Institute, entitled Particles and the Universe, was held from February 16-22, 2003 at the Chateau Lake Louise, located in the scenic Canadian rocky Mountains. The format of the Winter Institute consisted of a mixture of pedagogical invited talks and short contributed talks presenting the latest results from experiments and new developments in theory. As usual, the sessions were held in the mornings and evenings, leaving the afternoons free for recreation and enjoyment of the winter wonderland in the Rockies.

The pedagogical talks focused on the recent results from RHIC with an outlook for observing the quark-gluon plasma. Recent data from B-factories with particular emphasis on CP violation was presented. The intriguing and interesting topic of neutrino physics was presented and its propects for the future were dealt with at length. Important experiments essential for our understanding of nuclear astrophysics were presented. Recent developments in cosmology were presented with its close connection to particle physics. Finally the possible physics that will be explored at future accelerators was considered at length. These pedagogical talks were complemented by a series of short contributed talks.

We wish to express our sincere thanks to Lee Grimard, who carried out all the organizational duties with patience and skill. Many thanks go to Suzette Chan for putting together numerous diverse contributions into a nice volume. We thank David Maybury for his outstanding support with the logistics and transportation of participants to the Winter Institute.

Finally, we wish to acknowledge support from the Canadian Institute of Theoretical Astrophysics, which assisted six students to attend the Winter Institute. We thank the University of Alberta Conference Fund, the Dean of Science, the Institute of Particle Physics and TRIUMF for generous financial support. The Department of Physics at the University of Alberta is thanked for all the infrastructure support.

Organizing committee: A. Astbury B.A. Campbell

F.C. Khanna M.G. Vincter

V

CONTENTS

Preface

Contents

I. Exploring QCD with Heavy Ion Collisions M. D. Baker

11. Physics @ Future Accelerators J. Ellis

111. B Physics and CP Violation R. V. Kowalewski

IV. Nuclear Astrophysics and Nuclei Far from Stability H. Schatz

V. Neutrino Physics: Status and Prospects K. Scholberg

Semileptonic B Decays at LEP: Extraction of VCB and B -+ D **tv P. Amaral

B Physics at CDF K. Anikeeu

Triple and Quadric Gauge Couplings a t LEPP I. Bailey

Recent Results on New Phenomena from DO F. Beaudette

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vii

1

31

91

118

132

162

168

175

181

Search for a Fourth Generation b'-Quark a t the Delphi Experiment at LEP 187 N. Castro

CLEO Results on B -+ D*p and B + DK G. P. Chen

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vii

... Vl l l

SUSY Searches and Measurements with the ATLAS Experiment at the Large Hadron Collider D. Costanzo

Measurement of the W Boson Mass at LEP J. D’Hondt

In-Situ Calibration of the CMS Electromagnetic Calorimeter D. I. Futyan

Spin Physics and Ultra-Peripheral Collisions at STAR C. A. Gagliardi

Latest Results on Time-Dependent CP Violation from Belle T. J . Gershon

Global Observables and Identified Hadrons in the PHENIX Experiment at RHIC H. -A. Gufstafsson

LEP Limits on Higgs Boson Masses in the SM, in the MSSM and in General 2HD Models S. Haug

The AMS-02 Experiment R. Henning

Rare B Decays in BaBar A. Hicheur

Recent Results in B-Physics and Prospects for Higgs Searches at DId M. Hohlfeld

The HARP Hadron Production Experiment and Its Significance for Neutrino Factory Design L. C. Howlett

A Monte Carlo Test of the Optimal Jet Definition E. Jankowski

199

205

211

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224

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236

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254

260

266

ix

Single Photoelectron Detection in LHCB Pixel HPDS S. Jolly

272

Nonequilibrium Phase Transitions in the Early Universe S. P. Kim

278

Recent Results in Electroweak and Top Physics at D 0 M. Klute

284

Searches for Higgs Bosons Beyond SM and (Standard) MSSM at LEP M. Kupper

290

Polarization Dependence of Basic Interactions in Strong Magnetic Fields D. A. Leahy

Selected Charm Physics Results from BaBar W. S. Lockman

Searches for New Physics at HERA N. M. Malden

Quantum Chaos in the Gauge Fields at Finite-Temperature D. U. Matrasulov

Galactic Dark Matter Searches with Gas Detectors B. Morgan

Measurement of W Polarisation with L3 a t LEP R. A. Ofierzynski

A Search for CP Violation in, and a Dalitz Analysis of Do --t n- n+ no Decays in CLEO 1I.V C. Plager

Measurement of High-P, and Leptonic Observables with the PHENIX Experiment at RHIC T. Sakaguchi

Nonequilibrium Evolution of Correlation Functions S. Sengupta

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303

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3 14

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326

332

338

344

X

Recent Results from BELLE R. Seuster

Renormalization-Group Improvement of Effective Actions Beyond Summation of Leading Logarithms A. Squires

Neutral Current Detectors in the Sudbury Neutrino Observatory L. C. Stonehill

Energy and Particle Flow Measurements a t HERA K. Tokushuku

High PT Je t Production and as Measurements in Electron-Proton Collisions K. Tokushuku

Study of the e+e- -+ Z e'e- Process at LEP R. Vasquez

Investigation of Higgs Bosons in the Low Mass Region with ATLAS M. Wielers

Unified Approach for Modelling Neutrino and Electron Nucleon Scattering Cross Sections from High Energy to Very Low Energy U.-K. Yang

Charmonium and B-Quark Production a t HERA-B T. Zeuner

AMSOl Results P. Zuccon

List of Participants

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EXPLORING QCD WITH HEAVY ION COLLISIONS

M. D. BAKER Brookhaven National Laboratory,

Bldg. 5554, P.O. Box 5000 Upton, N Y 11973-5000, USA E-mail: Mark.BakerQbnl.gov

After decades of painstaking research, the field of heavy ion physics has reached an exciting new era. Evidence is mounting that we can create a high temperature, high density, strongly interacting “bulk matter” state in the laboratory - perhaps even a quark-gluon plasma. This strongly interacting matter is likely to provide qualitative new information about the fundamental strong interaction, described by Quantum Chromodynamics (QCD). These lectures provide a summary of experimental heavy ion research, with particular emphasis on recent results from RHIC (Relativistic Heavy Ion Collider) at Brookhaven National Laboratory. In addition, we will discuss what has been learned so far and the outstanding puzzles.

1. Introduction

While the universe as we know it is well described by the standard model of particle physics, some important questions remain unanswered. Perturba- tive Quantum Chromodynamics (pQCD) - a part of the standard model - is a very successful description of hard, or short-distance, phenomena l, where the “strong interaction” becomes weak due to asymptotic freedom. For example, the production of jets in pp collisions at 1.8 TeV is well described for jet transverse energies from 10-400 GeV 2. There is, however, an important set of soft physics phenomena that are not well understood from first principles in QCD: color confinement, chiral symmetry breaking, and the structure of the vacuum. These phenomena are important: almost all of the visible mass of the universe is generated by soft QCD and not by the direct Higgs mechanism. The current masses of the three valence quarks make up only about 1% of the mass of the nucleon 3 .

In order to study these phenomenon, we seek to separate color charges by heating matter until a quark-gluon plasma is formed. A conventional electromagnetic plasma occurs at temperatures of about 104-105 K, corresponding to the typical ionization energy scale of 1-10 eV. Theoretical

1

2

studies of QCD on the lattice indicate that the typical energy scales of thermally driven color deconfinement are in the vicinity of 170 MeV, or 2 x 10l2 K. In addition to providing information about the strong interaction, achieving such temperatures would also provide a window back in time. The color confinement phase transition is believed to have occurred within the first few microseconds after the big bang.

In order to achieve such high temperatures under laboratory conditions, it is necessary to use a small, dynamic system. For instance, experimental fusion reactors heat a conventional plasma up to temperatures as high as lo8 K over distance scales of meters and lasting for seconds. By colliding gold ions at nearly the speed of light, we expect to achieve temperatures of order 10l2 K over distance scales of order 10 fm and time scales of order 10- 100 ysa. Clearly one of the challenges in this endeavor will be to determine whether such small and rapidly evolving systems can elucidate the bulk behavior that we are interested in. Another challenge will be to use some of the rarer products of the collisions to probe the created “bulk” medium.

The focus of these lectures will be on the results coming out of the Rel- ativistic Heavy Ion Collider (RHIC) experiments at Brookhaven National Laboratory (BNL) . Earlier experimental results and some theoretical work will be mentioned as needed, but a comprehensive review of heavy ion physics will not be attempted. The RHIC spin physics program using polarized protons will also not be covered.

2. The Machine and Detectors

The RHIC data described in these lectures were taken during the last three years of running at RHIC, starting in the summer of 2000, as summarized in Table 1. The runs were characterized by their species and their 6which is the cm collision energy of one nucleon taken from each nucleus. For instance, a AuAu collision with 100 x A GeV on 100 x A GeV would have 6 = 200 GeV. Most of the runs were several weeks in duration, with two exceptions. The 56 GeV run, not intended as a physics run, was only 3 hours long and data is only available from a preliminary subsystem of one experiment (PHOBOS). The 19.6 GeV run was 24 hours long and usable data were taken by three experiments. For the 130 and 200 GeV runs, all four detectors participated: two large detectors/collaborations with 300-400 collaborators each and two small detectors/collaborations

aRecall that one yoctosecond = lo-’* s.

3

with 50-70 collaborators each. These four detectors complement each other and have provided a broad range of physics results. The BRAHMS experiment (Broad RAnge Hadron Magnetic Spectrometer) focuses on tracking and particle ID at high transverse momentum over a broad range of rapidity from 0-3. The PHENIX experiment (Pioneering High Energy Nuclear Interaction experiment) provides a window primarily at mid-rapidity, but specializes in high rate and sophisticated triggering along with a capability to measure leptons and photons as well as hadrons. The PHOBOS experiment (descendant of the earlier MARS experiment) provides nearly 47r coverage for charged particle detection, good vertex resolution, and sensitivity to very low p , particles. The STAR experiment (Solenoidal Tracker At Fthic) provides large solid angle tracking and complete coverage of every event written to tape. More details concerning the capabilities of the accelerator and experiments can be found in NIM journal issue dedicated to the RHIC accelerator and detectors 5 .

Table 1. RHIC running conditions to date.

19.6, 200 GeV

Jan. 2002 200 GeV

Some data will also be shown from lower energy heavy ion collisions, particularly from the CERN-SPS (Conseil European pour la Recherchk Nu- Claire - Super Proton Synchrotron) will also be discussed. The top CERN energy is 6 = 17.2 GeV.

3. Strongly Interacting Bulk Matter

In order to learn anything about QCD from heavy ion collisions, we must first establish that we have created a state of strongly interacting bulk matter under extreme conditions of temperature and pressure.

3.1. How Much Matter?

Figure 1 shows the charged particle distribution for central (head-on) AuAu collisions in the pseudorapidity variable: q G - In tan(Ol2). These data imply a total charged multiplicity of 1680 f 100 for the 19.6 GeV data and 5060 f 250 for the 200 GeV data 6 . While this number is considerably

4

-5 0

Figure 1. ,/T& = 19.6, 130, and 200 GeV. Data taken from PHOBOS 6 .

Pseudorapidity distributions, dN,h/dq, for central (6%) AuAu collisions at

smaller than Avagadro’s number, it is substantial thermodynamically since small-system corrections to conventional thermodynamics start to become unimportant for systems with about 1000 particles or more 7.

The number of particles produced in a given AuAu collision varies widely due to the variable geometry of the collision. Some collisions are nearly head-on with a small impact parameter, while most collisions have a larger impact parameter, with only a partial overlap of the nuclei. These cases can be sorted out experimentally, using both the number of produced particles and the amount of “spectator” neutrons seen at nearly zero degrees along the beam axis. The impact parameter or “centrality” of the collision is characterized by the number of nucleons from the original ions which participate in the heavy ion collision, (Npart) , or the number of binary NN collisions, (Ncoll). More details can be found in Refs.

3.2. Elliptic Flow: Evidence for Collective Motion

Non-central heavy ion collisions have an inherent azimuthal asymmetry. The overlap region of two nuclei is roughly ellipsoidal in shape. If there is collective motion that develops early in the collision, this spatial anisotropy

5

Figure 2. Left panel: elliptic flow as a function of centrality as seen by STAR (data) compared to hydrodynamic models (rectangles) lo. Right panel: peak elliptic flow as a function of collision energy for ultrarelativistic collisions, taken from an NA49 compila- tion l l .

can be converted to an azimuthal asymmetry in the momentum of detected particles. This azimuthal asymmetry is characterized by a Fourier decomposition of the azimuthal distribution:

dN/dr$ = No(l+ 2w1 cos4 + 2212 COS(24)), (1)

where r$ is the azimuthal angle with respect to the reaction planeb. The left-hand panel of Fig. 2 shows that the elliptic flow parameter is quite large, nearly reaching the values predicted by hydrodynamic models. These models assume a limit of local equilibrium with collective motion of the bulk "fluid". The right-hand panel of Fig. 2 shows that this asymmetry is the largest ever seen at relativistic energies.

Elliptic flow, in addition to indicating that there is collective motion, can provide information about the type of motion. In particular, the p , dependence of elliptic flow can distinguish between two limits: the low density limit and the hydrodynamic limit (rapidly expanding opaque source). In the low density limit, some of the produced particles are absorbed or scattered once (and usually only once). In this case, for relativistic particles, v2 is nearly independent of p , . In the hydrodynamic limit, in contrast, we expect 212 oc p , for moderate values of p, . This effect comes about because the expansion causes a correlation between normal space and momentum

bThe true reaction plane is defined by the impact parameter vector between the gold ions. The experimental results shown have been corrected for the reaction-plane resolution, which would otherwise dilute the signal.

6

0.16

0.14

0.12

0.08

0.06

0.04 * -8- +

+

o m +-

P, ( G e W

Figure 3. Elliptic flow versus p , for all particles (left panel) lo, and for identified particles (right panel) from STAR 12. The curves in the right panel refer to a hydrodynamic model description.

space, forcing the highest p , particles to come from the surface, while low p , particles can come from anywhere in the volume. Data from the SPS favor the hydrodynamic limit 13. The left-hand panel of Fig. 3 shows a clear linear relationship between elliptic flow and transverse momentum at RHIC as well, while the right-hand panel shows that hydrodynamic models not only describe the overall trend, but even describe the pions and protons separately.

~0.06 I . . . I . . . I . . . I . . . I . * . I . . . I > PHOBOS Au-AU

01 I . A. I . . . I . . . I . . . ' . ' . I . . . I ' -6 -4 -2 0 2 4 6

rl

Figure 4. Elliptic flow as a function of pseudorapidity from PHOBOS 14.

Finally, elliptic flow can be examined as a function of pseudorapidity. The expectation was that the elliptic flow would be nearly independent of pseudorapidity as the basic physics of RHIC were expected to be invariant

7

under longitudinal boosts. Fig. 4 shows that w2 is strongly dependent on pseudorapidity, a result which has still not been explained.

Taken together, these results show clear evidence of collective motion and suggest a system at or near hydrodynamic equilibrium which is rapidly expanding in the transverse direction and which does not exhibit longitudinal boost-invariance.

3.3. Hanbury-Brown Twiss Effect: More Dynamics

Intensity interferometery, or the Hanbury-Brown Twiss effect 15, is a technique used to measure the size of an object which is emitting bosons (e.g. photons from a star or pions from a heavy ion collision). Boson pairs which are close in both momentum and position are quantum mechanically enhanced relative to uncorrelated boson pairs. Bosons emitted from a smaller spatial source are correlated over a broader range in relative momentum, which allows you to image a static source using momentum correlations.

For a given pair of identical particles, we can define their momentum difference, f, and their momentum average, z. We can further define the three directions of our coordinate system 16:

0 Longitudinal (Rl) - along the beam direction (S), 0 Outwards (R,) - In the (2 , k ) plane, I 2 , 0 Sidewards (R,) - I i & I i.

For a boost-invariant source, the measured sidewards radius at low pT will correspond to the actual physical transverse (rms) extent of the source at freezeout, while the outwards radius will contain a mixture of the spatial and time extent of the source. Particles emitted earlier look like they are closer to the observer, which artificially extends the apparent source in the out direction. In particular,

RZ - R: = iOf.2 - 2/31aZ, + (a: - a:), (2)

where is the transverse velocity associated with z, gT is the “duration of emission’’ parameter, ox and uv are the geometric size in the out and side directions, and ox,. is the space-time correlation in the out direction.

In the case of an azimuthally symmetric and transparent source, the last two terms are taken to be small or zero and we have

Given the assumption of a boost-invariant, azimuthally symmetric and transparent source, the HBT results from heavy ion collisions have been

8

c-2 1

0.5 - 8 E = 0 6 a

4

0 E895 H NA49 0 WA98 A E866 V NA44 * STAR

*+A + +T+

u)

. I

1.251 , * **+) , , ‘ii , , , , , , , I i; rr“ 1 2 n

1

Figure 5. HBT parameters as a function of colliding beam energy. 17.

perennially confusing. From Eq. 3, we expect R,/R, 2 4 since most sources should emit for a time which is of the same order as their size. Some models of the Quark-Gluon Plasma predict an even larger value for this ratio as the plasma might need to emit particles over a long time duration in order to get rid of the entropy Is. However, as can be seen in Fig. 5 , R,/R, is basically unity at RHIC energies, na’ively implying an instantaneous emission of particles over a moderately large volume.

This situation, along with the modest values of RI, has been termed the “HBT puzzle”. Primarily, though, these data indicate a need to improve the modeling of the collision. If you consider a source which is opaque, rapidly expanding and also not boost invariant, the meaning of RZ - R: changes

9

since we must use Eq. 2 and not Eq. 3. Opacity reduces the apparent R, value since you only see the part of the source closest to you in the out direction. Transverse expansion along with opacity will decrease the ratio further since particles emitted later are also emitted closer to the viewer, reducing the magnitude of R,. Finally, a general longitudinal expansion (not just coasting) must be taken into account since we know that the source is not boost invariant. This effect would explain the small size of Rl

and has also been shown l9 to reduce the ratio R,/R,. So, while HBT and elliptic flow have not been successfully described

in full detail by the hydrodynamic models yet, the qualitative message they provide is very similar. The source is rapidly expanding (probably in all three dimensions), opaque, and can be described as “hydrodynamically equilibrated bulk matter”.

3.4. Characterizing the Bulk Matter

Having established that the system has a large number of particles as well as collective behavior, we can now proceed to consider bulk quantities such as the temperature and baryon chemical potential of the system.

In conventional, static, thermodynamic systems, the temperature can be measured by directly measuring the average energy per particle. In a very dynamic system, such as a heavy ion collision, we have to separate the energy contributed by collective motion from the thermal energy. To do this, we make use of the fact that the collective velocity contributes more to the momentum of heavy particles than to lighter particles. Ther- mal fits 2o to (pT)(rn) yield a temperature of approximately 100 MeV and an average transverse expansion velocity of 0.55 c. This large expansion velocity supports the picture given by the elliptic flow and HBT.

Another thermometer is provided by the fact that the ratios of particles of different masses are sensitive to the temperature. In addition, ratios of particles with the same mass, but different quark content, such as p / p and K-/K+, are sensitive to the balance between matter and antimatter, characterized by the baryon chemical potential p ~ . Positive values of pug refer to a matter (baryon) excess in a system. Fig. 6 shows particle abundance ratios and a thermal fit. This fit yields a constant temperature of 176-177 MeV at both energies, but a falling baryon density (41 MeV at 130 GeV and 29 MeV at 200 GeV). The falling baryon density is expected. Higher energy collisions dilute the fixed initial baryon excess from the original gold nuclei and also make it harder to transport the baryon excess to

10

Figure 6. gies 21.

Particle abundance ratios and a thermal fit for the two highest RHIC ener-

midrapidity. We are immediately faced with a dilemma: our kinetic thermometer,

based on energy per particle, indicated a temperature of - 100 MeV, while our chemical thermometer, based on particle abundances, indicated a much higher temperature of - 175 MeV. The resolution of this paradox lies in the fact that only inelastic collisions can change the particle abundances while both elastic and inelastic collision serve to equalize the energy between particles. Using the terminology of cosmology, we can define an approximate “freezeout hypersurface” which contains the spacetime points of the final collisions suffered by each particle. In the case of a heavy ion collision, the chemical freezeout can occur earlier than the kinetic freezeout. This resolves our dilemma, but with the unavoidable consequence of making our picture of the collision somewhat more complicated. It should be noted that the HBT results are actually imaging the kinetic freezeout boundary as the source.

3.5. “Little Bang Cosmology”

As in cosmology, we are interested in understanding what happened before the freezeout. We can estimate the energy density from the transverse energy produced in the collision and the cylindrical volume occupied shortly after the collision occurred. This leads to the formula 2 2 :

(4) 1 1 dET c=---

xR2 CTO dy

where the radius R is the nuclear radius and TO is the time it takes for the transverse energy to be effectively equilibrated (0.2-1.0 fm/c).

11

g - 4-

z V -F

0 - PHENZX 0 - WA98

a)

A RHIC comb. 130 GeV

0 NA49(SPS) - W PHOBOS56GeV

I 0 EEWE917(AGS) - - UA!i(G)

0' ' I ' ' ' ' " Npart

0 100 200 300

Figure 7. Transverse energy at midrapidity as a function of centrality for 130 GeV and 17 GeV collisions. Left panel: per participating nucleon, right panel: per produced particle. Data taken from PHENIX 23.

I 1

1 o3 s i i (GeV)

10 1 o2

Figure 8. as a function of beam energy 2 4 .

Charged particle multiplicity per participating nucleon pair at midrapidity

Figure 7 (right panel) shows that the transverse energy per particle is about 800 MeV at RHIC while Fig. 8 shows the multiplicity. Combining these results, using Eq. 4 yields E =5-25 GeV/fm3 for central collisions at the highest RHIC energy. Fig. 9 shows the theoretical relationship, based on lattice QCD calculations 4 , between energy density and temperature. The expected T4 dependence of an ideal gas has been divided out, leading to a a constant value for high temperature, proportional to the number of

12

3flavour - 2 t 1 flilvocir -

2flavour -

1.0 1.5 2.0 2.5 3.0 3.5 4.0

Figure 9. Energy density scaled by T4 (natural units f i = c = k = 1) as as a function of temperature scaled by the critical temperature (T/T,). The arrows on the right indicate the Stefan-Boltzmann values for an ideal non-interacting gas. Figure taken from Ref. 4.

degrees of freedom in the quark-gluon plasma phase. Combining the data with the theoretical curves leads to an estimated

initial temperature of 300 f 50 MeV for central AuAu collisions at the top RHIC energy. This is significantly higher than the theoretical transition temperature of - 170 MeV. A similar exercise at the top CERN-SPS energy

=17 GeV, yields an estimated initial temperature of 240 f 50 MeV. It should be noted that if we assume a hadronic description rather than a phase transition, the number of degrees of freedom should actually be lower, implying an even higher initial temperature (about twice as high). This means that the estimated initial temperatures of - 300 and 240 MeV for RHIC and CERN actually represent lower limits.

3.6. Summary: Bulk Matter

Figure 10 shows the phase diagram based on the chemical freezeout points measured at various energies in heavy ion collisions including the 130 GeV point from RHIC. The 200 GeV point from RHIC would be at basically the same temperature, but p~g = 29 MeV rather than pg = 41 MeV. The curve through the data implies freezeout at a fixed energy per particle of about 1 GeV, while the bands indicate the theoretical expectation for the transition between confined and deconfined matter. The initial temperatures estimated for both RHIC and CERN are not shown, but they would lie above the theory curve, with the RHIC temperature being 300 f 50 MeV.

13

200

150

100

50

0

T [MeV]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Figure 10. Phase diagram of heavy ion collisions from Ref. 2 5 . The data points represent heavy ion collisions over a broad range of energies. The curve through the data points represents a fixed energy per particle. The upper band represents an estimate of the phase boundary. The lower band represents a constant energy density (0.6 GeV/fm3). The isolated point above the theory curves represents a theoretical critical point.

The constant freezeout temperature for high energy ion collisions, appear- ing at the theoretical boundary between confined and deconfined matter is provocative. It could be an accident, but it is similar to a situation where you have a detector which only detects liquid, you determine indirectly that you created matter at 200"C, and you directly detect droplets of water at a temperature of 100°C.

To summarize this section, we have produced a dense, hot, rapidly expanding bulk matter state. We have seen a universal freezeout curve and it is suggestively close to the expected boundary between deconfined and confined matter. Furthermore, we have indications that the initial collision reaches energy densities (and therefore temperatures) well in excess of that expected to be needed for deconfinement.

Efforts to probe this state quantitatively are just beginning, but show promise. This will be the subject of the next section.

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4. Probing the Earliest, Hottest Part of the Collision

While the freezeout temperature measurements are on solid footing, the estimates presented above for the initial temperature are indirect. As the RHIC program develops, we can go beyond these qualitative discussions of the early times and start probing them more quantitatively.

4.1. Electromagnetic and Hidden Flavor Probes

Perhaps the cleanest method, from a theoretical perspective] would be to examine thermal photons and leptons that originate from the early part of the collision when the temperature was higher. These weakly interacting particles are expected to decouple thermally (or “freezeout”) from the bulk strongly interacting matter much earlier than hadrons. Combined with a measurement of the energy density this would effectively measure the number of degrees of freedom in the initial state. While it is theoretically very clean, this measurement is experimentally very challenging. A typical central collision at RHIC produces thousands of neutral pions which decay into thousands of photons in each event and serve as a background to this measurement. A typical RHIC detector also has literally tons of material in which background photons (and leptons) can be produced.

Despite the difficulty, these measurements and fits have been attempted at the SPS, both in terms of direct photon spectra 26 and thermal leptons 27.

These results lead to an estimated initial temperature at the SPS of N

200 MeV, consistent with our estimate above for partonic matter. These results, however, are very sensitive to details of how the backgrounds are handled.

Hidden heavy flavor measurements (strangeness, charm, and beauty) also show promise as potentially sensitive probes of the density of the medium and of chiral symmetry restoration. Fig. 11 shows the suppression of the J/+ (hidden charm) compared to collision scaling at RHIC and the SPS. Sensitivity can also be found in the mass, line shape, and yield of the q5 particle (hidden strangeness), seen by its hadronic and leptonic decay modes 28. So far at RHIC, these measurements suffer from lack of statistical power.

One common denominator that would make many of these signals clearer would be a clean measurement of open heavy flavor (D and B particles). These measurements should be forthcoming from RHIC following upgrades to the detectors and improved luminosity from the collider.

15

o.5 ~10’‘ c t I

Number of Participants

Figure 11. (black squares and arrows) 29.

Measured yield of J/$J by NA50 at CERN (stars) and by PHENIX at RHIC

4.2. Hadron Suppression: Jet Quenching?

In addition to measuring the initial temperature, we would like to have a more direct measure of the energy density of the bulk matter that we have created. One handle on this quantity is to study the behavior of high momentum particles in heavy ion collisions. In particular, partons with relatively high transverse momentum are predicted to lose energy when traveling through dense matter, in a phenomenon known as “jet quenching”. The amount of energy loss is proportional to the energy density of the matter traversed, so this is potentially a very sensitive probe.

All four experiments at RHIC measured particle spectra 3 0 1 3 1 3 3 2 , 3 3 , 3 4 , 3 5 .

These spectra need to be compared to a reference sample, appropriately scaled. The simplest such reference sample is to consider each NN collision in the initial AA collision geometry as being independent. This leads us to define a “nuclear modification factor” :

At high momentum, ( p ~ > 2 GeV/c) this ratio should approach unity if the collisions are independent and the jets are not affected by the material. Jet energy loss in the medium should show up as a suppression of high momentum hadrons. In lower energy AA collisions 36 and pA collisions 37,

an excess has been observed rather than a suppression. This effect is interpreted as being caused by multiple scattering during the initial collision.

16

0 2 4 0 2 4 PT (GeV/c) p,(GeW

Figure 12. and peripheral 130 GeV AuAu collisions compared to scaled reference samples 35.

Yields from PHENIX for a) charged particles and b) neutral pions for central

The results at RHIC energies are strikingly different from lower energy data as can be seen in Fig. 12 from PHENIX. Invariant yields for produced particles in central and peripheral 130 GeV AuAu data are compared to a scaled-up pp reference sample. For p , > 2 GeV, the peripheral data scales as expected, while the central AuAu data shows a substantial suppression. The dramatic difference between the different energies is even more apparent in Fig. 13 where the scaled reference data are divided out to yield RAA, the nuclear modification factor of Eq. 5. Clearly, something qualitatively different is occurring at RHIC energies. Similar results were seen by STAR at 130 GeV 30 and all four experiments at 200 GeV 3 1 t 3 2 9 3 3 7 3 4 . Since the peripheral data scales as expected, it is also possible to measure hadron suppression by taking the ratio of central/peripheral data, scaled by the ratio of Ncoll. At 200 GeV, this technique was used to establish that this hadron suppression persists to very high transverse momentum, as seen in Fig. 14. As indicated above, this hadron suppression may be a signature of jet quenching, in which case we have clear evidence of a system with very high energy density.

Another view of this hadron suppression, from PHOBOS and PHENIX, shows how strong the effect is. Fig. 15 (left panel) shows the yield in AuAu

17

d Au+AujsN,=l30'GeV' ' ' ' ' ' .................................................. . ........ t central 0-1 0%

............

I (h++h-)/2 /' . no ! Pb+Pb(Au) CERN-SPS

1 1 a+a CERN-ISR / A no

....................................... .......... ............

. . . -; i

<. i /,' i t i j

binary scaling . > ,>a . . .. i ..... c ........................................................

O h ' ' ' 2 ' ' ' ' 4 ' ' I '

PT (GeV/c)

Figure 13. Nuclear modification factor for charged particles and neutral pions for 17 GeV PbPb collisions at CERN and central 130 GeV AuAu collisions from PHENIX 35.

Figure 14. collisions at 200 GeV from STAR, using two different choices of peripheral data 33.

Scaled ratio of charged particle production in central to peripheral AuAu

18

3 U

1.2 7 .

1

w i i

1 . 4 1 " ' " " " ' I ' " I '

:- ............................................................. :

........... .....

5 0 100 200 300 0 100 200 300

0.8 0.6 0.4 - 0.2

4 - % 3:

U

1

" P 4 4

,m c P 7

L L

0 1 : : : I : : I : ; ; I ; : I I : : -

- i

1 pT>3.6GeVlc - 4 0 2.6 < pT < 3.6 GeVlc 1 ; ............................................................ t...1.6<~,.<.?!6.G~V!C ............ I

o ~ ~ " " ' " " " ~ ' " ~ l 100 200 300 400 %art

Figure 15. Scaling of charged hadron yields from AuAu collisions from PHOBOS and PHENIX. Left panel: Yield scaled per participant pair ((Npart)/2) normalized to the yield of the most peripheral bin (45-50%) 31. Right panel (lower plot): Yield scaled per participant pair with reference to pp data 38.

collisions for fixed values of p , , scaled by mid-central data ( (Npart) N 65) and normalized by (Npart). Consider the lower-right hand plot, with p , = 4.25 GeV/c. The dashed curve shows the expectation if Ncoll (A4 /3 ) scaling held true over the centrality range shown, while the solid line shows the expectation of Npart (A') scaling . For Npart > 65, we see approximate A' scaling of high p , particle production. Fig. 15 (right panel) shows a similar result, normalized to pp data, from PHENIX. The lower plot is normalized per participant and the result for p , > 3.6 GeV/c is relatively flat for (Npart) > 80. This particular form of high p , suppression could be an indication that jet quenching reaches a geometric maximum involving

Another piece of evidence in favor of the jet quenching interpretation for this data comes from STAR. Jets in pp collisions can be seen by triggering on a high momentum particle and then looking for correlations of moderate p , particles azimuthally. In pp collisions, this leads to a clear two-jet signal with a cluster of particles near the trigger particle in azimuth and another cluster at A+ = 7r (back-to-back correlation). This signal indicates that jets are created and acquire large transverse momentum in conventional 2 + 2 parton scattering processes and that the jets survive. For peripheral AuAu collisions, one expects a similar result as found in pp, with a small

one power of length scale R A ~ 0: Npart 113 (see e.g. Ref. 39).

19

correction due to correlations induced by elliptic flow‘.

0 Au+Audata o p+pdala+flow 1.4, I I I I I I I I I I I I I I I I I I t I I 1 I I I I I I I 1 4

6 4 p#g) c 8 GeVlc STAR PRELIMINARY

1 1 1 , 1 1 1 1 1 1 1

-3 -2 -1 0 1 2 3 A Q (radians)

Figure 16. Azimuthal correlation functions from STAR 40. Left panel: Data from peripheral AuAu collisions (filled circles) compared to a jet+flow reference sample (open circles) and a flow-only reference curve. Right panel: Data from central AuAu collisions (points) compared to a jet+flow reference sample (upper curve) and a flow-only reference curve (lower curve).

-3 -2 -1 0 1 2 3 A+ (radians)

Figure 16 (left panel) shows that the reference sample constructed from pp collisions and the measured elliptic flow successfully describes the peripheral AuAu data: jets are created back-to-back and survive. In contrast, Fig. 16 (right panel) shows the result for central AuAu data. In this case, the azimuthal correlation function agrees with the jet+flow reference for A4 - 0 while it agrees with the flow-only reference for A$ N 7r. This means that the near-side jet survives, but the away-side jet disappears. The main point here is that this measurement shows that the hadron suppression is a jet phenomenon. If back-to-back jets are indeed produced as expected in central AuAu collisions, then the away-side jet is quenched by the bulk matter.

4.3. Is Jet Quenching the Only Possible Explanation?

Triggered by the observation that the scaling is approximately proportional to Npart, or Al, at large p , , Kharzeev, Levin, and McLerran showed that the “suppression” of jets in AuAu compared to NN could simply be due to

‘Since particles are preferentially produced in the event plane, a trigger particle in the event plane will tend to pick up particles at A 4 = 0 or 7r. This means that the appropriate reference is C 2 ( p + p ) + A ( l + 2 4 cos(2A4)).

20

*

initial state effects already present in the gold nuclear wavefunction 41. Par- ton recombination (or saturation) can cause gluons from different nucleons in the gold nuclei to recombine, leading to a smaller number of partons with a higher transverse momentum per parton. Qualitatively, this is difficult to distinguish from jet quenching since it reproduces both effects:

(1) There are fewer high p , jets than expected because the gold nuclei are not simple linear superpositions of nucleons and there are just fewer quarks and gluons to begin with than expected.

(2) Jets do not necessarily come out back-to-back. The usual argument for back-to-back jets assumes two incoming partons with p, - 0 followed by a large angle 2 2 scatter into two back-to-back jets. However, multiple parton collisions in the initial state lead to partons with non-zero p , compensated by multiple partners, which need not appear at Aq5 = T.

( l/Nevt) d2N/d2ptdq(GeV2)

lo 1 Au + Au W=130 GeV at q= 0

1

10

10

10

Figure 17. Invariant yield from PKENIX compared to the KLM saturation model 41.

These authors also showed that the initial state saturation model could be made to agree quantitatively with the data (see Fig. 17), including the effect of approximate jvpart scaling 4 1 .

21

The saturation model also describes the overall particle production. In fact, this ability is more natural since parton saturation effects are strongest for the softest partons where the parton densities are the highest. The saturation model relates the gluon distribution at low x in deep inelastic scattering from protons with the energy, centrality, and pseudorapidity dependence of particle production in heavy ion collisions 42.

800

600

400 F P 200 s s o

300

200

100

00 1 2 3 4 0 1 2 3 4 5 9 9

Figure 18. The charged particle pseudorapidity distributions and Kharzeev-Levin saturation model fits. Left panel: PHOBOS data at 130 GeV 42. Right panel: BRAHMS data at 200 GeV 43.

It should also be noted that the saturation model was one of the few models to correctly predict all of the following: the 130 and 200 GeV midrapidity multiplicity 24144 and the centrality dependence at all three energies 45. Figure 18 shows the fits to 130 and 200 GeV data from PHOBOS and BRAHMS respectively. The pseudorapidity and energy dependence are primarily controlled by the X parameter, which is extracted from deep inelastic scattering data.

So the initial state saturation model describes well the bulk of soft particle production and, if pushed, may also describe the moderately high p , particle production behavior. More importantly, the hadron suppression or “jet quenching” effect which we want to use as a probe of the density of the strongly interacting bulk medium may not be a final state effect at all, but may be actually be present in the gold wavefunction.

4.4. Initial or Final State Effect?

At the time of these lectures, RHIC was running deuteron-gold collisions in order to resolve this issue. Initial state effects, such as parton saturation,

22

should still occur in dAu since they are associated with the gold nucleus itself and not the collision. Final state effects, such as jet quenching, should go away in dAu since we do not expect a large bulk medium to form. Some preliminary hints already indicated that the suppression was probably a final state effect rather than an initial state effect.

Since charm quarks are primarily formed by gluon-gluon fusion and are not expected to be quenched in the final state 46, charm serves as a measure of the number of gluons available for hard scattering from the initial state. Open charm production, which was found to scale with the number of collisions 47, implies that parton saturation does not affect hard scattering.

0.05 minbias, 130 GeV

0.9 0.8

0 1 2 3 4 5 6

PT ( G e W

Figure 19. their ratio) from STAR 48.

Elliptic flow of charged particles in 130 and 200 GeV AuAu collisions (and

The behavior of elliptic flow at high p , also suggests that high p , particles are strongly absorbed in the final state. Figure 19 shows that elliptic flow reaches a constant value at high p , , independent of 6. Further- more, the value is so large that it is essentially the maximum allowable asymmetry from a geometric point of view 49. This implies that only jets emitted close to the surface make it out as was also indicated by the approximate Npa,.t scaling of high p , particles. Since the transverse geometry of the collision is a final state effect and not present in a single initial gold wavefunction, high p , particles must be strongly absorbed or rescattered in the final state, such that the collision geometry leaves its imprint on the final state momentum distribution. It should be noted that a 212 value of 0.17 implies that twice as many particles are emitted in-plane as out-of- plane, a huge effect. This effect has been shown by STAR 48 to persist to

p , > 8 GeV/c. Taken together,

particle production the results on overall particle production and high p , are very suggestive. The system appears to be made

up of hydrodynamic bulk matter. The system is opaque and expanding ex- plosively, probably in all three dimensions. The estimated energy density is much higher than that of the theoretical transition. There is a freezeout along a universal curve near the theoretical transition. There is a strong suppression of inclusive high p , yields and back-to-back pairs and an azimuthal anisotropy at high p , . The natural implication is that there is a large parton energy loss and surface emission.

These results are tantalizing, but there are some caveats. First of all, we not yet have a complete 3D hydrodynamic description of the collision which is consistent with all of the data. Additionally, there are some outstanding puzzles from PHOBOS and PHENIX. Finally, data from dAu collisions are needed to really disentangle initial state effects. We will turn to the puzzles and dAu data next.

5. Some Puzzles at RHIC

In addition to the surprising features mentioned above (blackness and 3D explosiveness of the source), there are two deep puzzles in the data: the behavior of protons at moderately high p , and the apparent universality of particle production at high &.

5.1. Scaling Puzzle I: Baryon/Meson Differences

0 05 1 1.5 2 2.5 3 3.5 4 pr I G e W

0.4 0.2

0 0.5 1 1.5 2 2.5 3 3.5 4 p r I G e W

Figure 20. Proton to pion ratio for 200 GeV AuAu collisions from PHENIX 5 0 ,

The first puzzle, emphasized initially by PHENIX, concerns the remark- able number of protons (compared to pions) at large transverse momentum,

23

24

as shown in Fig. 20. PHENIX has also shown that pions are more suppressed than protons in the intermediate p , region from 2-5 GeV/c 51. This effect is also seen in neutral mesons and baryons by STAR 5 2 .

Why are pions more suppressed than protons? The current ideas include a modification to the fragmentation function in the hot medium or a difference in gluon jet and quark jet quenching in the hot medium. Perhaps the most intriguing explanation is that, in the presence of jet quenching, a different production mechanism - quark coalescence - starts to dominate hadron production. Instead of the usual jet fragmentation, this is a multi- parton mechanism: three independent quarks coalesce into a baryon or an independent quark and antiquark coalesce into a meson 53.

Transverse Momentum p+n (GeV/c)

Figure 21. per constituent quark for lambdas and neutral kaons for 200 GeV AuAu 5 2 .

Elliptic flow per constituent quark as a function of transverse momentum

Since (1 + 2212 c 0 s 2 4 ) ~ M (1 + 2Nvg C O S ~ ~ ) , the coalescence model 53 predicts a scaling in elliptic flow per constituent quark versus p , per constituent quark. Figure 21, from STAR, shows this scaling effect for elliptic flow. This model also explains the fact that, in AuAu collisions at high p , , baryons and mesons behave similarly while mesons are suppressed (and reach maximum v g ) at lower momentum.

While this explanation is intriguing, this result remains a puzzle because it is unclear that this model should apply to dAu data (see Section 6 ) .

25

A I I . , , , . , , I , , , , , , , , 1 I I I I

1 10 1 o2 lo3

&(GeV)

Figure 22. Comparison of the total charged multiplicity versus collision energies for AA, e+e-, pp, and pp data, as described in the text, from PHOBOS 54. In the upper panel, the curve is a perturbative QCD expression fit to the e+e- data. In the lower panel, the data have all been divided by the e+e- fit.

5.2. Scaling Puzzle 11: Similarity of A A and e+e- at High

Figure 22 shows the total charged multiplicity for AA collisions (scaled by (Npar t ) /2) compared to pp, pp, and efe-, as a function of the appropriate & for each system 54 , The e+e- data serve as a reference, describing the behavior of a simple color dipole system with a large fi. The curve is a description of the e+e- data, given by the functional form: C c r s ( ~ ) Awith the parameters A and B calculable in perturbative QCD and the constant parameter C determined by a fit to the e+e- data 5 5 . In order to compare them with e+e-, the pp and pp data were plotted at an effective energy Jseff = &/2, which accounts for the leading particle effect 56 .

Energy

26

Finally, central AA collisions, AuAu from the AGS and RHIC, and PbPb from CERN are shown. Over the available range of RHIC energies from 19.6 to 200 GeV, the AuAu results are consistent with the e+e- results, suggesting a universality of particle production at high energy. In addition, the AuAu data approximately agrees with the scaled pp and pp data suggesting that the effective energy of a high energy AA collision is just - 6. This result is not understood theoretically and remains a puzzle.

6. The Latest Results from RHIC

At the time of the lectures, the critical dAu "control" run at RHIC was not complete. Since then, results from this run have been published by all four collaborations 3 4 3 5 7 9 5 8 i 5 9 . These results show no hadron or jet suppression in dAu implying that the suppression is NOT present in the nuclear wavefunction. This strongly favors the jet quenching interpretation for hadron suppression in AuAu and has led to a lot of theoretical activity.

a %

K

Figure 23. The nuclear modification factor. Left panel: Midrapidity result from PHENIX. Minimum bias dAu charged hadron result compared to central AuAu charged hadrons and minimum bias dAu neutral pions 57. Right panel: PHOBOS results slightly forward of mid-rapidity (0.2 < 11 < 1.4). The centrality dependence of the nuclear modification factor for charged hadrons in dAu compared to central AuAu 58.

Figure 23 (left panel) shows the minimum bias dAu results from PHENIX at midrapidity. The charged hadrons are enhanced rather than

27

suppressed, in sharp contrast to AuAu, a result confirmed by BRAHMS 34. Furthermore, the pions show collision scaling, again in sharp contrast to the strong suppression seen in AuAu.

This contrast is striking, but the comparison of minimum bias dAu to central AuAu is not fully decisive. Any nuclear effects in dAu are expected to manifest themselves primarily in central collisions and can be washed out in minimum bias collisions. Fig. 23 (right panel) shows the centrality dependence of RdAu from PHOBOS, slightly forward of midrapidity (from the deuteron’s point of view). Even the most central dAu collisions show no suppression.

d+AU FTPC-AU 0-20% A d+Au min. bias

A@ (radians) 0 n12 R

Figure 24. AuAu collisions compared to pp from STAR 59.

Azimuthal correlations for minimum bias dAu, central dAu, and central

Finally, Fig. 24, from STAR, shows that the jet structure in central dAu collisions can be understood based on a pp reference sample. There is no significant reduction of back-to-back jets in head-on dAu collisions. The complete suppression of the away-side jet in central AuAu collisions is also repeated in this plot for comparison.

Taken together, these results indicate that jets are quenched in AuAu collisions at RHIC energies (6 of 130 and 200 GeV), while there is little or no evidence of such quenching in dAu or in lower energy AA.

28

The production and behavior of protons in dAu collisions is again surprising, however. Figure 23 shows that midrapidity pions scale like Ncoll

at high momentum while total charged particles (including protons) are enhanced. This may explain why PHOBOS (Fig. 23) sees little enhancement of charged particles (fewer protons for 77 - 0.8). The mystery comes from the fact that the explanations put forward for the relative behavior of protons and pions in AuAu do not explain their behavior in dAu.

7. Summary

The field of heavy ion physics has indeed reached an exciting new era. We have created a high temperature, high density, strongly interacting bulk matter state in the laboratory, and we have achieved temperatures higher than needed to theoretically create a quark-gluon plasma. This bulk matter exhibits interesting properties. It appears to be very dense and opaque even at high p,, generating the maximum possible elliptic flow and strongly quenching any jets which are not formed on the surface of the material. Furthermore, the system appears to be exploding in all three dimensions.

Some puzzles remain. Why are there so many protons at high p T , and why do protons and pions behave differently even in dAu collisions? Is the particle production universal between AA, pp, pp, and e+e- at high energy, and if so, why?

Much work remains to be done to study this strongly interacting matter more quantitatively and to resolve the puzzles. Fortunately, the detectors and accelerator are undergoing continuous upgrades and the prospects for a continued rich harvest of physics from RHIC look excellent.

Acknowledgments

Essential help in the assembly of this proceedings was provided by David Hofman (U. Illinois, Chicago). Some of the material in the original lecture presentation was provided by Barbara Jacak (SUNY, Stony Brook) and Thomas Ullrich (BNL). This work was partially supported by U.S. DOE grant DEAC02-98CH10886.

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5. Nucl. Inst. and Meth. A499 (2003) Iff. 6. PHOBOS Collaboration (B.B. Back et d.), Phys. Rev. Lett. 91 (2003)

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New York, New York. 8. PHENIX Collaboration (K. Adcox et d.), Phys. Rev. Lett. 86 (2001) 3500. 9. PHOBOS Collaboration (B.B. Back et d.), Phys. Rev. C65 (2002) 031901.

10. STAR Collaboration (K.H. Ackerman et d,), Phys. Rev. Lett. 86 (2001) 402. 11. NA49 collaboration (C.A. Alt et d.), arXiv:nucl-ex/0303001. 12. STAR Collaboration (C. Adler et d.), Phys. Rev. Lett. 87 (2001) 182301. 13. Heiselberg, Levy, Phys. Rev. C59 (1999) 2716. 14. PHOBOS Collaboration (B.B. Back et aZ), Phys. Rev. Lett. 89 (2002) 222301,

Nucl. Phys. A715 (2003) 611. 15. R. Hanbury-Brown, R. Q. Twiss, Phil. Mag. Ser. 7, Vol. 45, No. 366 (1954)

663, Nature 178 (1956) 1046. 16. S. Pratt, Phys. Rev. D33 (1986) 1314, G.F. Bertsch, Nucl. Phys. A498

(1989) 173, U. Heinz, Nucl. Phys. A610 (1996) 264. 17. STAR Collaboration (C. Adler et d.), Phys. Rev. Lett. 87 (2001) 082301. 18. D. Rischke, M. Gyulassy, Nucl. Phys. A608 (1996) 479. 19. D. Rischke, RIKEN/BNL Workshop on particle interferometry and elliptic

flow at RHIC, Upton, NY (2002) - no proceedings. 20. STAR Collaboration (G. van Buren et ul.), Nucl. Phys. A715 (2003) 129. 21. T.S. Ullrich, Nucl. Phys. A715 (2003) 399. 22. J. D. Bjorken, Phys. Rev. D27, (1983) 140. 23. PHENIX Collaboration (K. Adcox et ul.), Phys. Rev. Lett. 87 (2001) 052301. 24. PHOBOS Collaboration (B.B. Back et u Z . ) , Phys. Rev. Lett. 85 (2000) 3100,

Phys. Rev. Lett. 88 (2002) 22302. 25. P. Braun-Munzinger, K. Redlich, J. Stachel, arXiv:nucl-th/0304013. 26. WA98 Collaboration (M.M. Aggarwal et d), Phys. Rev. Lett. 85 (2000)

3595. 27. R. Rapp, E.V. Shuryak, Phys. Lett. B473 (2000) 13. 28. PHENIX Collaboration (D. Mukhopadhyay et d.), Nucl. Phys. A715 (2003)

494. 29. PHENIX Collaboration (S.S. Adler et d.), arXiv:nucl-ex/0305030. 30. STAR Collaboration (C. Adler et d.), Phys. Rev. Lett. 89 (2002) 202301. 31. PHOBOS Collaboration (B.B. Back et d), arXiv:nucl-ex/0302015. 32. PHENIX Collaboration (S.S. Adler et d.), arXiv:nucl-ex/0304022. 33. STAR Collaboration (J. Adams et ul.), arXiv:nucl-ex-0305015. 34. BRAHMS Collaboration (I. Arsene et d.), Phys. Rev. Lett. (2003) in press.

arXiv:nucl-ex/0307003 35. PHENIX Collaboration (K. Adcox et d.), Phys. Rev. Lett. 88 (2002) 022301. 36. E. Wang, X.N. Wang, Phys. Rev. C64 (2001) 034901. 37. J.W. Cronin et aZ., Phys. Rev. D11 (1975) 3105. 38. PHENIX Collaboration (K. Adcox et d.), Phys. Lett. B 561 (2003) 82. 39. B. Muller, Phys. Rev. C67 (2003) 061901. 40. STAR Collaboration (C. Adler et d.), Phys. Rev. Lett. 90 (2003) 082302,

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STAR Collaboration (D. Hardtke et al.), Nucl. Phys. A 715 (2003) 272. 41. D. Kharzeev, E. Levin, L. McLerran, Phys. Lett. B561 (2003) 93. 42. D. Kharzeev, E. Levin, Phys. Lett. B523 (2001) 79. 43. BRAHMS Collaboration (I. G. Bearden e t al,) , Phys. Rev. Lett. 88, (2002)

202301. 44. S.A. Bass et al., Nucl. Phys. A661 (1999) 205. 45. PHOBOS Collaboration (M.D. Baker et al.), Nucl. Phys. A715 (2003) 65. 46. Y.L. Dokshitzer, D.E. Kharzeev, Phys. Lett. B519 (2001) 199. 47. PHENIX Collaboration (K. Adcox et al.), Phys. Rev. Lett. 88 (2002) 192303. 48. STAR Collaboration (K. Filimonov et aZ.), Nucl. Phys. A715 (2003) 737. 49. S.A. Voloshin, Nucl. Phys. A715 (2003) 379, E.V. Shuryak, Phys. Rev. C66

(2002) 027902. 50. PHENIX Collaboration (T. Chujo et al.), Nucl. Phys. A715 (2003) 151. 51. PHENIX Collaboration (S.S. Adler et al.), arXiv:nucl-ex/0305036. 52. STAR Collaboration (J. Adams et al.), arXiv:nucl-ex/0306007. 53. R.J. Fries, B. Muller, C. Nonaka, S.A. Bass, nrXiv:nucl-th/0306027. 54. PHOBOS Collaboration (B. B. Back et al.), arXiv:nucl-ex/0301017. 55. A. H. Mueller, Nucl. Phys. B213 (1983) 85. 56. M. Basile et al., Phys. Lett. B92 (1980) 367, Phys. Lett. B95 (1980) 311. 57. PHENIX Collaboration (S.S. Adler et al.), Phys. Rev. Lett. (2003) in press,

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arXiv:nucl-ex/0306024.

PHYSICS '33 FUTURE ACCELERATORS

JOHN ELLIS Theoretical Physics Division, CERN, CH- 121 1 Geneva 23, Switzerland

E-mail: John.EllisOcern.ch

A roadmap for possible physics beyond the Standard Model is presented, focussing on Higgs physics, supersymmetry and neutrino physics. The prospects for discovering the Higgs boson and/or supersymmetry at the LHC are then discussed, followed by those of measuring their properties at a linear e+e- collider with centre-of-mass energy 5 1 TeV, and at CLIC, a concept for linear e+e- collider capable of reaching 3 TeV in the centre of mass. Also mentioned are the prospects at 77 and p+p- colliders. After reviewing the status of neutrino physics, future prospects with super beams, beta beams and a neutrino factory are mentioned, as well as flavour-changing decays of charged leptons. The implications of the WMAP data for neutrino physics and supersymmetry are included, and they are shown to be compatible with the hypothesis that the inflaton can be identified with a heavy sneutrino. This is also shown to have characteristic predictions for the flavour-changing decays of charged leptons, that may be observable at future accelerators.

1. Roadmap to Physics beyond the Standard Model

1.1. So you think you have problems?

The Standard Model agrees with all confirmed experimental data from accelerators, but is theoretically very unsatisfactory 19273. It does not explain the particle quantum numbers, such as the electric charge &, weak isospin I , hypercharge Y and colour, and contains at least 19 arbitrary parameters. These include three independent vector-boson couplings and a possible CP-violating strong-interaction parameter, six quark and three charged-lepton masses, three generalized Cabibbo weak mixing angles and the CP-violating Kobayashi-Maskawa phase, as well as two independent masses for weak bosons. As seen in Fig. 1, the experimental data from LEP agree (too) perfectly with the theoretical curves, at all energies up to above 200 GeV 4. This sounds great, but there are plenty of questions left open by the Standard Model.

The Big Issues in physics beyond the Standard Model are conveniently

31

32

grouped into three categories 1,273. These include the problem of Mass: what is the origin of particle masses, are they due to a Higgs boson, and, if so, why are the masses so small; Unification: is there a simple group framework for unifying all the particle interactions, a so-called Grand Uni- fied Theory (GUT); and Flavour: why are there so many different types of quarks and leptons and why do their weak interactions mix in the pe- culiar way observed? Solutions to all these problems should eventually be incorporated in a Theory of Everything (TOE) that also includes gravity, reconciles it with quantum mechanics, explains the origin of space-time and why it has four dimensions, makes coffee, etc. String theory, perhaps in its current incarnation of M theory, is the best (only?) candidate we have for such a TOE 5 , but we do not yet understand it well enough to make clear predictions at accessible energies.

0 20 40 60 80 100 120 140 160 180 200 220 Centre-of-mass energy (CeV)

Figure 1. tions of the Standard Model '.

Data from LEP and other e+e- experiments agree perfectly with the predic-

As if the above 19 parameters were insufficient to appall you, a t least nine more parameters must be introduced to accommodate the neutrino oscillations discussed later: 3 neutrino masses, 3 real mixing angles, and 3 CP-violating phases, of which one is in principle observable in neutrino- oscillation experiments and the other two in neutrinoless double-beta decay experiments. In fact even the simplest models for neutrino masses involve 9 further parameters, as discussed later.

Moreover, there are many other cosmological parameters that we should also seek to explain. Gravity is characterized by at least two parameters, the Newton constant GN and the cosmological vacuum energy. We may also

33

want to construct a field-theoretical model for inflation, and we certainly need to explain the baryon asymmetry of the Universe. So there is plenty of scope for physics beyond the Standard Model.

1.2. The Electroweak Vacuum

The generation of particle masses requires the breaking of gauge symmetry in the vacuum:

mw,z # 0 * (OIXI,I,IO) # 0 (1)

for some field X with isospin I and third component 13. The measured ratio

tells us that X mainly has I = 1/2 6 , which is also what is needed to generate fermion masses. The key question is the nature of the field X : is it elementary or composite? A fermion-antifermion condensate w = (OlXlO) = (OIFFIO) # 0 would be analogous to what we know from QCD, where (01ijqIO) # 0, and conventional superconductivity, where (Ole-e- 10) # 0. However, analogous ‘technicolour’ models of electroweak symmetry breaking fail to fit the values of the radiative corrections E$ to p and other quantities extracted from the precision electroweak data provided by LEP and other experiments s. One cannot exclude the possibility that some calculable variant of technicolour might emerge that is consistent with the data, but for now we focus on elementary Higgs models.

The Higgs mechanism can be phrased in quite physical language. It is well known that a massless vector boson such as the photon y or gluon g has just two polarization states: X = fl . However, a massive vector boson such as the p has three polarization states: X = 0, f l . This third polarization state is provided by a spin-0 field. In order to make mwi,zo # 0, this should have non-zero electroweak isospin I # 0, and the simplest possibility is a complex isodoublet (++’ +O), as assumed above. This has four degrees of freedom, three of which are eaten by the W* amd 2’ as their third polarization states, leaving us with one physical Higgs boson H . Once the vacuum expectation value I(Ol+lO)l = w / d : w = p/& is fixed, the mass of the remaining physical Higgs boson is given by

m& = 2p2 = 4xw2, (3)

which is a free parameter in the Standard Model.

34

The precision electroweak measurements at LEP and elsewhere are sensitive to radiative corrections via quantum loop diagrams, in particular those involving particles such as the top quark and the Higgs boson that were too heavy to be observed directly at LEP ',lo. Many of the electroweak observables exhibit quadratic sensitivity to the mass of the top quark:

A c( G F m f . (4) The measurements of these electroweak observables enabled the mass of the top quark to be predicted before it was discovered, and the measured value:

m t = 174.3 f 5.1 GeV (5)

(6)

agrees quite well with the prediction

mt = 177.5 f 9.3 GeV

derived from precision electroweak data 4 . Electroweak observables are also sensitive logarithmically to the mass of the Higgs boson:

so their measurements can also be used to predict the mass of the Higgs boson. This prediction can be made more definite by combining the precision electroweak data with the measurement (5) of the mass of the top quark. Making due allowance for theoretical uncertainties in the Standard Model calculations, as seen in Fig. 2, one may estimate that 4:

m H = 91::; GeV, (8)

with a 95% confidence-level upper limit of 211 GeV. The Higgs production and decay rates are completely fixed as functions

of the unknown mass m H , enabling the search for the Higgs boson to be planned as a function of m H ll. This search was one of the main objectives of experiments at LEP, which established the lower limit:

m H > 114.4GeV, (9)

that is shown as the light yellow shaded region in Fig. 2 12. Combining this limit with the estimate (8), we see that there is good reason to expect that the Higgs boson may not be far away. Convoluting the likelihood function for the precision electroweak measurements with the lower limit established by the direct searches suggests that the Higgs mass is very likely to be below 125 GeV, as seen in Fig. 3 13. Indeed, in the closing weeks of

35

Figure 2. Estimate of the mass of the Higgs boson obtained from precision electroweak measurements. The blue band indicates theoretical uncertainties, and the different curves demonstrate the effects of different plausible estimates of the renormalization of the fine- structure constant at the Zo peak 4.

the LEP experimental programme, there was a hint for the discovery of the Higgs boson at LEP with a mass N 116 GeV, but this could not be confirmed 12.

If mH is too large, the quartic coupling that stabilizes the effective Higgs potential blows up, and if mH is too small, the quartic coupling turns negative at some scale A << mp. If the Higgs boson is indeed very light, the Standard Model probably breaks down at some energy scale S lo6 GeV, as seen in Fig. 4 The only remedy is to introduce some new physics below this scale, and a suitable candidate is supersymmetry 15, as we discuss next.

1.3. W h y s u p e r s y m m e t r y ?

The main theoretical reason to expect supersymmetry at an accessible energy scale is provided by the hierarchy problem 16: why is mw << mp, or equivalently why is GF N l /m& >> GN = l/m;? Another equivalent question is why the Coulomb potential in an atom is so much greater than the Newton potential: e2 >> GNm2 = m2/m$, where m is a typical particle mass?

Your first thought might simply be to set m p >> mw by hand, and forget about the problem. Life is not so simple, because quantum corrections to

36

Higgs boson mass [GeV]

Figure 3. convoluting the blue-band plot in Fig. 2

An estimated probability distribution for the Higgs mass 13, obtained by with the experimental exclusion 12.

- -

600 m, = 175 GeV - - a,(Mz) = 0.118

- 400 -

- -

not allowed - 200- aIlowed -

-

A [GeV]

Figure 4. The effective Higgs potential is well-behaved up the the Planck scale mp E

1019 GeV only for a narrow range of Higgs masses N 180 GeV. A larger Higgs mass would cause the coupling to blow up at lower energies, and a smaller Higgs mass would cause the potential to turn negative at some scale A << mp 14.

mH and hence mw are quadratically divergent in the Standard Model:

ff

lr 6rn&,, N O(-)A2,

37

which is >> m& if the cutoff A, which represents the scale where new physics beyond the Standard Model appears, is comparable to the GUT or Planck scale. For example, if the Standard Model were to hold unscathed all the way up the Planck mass mp N 1019 GeV, the radiative correction (10) would be 36 orders of magnitude greater than the physical values of m&,w!

In principle, this is not a problem from the mathematical point of view of renormalization theory. All one has to do is postulate a tree-level value of rn& that is (very nearly) equal and opposite to the ‘correction’ (lo), and the correct physical value may be obtained by a delicate cancellation. However, this fine tuning strikes many physicists as rather unnatural: they would prefer a mechanism that keeps the ‘correction’ (10) comparable at most to the physical value 16.

This is possible in a supersymmetric theory, in which there are equal numbers of bosons and fermions with identical couplings. Since bosonic and fermionic loops have opposite signs, the residual one-loop correction is of the form

which is ,S m&,w and hence naturally small if the supersymmetric partner bosons B and fermions F have similar masses:

lmi -m%l 5 1 TeV2. (12)

This is the best motivation we have for finding supersymmetry at relatively low energies 16. In addition to this first supersymmetric miracle of removing (11) the quadratic divergence (lo), many logarithmic divergences are also absent in a supersymmetric theory 17, a property that also plays a r61e in the construction of supersymmetric GUTS ’.

Could any of the known particles in the Standard Model be paired up in supermultiplets? Unfortunately, none of the known fermions q , C can be paired with any of the ‘known’ bosons y, W*Zo, g, H , because their internal quantum numbers do not match 18. For example, quarks q sit in triplet representations of colour, whereas the known bosons are either singlets or octets of colour. Then again, leptons C have non-zero lepton number L = 1, whereas the known bosons have L = 0. Thus, the only possibility seems to be to introduce new supersymmetric partners (spartners) for all the known particles, as seen in the Table below: quark + squark, lepton + slepton, photon + photino, Z + Zino, W + Wino, gluon + gluino, Higgs + Higgsino. The best that one can say for supersymmetry is that it economizes on principle, not on particles!

38

Particle Spin Spartner Spin

quark: q a squark: 4 0

lepton: c f slepton: E 0

photon: y 1 photino:

1 W 1 wino: W 2

1 2 z 1 zino: Z

Higgs: H 0 higgsino: H

The minimal supersymmetric extension of the Standard Model (MSSM) l9 has the same vector interactions as the Standard Model, and the particle masses arise in much the same way. However, in addition to the Standard Model particles and their supersymmetric partners in the Table, the minimal supersymmetric extension of the Standard Model (MSSM), requires two Higgs doublets H , H with opposite hypercharges in order to give masses to all the matter fermions, whereas one Higgs doublet would have sufficed in the Standard Model. The two Higgs doublets couple via an extra coupling called p, and it should also be noted that the ratio of Higgs vacuum expectation values

is undetermined and should be treated as a free parameter.

1.4. Hints of Supersymmetry

There are some phenomenological hints that supersymmetry may, indeed, appear at the TeV scale. One is provided by the strengths of the different Standard Model interactions, as measured at LEP 20. These may be extrapolated to high energy scales including calculable renormalization effects 21, to see whether they unify as predicted in a GUT. The answer is no, if supersymmetry is not included in the calculations. In that case, GUTS

39

would require a ratio of the electromagnetic and weak coupling strengths, parametrized by sin2Bw, different from what is observed, if they are to unify with the strong interactions. On the other hand, as seen in Fig. 5 , minimal supersymmetric GUTS predict just the correct ratio for the weak and electromagnetic interaction strengths, i.e., value for sin2 Ow 22.

0 10' lo5 10' 1 0 ' ~ 1 0 ~ ~ 1 1

6

Figure 5. value if supersymmetry is included 20.

The measurements of the gauge coupling strengths at LEP evolve to a unified

A second hint is the fact that precision electroweak data prefer a relatively light Higgs boson weighing less than about 200 GeV '. This is perfectly consistent with calculations in the MSSM, in which the lightest Higgs boson weighs less than about 130 GeV 23.

A third hint is provided by the astrophysical necessity of cold dark matter. This could be provided by a neutral, weakly-interacting particle weighing less than about 1 TeV, such as the lightest supersymmetric particle (LSP) x 24. This is expected to be stable in the MSSM, and hence should be present in the Universe today as a cosmological relic from the Big Bang 25*24.

It is stable because of a multiplicatively-conserved quantum number called R parity, that takes the values +1 for all conventional particles and -1 for all sparticles '*. The conservation of R parity can be related to that of baryon number B and lepton number L, since

(14) R = ( -1)3B+L+2S

where S is the spin. There are three important consequences of R conser-

40

vation:

(1) sparticles are always produced in pairs, e.g., jjp -+ @jX, e+e- +

(2) heavier sparticles decay to lighter ones, e.g., 4 -+ qij, ,Ci -+ p?, and (3) the lightest sparticle (LSP) is stable, because it has no legal decay

b+b- 1

mode.

This last feature constrains strongly the possible nature of the lightest supersymmetric sparticle 24. If it had either electric charge or strong interactions, it would surely have dissipated its energy and condensed into galactic disks along with conventional matter. There it would surely have bound electromagnetically or via the strong interactions to conventional nuclei, forming anomalous heavy isotopes that should have been detected. We conclude 24 that it should have only weak interactions.

A priori, the LSP might have been a sneutrino partner of one of the 3 light neutrinos, but this possibility has been excluded by a combination of the LEP neutrino counting and direct searches for cold dark matter. Thus, the LSP is often thought to be the lightest neutralino x of spin 1/2, which naturally has a relic density of interest to astrophysicists and cosmologists:

A fourth hint may be coming from the measured value of the muon’s anomalous magnetic moment, gp - 2, which seems to differ slightly from the Standard Model prediction 2 6 7 2 7 . If there is indeed a significant discrepancy, this would require new physics at the TeV scale or below, which could easily be provided by supersymmetry, as we see later.

Finally, we note another attractive feature of supersymmetry. Radiative corrections to the effective Higgs mass, calculated using supersymmetric renormalization-group equations, drive its square negative, enabling electroweak symmetry breaking to occur in a natural way 28.

O,h2 = O(O.1) 24.

1.5. Constraints on Supersymmetric Models

Important experimental constraints on supersymmetric models have been provided by the unsuccessful direct searches at LEP and the Tevatron collider . When compiling these, the supersymmetry-breaking masses of the different unseen scalar particles are often assumed to have a universal value mo at some GUT input scale, and likewise the fermionic partners of the vector bosons are also commonly assumed to have universal fermionic masses mll2 at the GUT scale, as are the trilinear soft supersymmetry-breaking pa-

41

rameters A0 - the so-called constrained MSSM (CMSSM) that might (but not necessarily) arise from a minimal supergravity theory. These input values are then renormalized by (supersymmetric) Standard Model interactions between the GUT and electroweak scales.

The allowed domains in some of the (ml12, mo) planes for different values of tan@ and the sign of p are shown in Fig. 6. Panel (a) of this figure features the limit mx* 2 104 GeV provided by chargino searches at LEP 29.

The LEP neutrino counting and other measurements have also constrained the possibilities for light neutralinos, and LEP has also provided lower limits on slepton masses, of which the strongest is m6 2 99 GeV 30, as also illustrated in panel (a) of Fig. 6. The most important constraints on the supersymmetric partners of the u, d, s, c, b squarks and on the gluinos are provided by the FNAL Tevatron collider: for equal masses mg = mg 2 300 GeV. In the case of the f, LEP provides the most stringent limit when m,- - m, is small, and the Tevatron for larger m,- - m, 29.

Another important constraint in Fig. 6 is provided by the LEP lower limit on the Higgs mass: m H > 114.4 GeV 12. Since mh is sensitive to sparticle masses, particularly m,-, via loop corrections:

the Higgs limit also imposes important constraints on the soft supersymmetry-breaking CMSSM parameters, principally ml12 33 as displayed in Fig. 6.

Also shown in Fig. 6 is the constraint imposed by measurements of b + s y 32. These agree with the Standard Model, and therefore provide bounds on supersymmetric particles, such as the chargino and charged Higgs masses, in particular.

The final experimental constraint we consider is that due to the measurement of the anomalous magnetic moment of the muon. Following its first result 34, the BNL E821 experiment has recently reported a new measurement 26 of a, = i(g, - 2), which deviates by about 3 standard deviations from the best available Standard Model predictions based on low-energy e+e- + hadrons data 27. On the other hand, the discrepancy is more like 0.9 standard deviations if one uses T + hadrons data to calculate the Stan- dard Model prediction. Faced with this confusion, and remembering the chequered history of previous theoretical calculations 35, it is reasonable to defer judgement whether there is a significant discrepancy with the Stan- dard Model. However, either way, the measurement of a, is a significant

42

800

71x1

6w

9 5w B 4w

3w

100

0

Iwo 15W

h 5 % 1Mx)

B B 9 9

0 0 1w 1000 2wo 3wo

mU2 ( G W mm (GeV

Figure 6. Compilations of phenomenological constraints on the CMSSM for (a) tan p = 10,p > 0, (b) tan@ = 10,p < 0, (c ) t a n p = 35,p < 0 and (d) t a n p = 50,p > 0 31. The near-vertical lines are the LEP limits m x i = 104 GeV (dashed and black) 29, shown in (a) only, and mh = 114 GeV (dotted and red) 12. Also, in the lower left corner of (a), we show the mg = 99 GeV contour 30. The dark (brick red) shaded regions are excluded because the LSP is charged. The light (turquoise) shaded areas have 0.1 5 Rxh2 5 0.3, and the smaller dark (blue) shaded regions have 0.094 5 Rxh2 5 0.129, as favoured by WMAP 31. The medium (dark green) shaded regions that are most prominent in panels (b) and (c) are excluded by b + sy 32. The shaded (pink) regions in panels (a) and (d) show the f 2 u ranges of gp - 2 26.

constraint on the CMSSM, favouring p > 0 in general, and a specific region of the (mll2, mo) plane if one accepts the theoretical prediction based on e+e- + hadrons data 36. The regions preferred by the current g - 2 experimental data and the e+e- + hadrons data are shown in Fig. 6.

43

Fig. 6 also displays the regions where the supersymmetric relic density px = RxPcritical falls within the range preferred by WMAP 37:

0.094 < R,h2 < 0.129 (16)

at the 2-a level. The upper limit on the relic density is rigorous, but the lower limit in (16) is optional, since there could be other important contributions to the overall matter density. Smaller values of R,h2 correspond to smaller values of (m1l2, mo), in general.

We see in Fig. 6 that there are significant regions of the CMSSM parameter space where the relic density falls within the preferred range (16). What goes into the calculation of the relic density? It is controlled by the annihilation cross section 24:

where the typical annihilation cross section aann N 1 /mi . For this reason, the relic density typically increases with the relic mass, and this combined with the upper bound in (16) then leads to the common expectation that mx S 0(1) GeV.

However, there are various ways in which the generic upper bound on m, can be increased along filaments in the (m1/2,mo) plane. For example, if the next-to-lightest sparticle (NLSP) is not much heavier than x: Amlm, S 0.1, the relic density may be suppressed by coannihilation: a(x+NLSP-+ . . .) 38. In this way, the allowed CMSSM region may acquire a ‘tail’ extending to larger sparticle masses. An example of this possibility is the case where the NLSP is the lighter stau: ?I and mF1 - mx, as seen in Figs. 6(a) and (b) 39.

Another mechanism for extending the allowed CMSSM region to large m, is rapid annihilation via a direct-channel pole when mx - p H i g g s 40941. This may yield a ‘funnel’ extending to large ml12 and mo at large tan p, as seen in panels (c) and (d) of Fig. 6 41. Yet another allowed region at very large mo (not shown) is the ‘focus-point’ region 42, which is adjacent to the boundary of the region where electroweak symmetry breaking ceases to be possible. The lightest supersymmetric particle is relatively light in this region.

1

1.6. Benchmark Supersymmetric Scenarios

As seen in Fig. 6, all the experimental, cosmological and theoretical constraints on the MSSM are mutually compatible. As an aid to understanding

44

better the physics capabilities of the LHC and various other accelerators, as well as non-accelerator experiments, a set of benchmark supersymmetric scenarios have been proposed 43. Their distribution in the (m lp , mo) plane is displayed in Fig. 7. These benchmark scenarios are compatible with all the accelerator constraints mentioned above, including the LEP searches and b + sy, and yield relic densities of LSPs in the range suggested by cosmology and astrophysics. The benchmarks are not intended to sample ‘fairly’ the allowed parameter space, but rather to illustrate the range of possibilities currently allowed.

+F I

Figure 7. The ‘WMAP lines’ display the regions of the ( r n 1 / 2 , m o ) plane that are compatible with 0.094 < R,h2 < 0.129 in the ‘bulk’, coannihilation ‘tail’, and rapid- annihilation ‘funnel’ regions, as well as the laboratory constraints, for (a) p > 0 and tan p = 5,10,20,35 and 50, and (b) for p < 0 and tan p = 10 and 35. The parts of the p > 0 strips compatible with gr - 2 at the 2-a level have darker shading. The updated post-WMAP benchmark scenarios are marked in red. Points (E,F) in the focus-point region are at larger values of mo 43,44.

In addition to a number of benchmark points falling in the ‘bulk’ region of parameter space at relatively low values of the supersymmetric particle masses, as seen along the ‘WMAP lines’ in Fig. 7, we also proposed 43

some points out along the ‘tails’ of parameter space extending out to larger masses. These clearly require some degree of fine-tuning to obtain the required relic density 45 and/or the correct Wk mass 46, and some are also disfavoured by the supersymmetric interpretation of the gp - 2 anomaly, but all are logically consistent possibilities. Fig. 8 displays estimates of the numbers of MSSM particles that could be detected at different accelerators discussed in subsequent sections.

45

CMSSM Benchmarks squarks II sleptons II xo,

40 40

30 20 1 0 p - I

0 30 r 20 00 0 2o a 10 10

E O

.-

a, G B L C J I M E H A F K D G B L C J I M E H A F K D

G B L C J I M E H A F K D

40

30

20

10

G B L C J I M E H A F K D

Figure 8. Estimates of the numbers of different types of CMSSM particles that may be detectable 43 at (a) the LHC 47, (b) a 0.5-TeV and (c) a 1-TeV linear e+e- collider 48,

(d) the combination of the LHC and a 1-TeV linear e+e- collider, and (e,f) a 3(5)- TeV e+e- 49 or p+p- collider 50951. Note the complementarity between the sparticles detectable at the LHC and at a 1-TeV linear e+e- collider.

2. LHC

The LHC under construction at CERN is a proton-proton collider with a centre-of-mass energy of 14 TeV that is capable of a luminosity L -

cm-2s-1, able to produce pairs of new particles each weighing N

1 TeV 47. It is also capable of accelerating lead nuclei to produce heavy- ion collisions with about 1.2 PeV in the centre of mass, for probing dense quark-gluon matter.

The LHC will be located in the former LEP tunnel, which has a circum- ference of 27 km and is located about 100 m underground 47. Four major experiments will be located in caverns around the ring. The ATLAS 52

and CMS 53 experiments will use the full LHC luminosity to search for new particles such as the Higgs boson and sparticles. The LHCb experiment 54

will study CP-violating effects in the decays of B particles, and the primary objective of ALICE 55 will be the search for the quark-gluon plasma in relativistic heavy-ion collisions.

46

The LHC magnets are designed to achieve fields of 8.3 Tesla operating at 1.8 degrees above absolute zero. Prototype magnets have reached fields above 9 Tesla, and the first magnets produced by industry also achieve fields beyond the design value. Progress in the construction, delivery and testing of the LHC magnets and other components can be monitored by consulting the 'LHC dashboard' 47.

Ahead of the LHC, the highest-energy operating accelerator is the Fer- milab Tevatron collider, which has a chance to detect the Higgs boson if it is light enough, and if the Tevatron collider can accumulate sufficient luminosity 56 . The LHC will be able to discover the Higgs boson, whatever it mass below about 1 TeV, as seen in Fig. 9 47. For any value of the Higgs mass, ATLAS and CMS should be able to observe two or three of its decay modes, including H + yy,bb and T+T- at low masses, H + 4 charged leptons at intermediate masses and H + W+W- and 22 at high masses. Depending on the Higgs mass, they should also be able to measure it to 1% or better. The days of the Higgs boson are numbered!

tM(H --t bb) A H + ZZ'" + 41 .: A + ww'" + lvlv ' A + zz + uvv

- Total signitieance v1

(no K-factors)

1 ' ' I ' I

lo2 lo? m, W V )

Figure 9. significance, whatever its mass, and may observe several of its decay modes 47152,53 .

The LHC experiments will be able to discover the Higgs boson with high

Many possible signatures of MSSM Higgs bosons at the LHC have been studied, and one or more of them can be detected in all the scenarios explored. As seen in Fig. 10, at large m ~ , the lightest MSMM Higgs boson h may be detected via its yy and/or bb decay modes, and many other channels

47

are accessible at low mA. At large tan@, the heavier H , A and H* bosons may be detected. but there is a Lwedge’ of parameter space extending out to large mA at moderate tan @ where only the lightest MSMM Higgs boson may be detectable at the LHC.

mA (GeV)

Figure 10. Regions of the MSSM parameter space where the various Higgs bosons can be discovered at the LHC via their decays into Standard Model particles, combining ATLAS and CMS and assuming 300 /fb per experiment. In the dashed regions, at least two Higgs bosons can be discovered, whereas in the dotted region only the lightest MSSM Higgs boson h can be discovered. In the region to the left of the rightmost contour, at least two Higgs bosons could be discovered with an upgraded LHC delivering 3000/fb per experiment 57.

The question then arises whether, in this region, detailed LHC measurements of the lightest MSMM Higgs boson might be able to distinguish it from a Standard Model Higgs boson with the same mass. As seen in Fig. 11, the LHC h + yy and bb decay signatures are unlikely to be greatly suppressed (or enhanced) compared to those of a Standard Model Higgs boson 5 8 , but the accuracy with which they can be measured may not be sufficient to distinguish the MSSM from the Standard Model. This may therefore be a task for the other accelerators discussed later 59.

The Fermilab Tevatron collider has already established the best limits on squarks and gluinos, and will have the next shot at discovering sparticles. In the CMSSM, the regions of parameter space it can reach are disfavoured indirectly by the LEP limits on weakly-interacting sparticles, the absence of a light Higgs boson, and the agreement of b + sy with the Standard Model 43. However, the prospects may be improved in variants of the

4w

3W

E 2W E"

1W

2w 4w €20 8W 1wO 12W 14W 2w 500 1wO 15W 20W

m,, I G W m,, IG'W

Figure 11. The cross section for production of the lightest CP-even CMSSM Higgs boson in gluon fusion and its decay into a photon pair at the LHC, u(gg + h ) x B ( h + y y ) , normalized to the Standard Model value for the same Higgs mass, is given in the regions of the (ml,z,mo) planes allowed before the WMAP data for p > 0, t anP = 10,50, assuming A0 = 0 and mt = 175 GeV. The diagonal (red) solid lines are the f2 - u contours for gw - 2 26*36. The near-vertical solid, dotted and dashed (black) lines are the mh = 113,115,117 GeV contours. The light shaded (pink) regions are excluded by b + sy 32. The (brown) bricked regions are excluded since in these regions the LSP is the charged T I .

MSSM that abandon some of the CMSSM constraints 60.

Fig. 12 shows the physics reach for observing pairs of supersymmetric particles at the LHC. The prime signature for supersymmetry - multiple jets (and/or leptons) with a large amount of missing energy - is quite distinctive, as seen in Fig. 13 61,62. Therefore, the detection of the supersymmetric partners of quarks and gluons at the LHC is expected to be quite easy if they weigh less than about 2.5 TeV 53. Moreover, in many scenarios one should be able to observe their cascade decays into lighter supersymmetric particles, as seen in Fig. 14 63 , or into the lightest MSSM Higgs boson h.

The LHC collaborations have analyzed their reach for sparticle detection in both generic studies and specific benchmark scenarios proposed previously 64. Based on these studies, Fig. 8 displays estimates how many different sparticles may be seen at the LHC in each of the newly-proposed benchmark scenarios 43. The lightest Higgs boson is always found, and squarks and gluinos are usually found, though there are some scenarios where no sparticles are found at the LHC. However, the LHC often misses heavier weakly-interacting sparticles such as charginos, neutralinos, sleptons and the other Higgs bosons, as seen in Fig. 15, leaving a physics opportunity for a linear e+e- linear collider.

Summarizing, a likely supersymmetric post-LHC physics scenario is

48

49

Figure 12. various integrated luminosities 53, using the missing energy + jets signature 6 2 .

The regions of the (mo,ml12) plane that can be explored by the LHC with

"0 500 1000 1500 2000 2 I0

Figure 13. the jet energies with the missing energy 64*61,62.

The distribution expected at the LHC in the variable M,ff that combines

50

= 90 GeV, m,, = 220 GeV 250

-& 200

B z B IJJ 1w

... . 150

-

50

0 0 100 2w 3w

M(I+I) (Gev)

Figure 14. in two different supersymmetric scenarios 6 4 9 5 3 7 6 2 .

The dilepton mass distributions expected at the LHC due to sparticle decays

Figure 15. Estimates of the numbers of MSSM particles that may be detectable at the LHC as functions of ml/2 along the WMAP lines shown in Fig. 7 for t a n p = 10 and 50 for ,u > 0. The locations of updated benchmark points 44 along these WMAP lines are indicated.

that: 0 The lightest Higgs boson will have been discovered and some of its

decay modes and other properties will have been measured, but its role in the generation of particle masses will not have been established, and the LHC will probably not be able to distinguish between a Standard Model Higgs boson and the lightest MSSM Higgs boson.

0 The LHC is likely to have discovered some supersymmetric particles, but not all of them, and there will in particular be gaps among the electroweakly-interacting sparticles. Furthermore, the accuracy with which sparticle masses and decay properties will have been measured will probably

51

not be sufficient to distinguish between different supersymmetric models. Thus, there are many supersymmetric issues that will require explo-

ration elsewhere, and the same is true in many other scenarios for new physics at the TeV scale 65 .

3. Linear e+e- Colliders

Electron-positron colliders provide very clean experimental environments, with egalitarian production of all the new particles that are kinematically accessible, including those that have only weak interactions. Moreover, polarized beams provide a useful analysis tool, and ey, yy and e-e- colliders are readily available at relatively low marginal costs 48.

For these reasons, linear e-e- colliders are complementary to the LHC. Just as LEP built on the discoveries of the W* and 2' to establish the Standard Model and give us hints what might lie beyond it, a linear e-e- colliders in the TeV energy range will be essential to follow up on the discoveries made by the LHC, as well as make its own. The only question concerns the energy range that it should be able to cover.

At the low end, there is considerable interest in producing a large sample of N lo9 Zo bosons with polarized beams, enabling electroweak measurements to be taken to the next level of precision 66. A large sample of e+e- + W+W- events close to threshold would also be interesting for the same reason.

Looking to higher energies, we do know of one threshold that occurs around 350 GeV, namely that for e-e- + Et. As discussed earlier, we are also quite confident that the Higgs boson weighs 5 200 GeV. However, we do not know where (if anywhere!) the thresholds for sparticle-pair production may appear. The first might appear just above the reach of LEP, but equally it might appear beyond 1 TeV in the centre of mass. We can hope that the LHC will provide crucial guidance, but for now we must envisage flexibility in the attainable energy range.

3.1. TeV-scale Linear Colliders

The physics capabilities of linear e+e- colliders are amply documented in various design studies @. If the Higgs boson indeed does weigh less than 200 GeV, its production and study would be easy at an e+e- collider with ECM - 500 GeV. With a luminosity of cm-2s-1 or more, many decay modes of the Higgs boson could be measured very accurately 48, as seen in Fig. 16.

52

Figure 16. measured with a linear e+e- collider 48.

Analysis of the accuracy with which Higgs decay branching ratios may be

One might be able to find a hint whether its properties were modified by supersymmetry, as seen in Fig. 17 59. The top panels show typical examples of the potential sensitivity of the reaction e+e- + Z + (h + 6b) to modifications expected within the CMSSM, and the bottom panels show the potential sensitivity in e+e- + 2 + (h + WW'). Fig. 18 59 compares the sensitivities of e+e-, yy and p+p- colliders to the CP-odd Higgs boson mass mA and the Higgs mixing parameter p, including the CMSSM as a special case.

Moreover, if sparticles are light enough to be produced directly, their masses and other properties can be measured very precisely, typical estimated precisions being 48

6mF N 0.3 GeV , drn; 21 5 GeV , 6m+ 21 0.04 GeV , (18) dm, N 0.2 GeV , 6m,- 4 GeV.

Moreover, the spin-parities and couplings of sparticles can be measured accurately. The mass measurements can be used to test models of supersymmetry breaking, as seen in Fig. 19 67.

As seen in Fig. 8, the sparticles visible at an e+e- collider largely complement those visible at the LHC 43. In most of the benchmark scenarios proposed, a 1-TeV linear collider would be able to discover and measure precisely several weakly-interacting sparticles that are invisible or difficult to detect at the LHC. However, there are some benchmark scenarios where the linear collider (as well as the LHC) fails to discover supersymmetry. Independently from the particular benchmark scenarios proposed, a linear e+e- collider with ECM < 0.5 TeV would not cover all the supersymmetric parameter space allowed by cosmology, as seen in Fig. 20, whereas a combination of the LHC with a ECM = 1 TeV linear e+e- collider would together

53

300

E 200

E"

100

200 400 600 800 1000 1200 1400 m,@ WVI

z 9 E"

a(e+e- -+ Zh)B(h -+ WW") 400

300

2 9 200

E"

100

200 400 600 800 1000 1200 1400 m,,> WVI

Figure 17. The deviations of u(e fe - + Zh)B(h --t 6b) (top row) and u(e+e- --t

Zh)B(h + WW') (bottom row) for the lightest CP-even CMSSM Higgs boson, normalized to the values in the Standard Model with the same Higgs mass, are given in the regions of the (mllz , mo) planes allowed before the WMAP data for p > 0, tan p = 10,50 and A0 = 0 59. The diagonal red thick (thin) lines are the f 2 - u contours for gp - 2: +56.3, +11.5 (+38.1, -4.7). The near-vertical solid, dotted short-dashed, dash-dotted and long-dashed (black) lines are the rnh = 113,115,117,120,125 GeV contours. The lighter dot-dashed (orange) lines correspond to mA = 500,700,1000,1500 GeV. The light shaded (pink) regions are excluded by b + sy. The (brown) bricked regions are excluded because the LSP is the charged ?I in these regions.

discover a large fraction of the MSSM spectrum, as seen in Fig. 21. There are compelling physics arguments for such a linear e+e- collider,

which would be very complementary to the LHC in terms of its exploratory

54

Variation of the (TB with mA

. . . . . . h->m I ( , , , , 1 , , --- , I , , , h->m , I , , ,I

h -> gg

h -w WW'

--- -8 .-.- -'800 350 400 450 500 550 600 650

MA I G W Figure 18. The numbers of standard deviations of the predictions in the MSSM as compared to the Standard Model are shown in the different rrB channels for e+e- (left column) and yy and p+p- colliders (right column), as functions of the CP-odd neutral Higgs boson mass mA 59. The corresponding CMSSM value of mA is indicated by light vertical (orange) lines. The other parameters have been chosen as ml/z = 300GeV, ma = 100 GeV, tan /3 = 10 and A0 = 0.

power and precision. It is to be hoped that the world community will converge on a single project with the widest possible energy range.

3.2. CLIC Only a linear collider with a higher centre-of-mass energy appears sure to cover all the allowed CMSSM parameter space, as seen in the lower panels of Fig. 8, which illustrate the physics reach of a higher-energy lepton collider, such as CLIC 49 or a multi-TeV muon collider 50t51.

CERN and its collaborating institutes are studying CLIC as a possible second step in linear e+e- colliders 49. This would use a double-beam technique to attain accelerating gradients as high as 150 MV/m, and the viability of accelerating structures capable of achieving this field has been demonstrated in the CLIC test facility 6 8 . Parameter sets have been calculated for CLIC designs with ECM = 3 and 5 TeV, and luminosities of

cmP2s-l or more. The prospective layout of CLIC is shown in Fig. 22, illustrating how RF power from the high-intensity, low-energy drive beam is fed to the low-intensity, high-energy colliding beams.

Various topics in Higgs physics a t CLIC have been studied 69. For

55

300

100

-100 I/ I I I I I I I I I I I I I I I I I I I I I I I I I I I I

1 o2 I o5 1 o8 10” 1 0 ~ ~ 1 0 ~ ~

Figure 19. Analogously to the unification of the gauge couplings shown in Fig. 5, measurements of the sparticle masses at future colliders (vertical axis, in units of GeV) can be evolved up to high scales (horizontal axis, in units of GeV) to test models of supersymmetry breaking, in particular whether squark and slepton masses are universal at some input GUT scale 67.

example, it may be possible to measure for the first time H -+ p+p- decay. Also, if the Higgs mass is light enough, WZH - 120 GeV, it will be possible to measure the triple-Higgs coupling X H H H more accurately than would be possible at a lower-energy machine, as seen in Fig. 23. CLIC would also have interesting capabilities for exploring the heavier MSSM Higgs bosons in the ‘wedge’ region left uncovered by direct searches at the LHC and a lower-energy linear e+e- collider.

In many of the proposed benchmark supersymmetric scenarios, CLIC would be able to complete the supersymmetric spectrum and/or measure in much more detail heavy sparticles found previously at the LHC, as seen in Fig. 24. CLIC produces more beamstrahlung than lower-energy linear e+e- colliders, but the supersymmetric missing-energy signature would still be easy to distinguish, and accurate measurements of masses and decay modes could still be made, as seen in Fig. 25 71 for the example of e+e- -+ fi+fi- followed by fi* -+ p*x decay. CLIC also has the potential to study heavier

56

Figure 20. Estimates of the numbers of MSSM particles that may be detectable at a 0.5-TeV linear e+e- collider as functions of mllz along the WMAP lines for t a n p = 10 and 50 for /I > 0. The locations of updated benchmark points 44 along these WMAP lines are indicated.

LHC+LC 1 TeV tan p = 10

I

LHC+LC 1 TeV tan p = 50

Figure 21. Estimates of the combined numbers of MSSM particles that may be detectable at the LHC and a 1-TeV linear e+e- collider as functions of mIl2 along the WMAP lines for t a n p = 10 and 50 for p > 0. The locations of updated benchmark points 44 along these WMAP lines are indicated.

neutralinos and charginos well beyond the reach of the LHC and a lower- energy linear e+e- collider.

3.3. yy Colliders

Before leaving the world of e+e- colliders, a plea should be entered for their yy collider options. One interesting possibility would be a relatively low-energy e+e- collider with EGM N 160 GeV and a laser system capable of producing a light Higgs boson weighing w 120 GeV via yy + H , as seen in Fig. 26 72. This could measure quite accurately the H -+ bb, WW and yy

57

LklrOUnann ,/ iull 130 "l w s9 m .I.l",,*or 1.228 ern X.'ld,m-n*MI. b'-tm- #!?%!?$ r .......... !?!!E..!?%!!? ........... I(

. . .d lUJ ~~ j! ~ i ~ l ~ ~ ~ U - m%3ed-%n5>mm- 16 nCiMEn I . 5 A l ,.tacxYic

................................. ........................................................................................................ x.- i<

M V

Figure 22. Conceptual layout for the CLIC linear e+e- collider, which is designed to be capable of reaching a centre-of-mass energy of 3 TeV or more. CLIC uses high-power but low-energy drive beams to accelerate less-intense colliding beams with a high gradient 49.

0.2 E 0.18

0 018

= 0.12

Ca 0.w

. 0.14

o= 0.1

0.w 0.04 o m

0

h 0.3 2 0.25 . r 0.2

3 0.15 Lo

0.1

OM

0

~ 1 2 3 4 5

Figure 23. sured with a linear e+e- collider, as a function of its centre-of-mass energy 70.

Analysis of the accuracy with which the triple-Higgs coupling may be mea-

couplings, as seen in Fig. 18 59. Operating at higher energies, a yy collider could be interesting for studying the heavier Higgs bosons of the MSSM.

58

CLIC 4% = 3.0 TeV tan p = 10 id6q"Brks..SleptONmX XSH

d = la. P. I

CLIC 4s = 3.0 TeV tan p 2 50

I

Figure 24. Estimates of the numbers of MSSM particles that may be detectable at the CLIC 3-TeV linear e+e- collider as functions of mll2 along the WMAP lines for tan p = 10 and 50 for p > 0. The locations of updated benchmark points 44 along these WMAP lines are indicated.

c 700 9 1 B

ex 680

660

640

620

I . . I c . . . I . , . I I ~ . . . . ~ . . . . I . . . . I . . . . I . . . . l . ~

1110 1120 1130 1140 1150 1160 1170 1180 1190 Smuon Mass (GeV)

Figure 25. of sparticle masses to be made, in this case the ji and the lightest neutralino x 71.

Like lower-energy e+e- colliders, CLIC enables very accurate measurements

4. Neutrino Factories

4.1. Neutrino Masses?

There is no good reason why either the total lepton number L or the individual lepton flavours Le,p,T should be conserved. Theorists have learnt that the only conserved quantum numbers are those associated with ex-

59

' I lo's - Design Luminosity 0 e600 3 3 Fs

400

200

100 125 150 17 2-Jet Invariant Mass (GeV

Figure 26. running so that the peak E c ~ ( 7 7 ) = 115 GeV 72.

Observability of the H --t 6 b decay mode for mH = 115 GeV, with CLICHE

act local symmetries, just as the conservation of electromagnetic charge is associated with local U(l) invariance. On the other hand, there is no exact local symmetry associated with any of the lepton numbers, so we may expect non-zero neutrino masses.

However, so far we have only upper experimental limits on neutrino masses 73. From measurements of the end-point in Tritium ,!? decay, we know that:

mVe 2 2.5 eV, (19)

which might be improved down to about 0.5 eV with the proposed KATRIN experiment 74. From measurements of T + pu decay, we know that:

mvr < 190 KeV, (20)

and there are prospects to improve this limit by a factor - 20. Finally, from measurements of r + n r u decay, we know that:

m,, < 18.2 MeV, (21)

and there are prospects to improve this limit to - 5 MeV.

60

Astrophysical upper limits on neutrino masses are stronger than these laboratory limits. The 2dF data were used to infer an upper limit on the sum of the neutrino masses of 1.8 eV 7 5 , which has recently been improved using WMAP data to 37

CVimvi < 0.7 eV, (22) as seen in Fig. 27. This impressive upper limit is substantially better than even the most stringent direct laboratory upper limit on an individual neutrino mass.

0.0clO 0.002 0.004 0.006 0.008 0.010 %h2

Figure 27. Likelihood function for Ruh2 (related to the sum of neutrino masses) provided by WMAP 37: the quoted upper limit on mu applies if the 3 light neutrino species are degenerate.

Another interesting laboratory limit on neutrino masses comes from searches for neutrinoless double+? decay, which constrain the sum of the neutrinos’ Majorana masses weighted by their couplings to electrons 76:

(m,), = ~ E , i m , i U ~ i ~ 5 0.35 eV, (23)

which might be improved to N 0.01 eV in a future round of experiments. Neutrinos have been seen to oscillate between their different

flavours 77t78, showing that the separate lepton flavours Le,p,r are indeed not conserved, though the conservation of total lepton number L is still an open question. The observation of such oscillations strongly suggests that the neutrinos have different masses.

61

4.2. Models of Neutrino Masses and Mixing

The conservation of lepton number is an accidental symmetry of the renormalizable terms in the Standard Model Lagrangian. However, one could easily add to the Standard Model non-renormalizable terms that would generate neutrino masses, even without introducing any new fields. For example, a non-renormalizable term of the form 79

1 - v H . v H , M

where M is some large mass beyond the scale of the Standard Model, would generate a neutrino mass term:

However, a new interaction like (24) seems unlikely to be fundamental, and one should like to understand the origin of the large mass scale M .

The minimal renormalizable model of neutrino masses requires the introduction of weak-singlet ‘right-handed’ neutrinos N. These will in general couple to the conventional weak-doublet left-handed neutrinos via Yukawa couplings Y, that yield Dirac masses m D = Y,(OIHIO) - mw. In addition, these ‘right-handed’ neutrinos N can couple to themselves via Majorana masses M that may be >> m w , since they do not require electroweak sum- metry breaking. Combining the two types of mass term, one obtains the seesaw mass matrix

where each of the entries should be understood as a matrix in generation space.

In order to provide the two measured differences in neutrino masses- squared, there must be at least two non-zero masses, and hence at least two heavy singlet neutrinos Na 8 1 i 8 2 . Presumably, all three light neutrino masses are non-zero, in which case there must be at least three Ni. This is indeed what happens in simple GUT models such as SO(lO), but some models 83 have more singlet neutrinos 84. Here, for simplicity we consider just three Ni.

The effective mass matrix for light neutrinos in the seesaw model may be written as:

M, = Y;-Y”, 1 2 , M

62

where we have used the relation mg = Yvv with v (OlHlO). Taking mg - m, or me and requiring light neutrino masses N 10-1 to eV, we find that heavy singlet neutrinos weighing N 1O1O to 1015 GeV seem to be favoured.

It is convenient to work in the field basis where the charged-lepton masses mei and the heavy singlet-neutrino mases M are real and diagonal. The seesaw neutrino mass matrix M , (27) may then be diagonalized by a unitary transformation U :

UTM,U = M,". (28)

This diagonalization is reminiscent of that required for the quark mass matrices in the Standard Model. In that case, it is well known that one can redefine the phases of the quark fields 85 so that the mixing matrix UCKM has just one CP-violating phase 8 6 . However, in the neutrino case, there are fewer independent field phases, and one is left with 3 physical CP-violating parameters:

U = ~ ~ V P O : Po = Diag (ei41, eib2, 1) . (29)

Here l3 = Diag (eiQ1, eiaz, eia3) contains three phases that can be removed by phase rotations and are unobservable in light-neutrino physics, though they do play a r61e at high energies, V is the light-neutrino mixing matrix first considered by Maki, Nakagawa and Sakata (MNS) 87, and PO contains 2 CP-violating phases 4 1 , ~ that are observable at low energies. The MNS matrix describes neutrino oscillations

' y ) , (30)

where cij cos8ij,sij f sin8ij. The three real mixing angles 612,23,13 in (30) are analogous to the Euler angles that are familiar from the classic rotations of rigid mechanical bodies. The phase 6 is a specific quantum effect that is also observable in neutrino oscillations, and violates CP, as we discuss below. The other CP-violating phases 41,2 are in principle observable in neutrinoless double+ decay (23).

v = ( -512 '12 '12 c12 ") 0 (i c:3 s:3) ( ' y o o 1 O -S23 ~ 2 3 - - ~ 1 3 e - ~ ' o ~ 1 3 e - ~ '

4.3. Neutrino Oscillations

The first of the mixing angles in (30) to be discovered was 623, in atmospheric neutrino experiments. Whereas the numbers of downward-going atmospheric up were found to agree with Standard Model predictions, a

63

deficit of upward-going up was observed, as seen in Fig. 28. The data from the Super-Kamiokande experiment, in particular 77, favour near-maximal mixing of atmospheric neutrinos:

e2, - 45", Am;, - 2.4 x lo-, eV2. (31)

Recently, the K2K experiment using a beam of neutrinos produced by an accelerator has found results consistent with (31) It seems that the atmospheric vp probably oscillate primarily into vT, though this has yet to be established.

450

W 350 0 300 3 250 i? 200

150

p o h

loo 50 1 0- -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1

cose cose

-1 -0.5 0 0.5 -1 -0.5 0 0.5 cose cose

Figure 28. downward-moving vI., which is due to neutrino oscillations 77.

The zenith angle distributions of atmospheric neutrinos exhibit a deficit of

More recently, the oscillation interpretation of the long-standing solar- neutrino deficit has been established, in particular by the SNO experiment. Solar neutrino experiments are sensitive to the mixing angle 012 in (30). The recent data from SNO 78 and Super-Kamiokande 89 prefer quite strongly the large-mixing-angle (LMA) solution to the solar neutrino problem with

- 30°, Am:, - 6 x eV2, (32)

though they were unable to exclude completely the LOW solution with lower 6m2. However, the KamLAND experiment on reactors produced by nuclear power reactors has recently found a deficit of v, that is highly

64

compatible with the LMA solution to the solar neutrino problem in Fig. 29, and excludes any other solution.

as seen

" ..._ j ,_...... . .._., 1 ...'

tan2 e

Figure 29. a deficit of reactor neutrinos that is consistent with the LMA neutrino oscillation parameters previously estimated (ovals) on the basis of solar neutrino experiments 91.

The KamLAND experiment (shadings) finds

Using the range of 812 allowed by the solar and KamLAND data, one can establish a correlation between the relic neutrino density R,h2 and the neutrinoless double+ decay observable (mv)e , as seen in Fig. 30 92. Pre- WMAP, the experimental limit on (m,)e could be used to set the bound

d R,h2 d 10-l. (33)

Alternatively, now that WMAP has set a tighter upper bound S2,h2 < 0.0076 (22) 37, one can use this correlation to set an upper bound:

< m, >e 2 0.1 eV, (34)

which is difficult to reconcile with the neutrinoless double-P decay signal reported in 76.

The third mixing angle 013 in (30) is basically unknown, with experiments such as Chooz 93 and Super-Kamiokande only establishing upper limits. A fortiori, we have no experimental information on the CP-violating phase 6.

65

Figure 30. The correlation between the relic density of neutrinos R,h2 and the neutrinoless double-P decay observable: the different lines indicate the ranges allowed by neutrino oscillation experiments 92.

The phase 6 could in principle be measured by comparing the oscillation probabilities for neutrinos and antineutrinos and computing the CP- violating asymmetry 94:

sin ( S L ) sin (%L) sin ( S L ) ,

as seen in Fig. 31 95. This is possible only if Am:, and s12 are large enough - as now suggested by the success of the LMA solution to the solar neutrino problem, and if ~ 1 3 is large enough - which remains an open question.

4.4. Concept for a Neutrino Factory

A number of long-baseline neutrino experiments using beams from accelerators are now being prepared in the United States, Europe and Japan, with the objectives of measuring more accurately the atmospheric neutrino oscillation parameters, Am;3, 623 and 613, and demonstrating the production of u, in a up beam.

Beyond these, ideas are being proposed for intense ‘super-beams’ of low- energy neutrinos, produced by high-intensity, low-energy accelerators such as the SPL proposed at CERN. A subsequent step could be a storage

66

'.8 7.8 8 8.2 8.4 7.6 7.8 8 8% z.4

. . . ,... *) aa F . . , ... , ' I

5:s -J3.,

Figure 31. Possible measurements of 013 and 6 that could be made with a neutrino factory, using a neutrino energy threshold of about 10 GeV. Using a single baseline correlations are very strong, but can be largely reduced by combining information from different baselines and detector techniques 95, enabling the CP-violating phase 6 to be extracted.

ring for unstable ions, whose decays would produce a ' p beam' of pure u, or i7, neutrinos. These experiments might be able to measure 6 via CP and/or T violation in neutrino oscillations 97.

A final step could be a full-fledged neutrino factory based on a muon storage ring, one conceptual layout for which is shown in Fig. 32. This would produce pure vp and 0, (or u, and Dp beams and provide a greatly enhanced capability to search for or measure 6 via CP violation in neutrino oscillations 98.

We have seen above that the effective low-energy mass matrix for the light neutrinos contains 9 parameters, 3 mass eigenvalues, 3 real mixing angles and 3 CP-violating phases. However, these are not all the parameters in the minimal seesaw model. As shown in Fig. 33, this model has a total of 18 parameters 999100. The additional 9 parameters comprise the 3 masses of the heavy singlet 'right-handed' neutrinos Mi, 3 more real mixing angles and 3 more CP-violating phases.

As illustrated in Fig. 33, many of these may be observable via renor-

67

Figure 32. Conceptual layout for a neutrino factory, based on an intense superconducting proton linac that produces many pions, whose decay muons are captured, cooled in phase space and stored in a ‘bow-tie’ ring. Their subsequent decays send neutrinos with known energy spectra and flavours to a combination of short- and long-baseline experiments 98.

malization in supersymmetric models 1011100~1021103, which may generate observable rates for flavour-changing lepton decays such as p -+ ey, T + py and T + ey, and CP-violating observables such as electric dipole moments for the electron and muon. In leading order, the extra seesaw parameters contribute to the renormalization of soft supersymmetry-breaking masses, via a combination which depends on just 1 CP-violating phase. However, two more phases appear in higher orders, when one allows the heavy singlet neutrinos to be non-degenerate lo2. Some of these extra parameters may also have controlled the generation of matter in the Universe via leptogenesis lo4.

Fig. 34 (left) is a scatter plot of B ( p -+ e-y) in one particular texture for lepton mixing, as a function of the singlet neutrino mass M N ~ . We see that p + ey may well have a branching ratio close to the present experimental upper limit, particularly for larger M N ~ . Analogous predictions for T + py decays are shown in Figs. 34 (right). The branching ratios decrease with increasing sparticle masses, but the range due to variations in the neutrino parameters is considerably larger than that due to the sparticle masses. The present experimental upper limits on T -+ py, in particular, already exclude significant numbers of parameter choices.

68

lo-

I Seesaw mechanism I

. . . . . . . . . . . ’ . . . .

I M” I 9 effective parameters

A

Leptogenesis Renormalization

13+3 parameters

15+3 physical parameters

Leptogenesis Renormalization

YuY,! M N ~ Y,!LYu , M N ~ 13+3 parameters

Figure 33. Roadmap for the physical observables derived from Yu and Ni lo5.

. .- , . . _ . . . m u a B m s m r o m 10’’

m? 1-.Vl

Figure 34. symmetric seesaw model for various values of its unknown parameters lo3.

Scatter plots of the branching ratios for p + ey and T + p-y in the super-

69

The decay p + ey and related processes such as p + 3e and p + e conversion on a heavy nucleus are all of potential interest for the front end of a neutrino factory lo6. Such an accelerator will produce many additional muons, beyond those captured and cooled for storage in the decay ring, which could be used to explore the decays of slow or stopped muons with high statistics. There are several options for studying rare 7- decays, such as the B factories already operating or the LHC, which will produce very large numbers of T leptons via W, 2 and B decays. Finally, CP-violating renormalization effects can be probed in experiments on the electric dipole moments of the electron and muon: the former does not require an accelerator, but the latter could also be done at the front end of a neutrino factory lo6.

4.5. The Leptogenesis Connection

The decays of the heavy singlet neutrinos N provide a mechanism for generating the baryon asymmetry of the Universe, namely leptogenesis lo4. In the presence of C and CP violation, the branching ratios for N -+ Higgs + l may differ from that for N + Higgs + e, producing a net lepton asymmetry in the very early Universe. This is then transformed (partly) into a quark asymmetry by non-perturbative electroweak sphaleron interactions during the period before the electroweak phase transition.

The total decay rate of a heavy neutrino Ni may be written in the form 1 8T

ri = -- ( Y ~ Y J ) ~ ~ M ~ .

One-loop CP-violating diagrams involving the exchange of heavy neutrino Nj would generate an asymmetry in Ni decay of the form:

where f(Mj/Mi) is a known kinematic function. Thus we see that leptogenesis lo4 is proportional to the product YuYJ,

which depends on 13 of the real parameters and 3 CP-violating phases. However, as seen in Fig. 35, the amount of the leptogenesis asymmetry is explicitly independent of the CP-violating phase S that is measurable in neutrino oscillations lo5. The basic reason for this is that one makes a unitary sum over all the light lepton species in evaluating the asymmetry E i j . This does not mean that measuring 6 is of no interest for leptogenesis: if it is found to be non-zero, CP violation in the lepton sector - one of the

70

key ingredients in leptogenesis - will have been established. On the other hand, the phases responsible directly for leptogenesis may contribute to the electric dipole moments of leptons.

a=o

Figure 35. Comparison of the CP-violating asymmetries in the decays of heavy singlet neutrinos giving rise to the cosmological baryon asymmetry via leptogenesis (left panel) without and (right panel) with maximal CP violation in neutrino oscillations lo5. They are indistinguishable.

In general, one may formulate the following strategy for calculating leptogenesis in terms of laboratory observables 1007105:

0 Measure the neutrino oscillation phase 6 and the Majorana phases

0 Measure observables related to the renormalization of soft supersymmetry-breaking parameters, that are functions of 6 , 4 1 , 2

and the leptogenesis phases, 0 Extract the effects of the known values of 6 and 41,2, and isolate

the leptogenesis parameters.

4 L 2 ,

In the absence of complete information on the first two steps above, we are currently at the stage of preliminary explorations of the multi-dimensional parameter space. As seen in Fig. 35, the amount of the leptogenesis asymmetry is explicitly independent of 6 lo5. However, in order to make more definite predictions, one must make extra hypotheses, as discussed later.

5 . Muon Colliders

Once the procedures for producing, capturing and storing large numbers of muons have been mastered, why not collide them? Muon colliders produce

71

Higgs bosons directly via p+p- annihilation in the s channel, unaccompa- nied by spectator particles. If the electroweak symmetry is indeed broken via the Higgs mechanism, hadron machines, such as the Tevatron collider 56

and the LHC 5 2 7 5 3 , will presumably discover at least one Higgs boson, but in an experimental environment contaminated by important backgrounds and accompanied by many other particles. An e+e- linear collider (LC) 48

would complement the hadron colliders by providing precise studies of the Higgs boson in a clean environment. However, the dominant production mechanisms create Higgs bosons in association with other particles, such as a Zo , two neutrinos or an e+e- pair. Moreover, the peak cross section for a p+p- collider to produce a Higgs of 115 GeV is around 60 pb, which can be compared with around 0.14 pb for an e+e- collider operating at 350 GeV 50951.

However, if the study of an s-channel resonance is to be pursued experimentally, the event rate must be sufficiently large. In the case of a Standard Model Higgs boson H , this means that the mass must be somewhat less than twice M w , otherwise the large width reduces the peak cross section lo7. This condition need not apply to more complicated Higgs systems, for instance the heavier neutral Higgses of supersymmetry 50i51.

5.1. A p+p- Higgs Factory

The effective cross section for Higgs production at ,/5 - m H is obtained by convoluting the standard s-channel Breit-Wigner resonance shape with the beam energy distribution, which we model as a Gaussian distribution with width (TE. At ,/5 = m H , initial-state radiation (ISR) effects can be approximated by a constant reduction factor 77, where 77 is a function of various parameters that we do not discuss here. In the limit where the resonance width r << m H , quite a compact expression can be derived for the peak cross section lo7:

x r ] 7 ~ ~ / ~ AeA2(1 - Erf(A)),

where 2 "

and Erf(z) = - e-t2dt. i r A=---- 2 f i UE J;;

The peak cross section depends critically on the beam-energy

(39)

spread (TE

72

compared to the resonance width I?. There are two important limits:

Figure 36(a) shows the & dependence of a(p+p- + H + bb) for a Stan- dard Model Higgs boson HSM weighing 115 GeV, compared with that the lightest MSSM Higgs boson, denoted here by H M S S M , for various values of the beam-energy resolution R f UE/&, neglecting ISR. The peak cross section is plotted as a function of R in Fig. 36 (b). As can be seen, gpe&

reaches a plateau for R << I?bb/mfJ, in accordance with (40), (41). Note also that the resonance is washed out in the limit I’/oE + 0.

b 1 1 5 GeV. u=M..-r-A=lTeV. IL.0

Figure 36. (a) Cross sections for pfp- -+ H -+ 6b as functions of fi for Standard Model and MSSM Higgs bosons, and (b) R dependences of the peak cross sections, for mb(mb) = 4.15 GeV (solid lines) and mb(mb) = 4.45 GeV (dashed lines) lo7.

Not only is the beam energy spread at a p+p- collider potentially very small, but also the energy can be calibrated very accurately using the decays of polarized muons in the circulating beams. The very fine energy resolution and precision in fi expected at the p+p- collider would allow the properties of the Higgs boson(s) to be determined with outstanding accuracy. One expects, for instance, to be able to measure the mass and width of a light ( m ~ < 2 M w ) Higgs boson to fractions of an MeV.

The most important decay mode of the Higgs boson at a p+p- collider is likely to be H + bb, as shown in Fig. 36. Other potential observables are the H + WW* and H + T+T- decay modes. As already seen in Fig. 18 59,

the 6b channel has the potential to distinguish between a Standard Model

73

Higgs boson and a light CMSSM Higgs boson with the same mass. We show in Fig. 37 the ratio [a(pU+pU- + h) x B(h -+ b b ) ] ~ ~ s s ~ in terms of standard deviations from the Standard Model value in the (mlp, mo) plane for p > 0 and two combinations of tan@ and Ao, together with the familiar constraints from B(b -+ sy), gp - 2 and cosmological dark matter (pre- WMAP) 59. We have assumed an accuracy of 3% in the determination of a(p+p- -+ h) x B(h -+ bb). No suppression of Higgs production can be observed for the CMSSM parameter space. The production and decay is always enhanced compared to the corresponding Standard Model value, and there are interesting prospects for distinguishing a Standard Model Higgs boson from its CMSSM counterpart.

F e E"

300

200

100

200 400 600 800 1000 1200 1400 m,,2 [GeVl

F $2 E"

Figure 37. The ratio [a(p+p- + h) x B(h + ~$)]CMSSM compared to the Standard Model value in the region of the (ml/zrmg) plane allowed before the WMAP data for p > 0 and tan p = 10, A0 = 0 (left plot) and tan p = 50, Ao = -2m1/2 (right plot) 59,

assuming an experimental accuracy of 3%. The bricked region is forbidden because the LSP is the lightest ?. The regions above and to the right of the (red) diagonal solid lines yield values of gr - 2 within 2 0 of the present central value. The light shaded (pink) region is excluded by B(b + sy) measurements. The solid leftmost (dotted middle, dashed rightmost) near-vertical line corresponds to mh = 113 (115, 117) GeV.

Within the MSSM, deviations from the Standard Model predictions are related to the masses of the heavier neutral Higgs bosons H , A, vanishing as they become large. Hence, measurements at the first Higgs peak could be used in principle to predict the H , A masses, as seen in Fig. 38 51.

74

I 8 9 10 11 mP

Figure 38. Comparison of the accuracies with which the mass of the CP-odd MSSM Higgs boson A could be estimated, based on measurements with the LHC and a 1-TeV linear e+e- collider (outer, green line) and p+p- Higgs factory (inner, red line) 51.

5.2. Higher-Energy p+p- Colliders

At a higher-energy p+p- collider, the H , A bosons would yield a twin-peak structure, as seen in Fig. 39, which would provide many opportunities for studying details of the MSSM 50,51J07.

Both the first p+p- Higgs factory and the second ( H , A ) factory will provide unique possibilities for studying CP violation in the Higgs sector of the MSSM, in particular using polarized p* beams. Some examples are shown in Fig. 40.

Looking beyond these Higgs factories, p+p- colliders could be interesting alternatives for reaching very high energies in lepton collisions 50751, since they emit very little synchrotron radiation, unlike e+e- colliders. There is, however, another snag, namely that muons decay. This is not a show-stopper at low energies, but can lead to a neutrino radiation hazard at energies above a TeV or so. However, before reaching this problem, much work is still required before even the basic feasibility of a p+p- collider can be demonstrated. It would need about an order of magnitude more muons than are foreseen in the neutrino factory, and it is not yet clear what combination of higher-efficiency beam preparation and increased proton power

75

396 398 400 402 404 4 s (GeV)

Figure 39. mA = 400 GeV and various values of tanp 51.

Line shapes of the H and A peaks as observable at a ,u+,u- collider, for

will be the most effective way to achieve this. Moreover, considerably more beam cooling would be required for a p+p- collider, and the bunch structure foreseen for a neutrino factory would need to be modified for a p+p- collider. A p + p - collider will not be built tomorrow!

6. In the Aftermath of WMAP

In this Section, we turn our attention from future accelerators to a past de- celerator, namely the early Universe. The early history of the Universe was dominated by particles and, conversely, cosmology provides important constraints on particle physics. We have already met some examples, namely the cosmological constraints on neutrinos and dark matter. These have recently been greatly sharpened by the observations of the cosmological microwave background radiation (CMB) by the WMAP satellite. Com- bined with other data, these provide the best available determinations of

76

Figure 40. The dependence of polarized-muon cross sections on the centre-of-mass energy &, as estimated in lo8 for the MSSM with explicit CP violation. The selected parameters are: t a n p = 3, M H + M 0.4 TeV, Msusy = 0.5 TeV, IAt,bl = 1p1 = 1 TeV and arg(pAt) = 0 (solid lines) and 90' (dashed lines).

the matter and energy content of the Universe 37:

RTOT = 1.02f 0.02 +0.009 RCDM h2 = O . l l l - ~ . ~ ~ ~

Rbh2 = 0.0224 f 0.0009 R, < 0.0076.

We have already incorporated the second and fourth of these numbers in our earlier discussion: here we shall explore the first and third numbers, arriving at possible predictions for future accelerators.

The measured value of RTOT is in excellent agreement with the prediction RTOT 21 1 of cosmological inflation, which is also consistent with many measured details of the CMB. So let us now review the theory of cosmological inflation '09J10.

77

6.1. Cosmological Inflation

One of the main motivations for inflation problem: why are distant parts of the Universe so similar:

is the horizon or homogeneity

In conventional Big Bang cosmology, the largest patch of the CMB sky which could have been causally connected, i.e., across which a signal could have travelled at the speed of light since the initial singularity, is about 2 degrees. So how did opposite parts of the Universe, 180 degrees apart, ‘know’ how to coordinate their temperatures and densities?

Another problem of conventional Big Bang cosmology is the size or age problem. The Hubble expansion rate in conventional Big bang cosmology is given by:

where k = 0 or f l is the curvature. The only dimensionful coefficient in (47) is the Newton constant, GN l/M$ : M p = 1.2 x 1019 GeV. A generic solution of (47) would have a characteristic scale size a N Cp 1 / M p N

s and live to the ripe old age of t - t p E Cp/c N s. Why is our Universe so long-lived and big? Clearly, we live in an atypical solution of (47)!

A related issue is the flatness problem. Defining, as usual

we have

Since p N aP4 during the radiation-dominated era and N a-3 during the matter-dominated era, it is clear from (49) that R(t) + 0 rapidly: for R to be 0(1) as it is today, IR- 11 must have been O(10-60) at the Planck epoch when t p - s. The density of the very early Universe must have been very finely tuned in order for its geometry to be almost flat today.

Then there is the entropy problem: why are there so many particles in the visible Universe: S N log0? A ‘typical’ Universe would have contained O(1) particles in its size - e3,.

78

All these particles have diluted what might have been the primordial density of unwanted massive particles such as magnetic monopoles and grav- itinos. Where did they go?

is that, at some early epoch in the history of the Universe, its energy density may have been dominated by an almost constant term:

The basic idea of cosmological inflation

leading to a phase of almost de Sitter expansion. It is easy to see that the second (curvature) term in (50) rapidly becomes negligible, and that

during this inflationary expansion. It is then apparent that the horizon would have expanded (near-) ex-

ponentially, so that the entire visible Universe might have been within our pre-inflationary horizon. This would have enabled initial homogeneity to have been established. The trick is not somehow to impose connections beyond the horizon, but rather to make the horizon much larger than naively expected in conventional Big Bang cosmology:

( 5 2 ) H r aH N a l e >> cr ,

where H r is the number of e-foldings during inflation. It is also apparent that the -$ term in (50) becomes negligible, so that the Universe is almost f lat with Riot N 1. However, as we see later, perturbations during inflation generate a small deviation from unity: 1Rtot - 11 N Following inflation, the conversion of the inflationary vacuum energy into particles reheats the Universe, filling it with the required entropy. Finally, the closest pre- inflationary monopole or gravitino is pushed away, further than the origin of the CMB, by the exponential expansion of the Universe.

An example of such a scenario is chaotic inflation 113, according to which there is no specific structure in the effective potential V($) , and no phase transition between old and new vacua. Instead, any given region of the Universe is assumed to start with some random value of the inflaton field q5 and hence the potential V(q5), which decreases monotonically to zero. If the initial value of V(q5) is large enough, and the potential flat enough, (our part of) the Universe will undergo sufficient expansion.

The above description is quite classical. In fact, one should expect quantum fluctuations in the initial value of the inflaton field q5, which would

79

cause the roll-over into the true vacuum to take place inhomogeneously, and different parts of the Universe to expand differently. These quantum fluctuations would give rise to a Gaussian random field of perturbations with similar magnitudes on different scale sizes, just as the astrophysicists have long wanted ‘14. The magnitudes of these perturbations would be linked to the value of the effective potential during inflation, and would be visible in the CMB as adiabatic temperature fluctuations 1097110:

where p V1I4 is a typical vacuum energy scale during inflation. As we discuss later in more detail, consistency with the CMB data from COBE et al., that find 6T/T N 10V5, is obtained if

p 21 10l6 GeV, (54) comparable with the GUT scale.

theory ‘15, described by a Lagrangian Let now consider in more detail chaotic inflation in a generic scalar field

1 L(4) = Z d W P 4 - V(4), (55)

where the first term yields the kinetic energy of the inflaton field 4 and the second term is the inflaton potential. One may treat the inflaton field as a fluid with density

and pressure

Inserting these expressions into the standard FRW equations, we find that the Hubble expansion rate is given by

as discussed above, the deceleration rate is given by

and the equation of motion of the inflaton field is

80

The first term in (60) is assumed to be negligible, in which case the equation of motion is dominated by the second (Hubble drag) term, and one has

V' 4 21 --, 3H

as assumed above. In this slow-roll approximation, when the kinetic term in (58) is negligible, and the Hubble expansion rate is dominated by the potential term:

H N .J'V(P). 3M:

where M p E 1 / J w N 2.4 x 10l8 GeV. It is convenient to introduce the following slow-roll parameters:

Various observable quantities can then be expressed in terms of E , V and 5, including the spectral index for scalar density perturbations:

ns = 1 - 6~ + 2q, (64)

the ratio of scalar and tensor perturbations at the quadrupole scale:

AT AS

T I - = 1 6 ~ ,

the spectral index of the tensor perturbations:

nT = - 2 E ,

and the running parameter for the scalar spectral index:

2 dlnk 3 - - dns - - [(n, - I > ~ - 4q2] + 25.

(65)

(67)

The amount eN by which the Universe expanded during inflation is also controlled by the slow-roll parameter c:

In order to explain the size of a feature in the observed Universe, one needs:

3 (69) 1016GeV 1 Vk 1 V,"14

114 + -In- - -In k

N = 62-In- -In aoHo ';I4 ve Preheating

81

where k characterizes the size of the feature, Vj is the magnitude of the inflaton potential when the feature left the horizon, V, is the magnitude of the inflaton potential at the end of inflation, and Preheating is the density of the Universe immediately following reheating after inflation.

As an example of the above general slow-roll theory, let us consider chaotic inflation 113 with a V = im242 potential motivated by the sneutrino inflation model ‘16 discussed later, and compare its predictions with the WMAP data 37. In this model, the conventional slow-roll inflationary parameters are

where 41 denotes the a priori unknown inflaton field value during inflation at a typical CMB scale k . The overall scale of the inflationary potential is normalized by the WMAP data on density fluctuations:

= 2.95 x lO-’A : A = 0.77f.0.07, (71) = 24n2 M:c

yielding

Va = M $ d c x 24n2 x 2.27 x lop9 = 0.027Mp x c a ,

miq5, = 0.038 x M:

(72)

corresponding to 3

(73)

in any simple chaotic d2 inflationary model. The above expression (69) for the number of e-foldings after the generation of the CMB density fluctuations observed by COBE could be as low as N N 50 for a reheating temperature TRH as low as lo6 GeV. In the q52 inflationary model, this value of N would imply

1 4; N = -- N 50, 4 M: (74)

corresponding to

4; N 200 x M:. (75)

Inserting this requirement into the WMAP normalization condition (72), we find the following required mass for any quadratic inflaton:

m E 1.8 x 1013 GeV. (76)

82

This is comfortably within the range of heavy singlet (s)neutrino masses usually considered, namely mN - 1O1O to GeV, motivating the sneutrino inflation model '16 discussed below.

Is this simple 42 model compatible with the WMAP data? It predicts the following values for the primary CMB observables 116: the scalar spectral index

8M; n, = I--- 21 0.96, @?

the tensor-to scalar ratio 32 M;

T = - N 0.16, q5?

and the running parameter for the scalar spectral index:

(77)

The value of n, extracted from WMAP data depends whether, for example, one combines them with other CMB and/or large-scale structure data. However, the q52 model value n, N 0.96 appears to be compatible with the data at the 1-0 level. The d2 model value T N 0.16 for the relative tensor strength is also compatible with the WMAP data. In fact, we note that the favoured individual values for n,,r and dn,/dlnk reported in an independent analysis '17 all coincide with the @2 model values, within the latter's errors!

One of the most interesting features of the WMAP analysis is the possibility that dn,/dlnlc might differ from zero. The q52 model value dn,/dlnlc N 8 x derived above is negligible compared with the WMAP preferred value and its uncertainties. However, dn,/dlnlc = 0 appears to be compatible with the WMAP analysis at the 2-a level or better, so we do not regard this as a death-knell for the q52 model.

What does all this inflation theory have to do with accelerator physics? The answer may be provided by the question in the following title.

6.2. Could the Inflaton be a Sneutrino?

This 'old' idea 11' has recently been resurrected l16 . We recall that seesaw models of neutrino masses involve three heavy singlet right-handed neutrinos weighing around lo1" to 1015 GeV, which certainly includes the preferred inflaton mass found above (76). Moreover, supersymmetry requires each of the heavy neutrinos to be accompanied by scalar sneutrino

83

partners. In addition, singlet (s)neutrinos have no interactions with vector bosons, so their effective potential may be as flat as one could wish. Moreover, supersymmetry safeguards the flatness of this potential against radiative corrections. Thus, singlet sneutrinos have no problem in meeting the slow-roll requirements of inflation.

On the other hand, their Yukawa interactions YD are eminently suitable for converting the inflaton energy density into particles via N + H + e decays and their supersymmetric variants. Since the magnitudes of these Yukawa interactions are not completely determined, there is flexibility in the reheating temperature after inflation, as we see in Fig. 41 '16. Thus the answer to the question in the title of this Section seems to be 'yes', so far.

1014

10l2

2 1o'O

s 1 o8

z

11111111 - lo6 lo8 1o1O lo1* 1014

Tm inGeV *

Figure 41. The solid curve bounds the region allowed for leptogenesis in the (TRH, M N ~ ) plane, assuming a baryon-to-entropy ratio YB > 7.8 x and the maximal CP asymmetry ~ ~ ~ ~ ( M j v ~ ) . In the area bounded by the red dashed curve leptogenesis is entirely thermal l 1 6 .

One possibility is that the inflaton might be a heavy singlet sneutrino '16. This hypothesis would require a mass N 1.8 x 1013 GeV for the lightest sneutrino, which is well within the range favoured by seesaw models. As discussed previously, this sneutrino inflaton model predicts values of the spectral index of scalar perturbations, the fraction of tensor perturbations and other CMB observables that are consistent with the WMAP data. The sneutrino inflaton model is quite compatible with a low reheating

84

temperature, as seen in Fig. 41. Moreover, because of this and the other constraints on the seesaw model parameters in this model, it makes predictions for the branching ratio for p + ey that are more precise than in the generic seesaw model. As seen in Fig. 42, it predicts that this decay should appear within a couple of orders of magnitude of the present experimental upper limit 116, and hence be accessible to the present or next generations of accelerators.

Figure 42. Calculations of B(p --f er) (left) and B(T --t p r ) (1eft)in the sneutrino inflation model. Black points correspond to sin813 = 0.0, Mz = 1014 GeV, and 5 x 1014 GeV < M3 < 5 x 1015 GeV. Red points correspond to sin813 = 0.0, Mz = 5 x 1014 GeV and M3 = 5 x 1015 GeV, while green points correspond to sin013 = 0.1, M2 = 1014 GeV and M3 = 5 x 1014 GeV l16. We assume for illustration that ( m l p r mo) = (800,170) GeV and tan /3 = 10.

7. Conclusions

We have seen in these lectures that there are good theoretical prospects for discovering exciting new physics beyond the Standard Model at foreseeable future accelerators, including the LHC, a TeV-scale linear e+e- collider, CLIC, a neutrino factory and p+p- colliders. Furthermore, the ‘past de- celerator’, the Big Bang, reinforces our expectations for new physics at the TeV scale, associated with cold dark matter. Data from past accelerators such as LEP do no prove what this new physics might be, though it offers hints for a relatively light Higgs boson and supersymmetry. Time and future accelerators will tell whether these hints reflect Nature’s choice of new physics.

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B PHYSICS AND CP VIOLATION

R. V. KOWALEWSKI* Department of Physics and Astronomy

P.O. Box 3055, University of Victoria

Vactoria, BC V8N2X3 CANADA

These lectures present the phenomenology of B meson decays and their impact on our understanding of CP violation in the quark sector, with an emphasis on measurements made at the e+e- B factories. Some of the relevant theoretical ideas such as the Operator Product Expansion and Heavy Quark Symmetry are introduced, and applications to the determination of CKM matrix elements given. The phenomenon of B flavor oscillations is reviewed, and the mechanisms for and current status of CP violation in the B system is given. The status of rare B decays is also discussed.

1. Flavor Physics with B Mesons

B decays provide a sensitive probe of the physics of quark mixing, described by the unitary Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix in the Standard Model (SM). The mixing of the weak and mass eigenstates of the quarks provides a rich phenomenology and gives a viable mechanism for the non-conservation of CP symmetry in the decays of certain hadrons. CP asymmetries in B decays can be large and allow a determination of the magnitude of the irreducible phase in the CKM matrix. The pattern of CP asymmetries observed in B decays can be compared with the detailed prediction of these asymmetries in the SM in an effort to tease out evidence of new physics (NP). The study of B decays allows direct measurement of the magnitudes of the elements IVual and lVc~l of the CKM matrix. The large mass of the top quark allows information on ll&l and ll&l to be extracted via higher order processes like Bozo oscillations and decays involving loop diagrams. These loop decays have accessible branching fractions (as large

*Work partially supported by the Natural Sciences and Engineering Research Council of Canada.

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as lov4) and allow sensitive searches for physics beyond the SM, as the effect of new particles or couplings in the internal loops can manifest itself in modifications to the rates for these decays.

In addition to probing the flavor sector of the SM, B decays provide a laboratory for testing our understanding of QCD. The scale of the short- distance physics (e.g. weak b quark decay) is in the perturbative regime of QCD while the formation of final state hadrons and the binding of the b quark to the valence anti-quark is clearly non-perturbative. Pow- erful theoretical tools have been developed to systematically address the disparate scales. The Operator Product Expansion (OPE) together with Heavy Quark Symmetry allow perturbative calculations to be combined with non-perturbative matrix elements, and provide relationships amongst the non-perturbative matrix elements contributing to different processes. This allows some non-perturbative quantities to be determined experimentally, and leads to the vibrant interplay between experiment and theory that has characterized this area of research in recent years.

2. Quark mixing

The mixing between the quark mass eigenstates and their weak interaction eigenstates, parameterized in the unitary 3 x 3 CKM matrix, is responsible for flavor oscillations in the neutral B and K mesons and leads to an irreducible source of CP violation in the SM through the non-trivial phase of the CKM matrix. The CKM matrix can be parameterized by 3 real angles and one imaginary phase. The presence of this irreducible phase is an unavoidable consequence of 3 generation mixing.” Many parameterizations of the CKM matrix have been suggested. One choice in widespread use is in terms of angles 612, 613, 623 and phase 6 (see [l]). The magnitudes of the elements in the CKM matrix decrease sharply as one moves away from the diagonal, suggesting a parameterization2 in terms of powers of A, the sine of the Cabibbo angle. An improved version3 of this “Wolfenstein parameterization” will be used here. The starting point is to let the parameters A, A, p and 77 satisfy the relations X = \Vusl, AX2 = lVcbl and AX3(p-i77) = IV&l and to write the remaining elements in terms of these four parameters, expanded in powers of A. Given that X = 0.2196 f 0.0026’, highly accurate approximate parameterizations can be obtained keeping only the first one or two terms in the expansion. The matrix to order X5 is given here.

&The number of irreducible phases for N-generation mixing is ( N - 2) (N - 1)/2.

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1 - ;A2 - QX4 X AX3 ( p - iq )

- X + iA2X5 [I - 2 ( p + iq)] 1 - $A2 - k X 4 ( l + 4A2) AX3 [1 - ( p + iq)(l- ;A2)] -AX2 + A ( ; - p - iq)X4 1 - iA2X4

AX2

This parameterization has several nice features. The smallness of the off-diagonal elements is taken up by powers of A, leaving the parameters A, p and q of order unity. It also makes clear the near equality of the elements lVcbl and Ivt,l, namely I k / v c b l = 1 + c1(X2).

The relations dictated by unitarity allow a convenient geometrical representation of the CKM parameters. The product of any row (column) of the matrix times the complex conjugate of any other row (column) results in three complex numbers that sum to zero, and can be drawn as a triangle in the complex plane. There are three such independent triangles. Two of the three have one side much shorter than the others (i.e. have one side that is proportional to a higher power of X than are the others), but the remaining triangle, formed by multiplying the first column by the complex conjugate of the third column, has all sides of order X3. It is this triangle that is usually discussed when considering the impact of experimental measurements on the parameters of the CKM matrix. These unitarity relations need to be verified experimentally; a violation of unitarity would point to new physics (e.g. a fourth generation, in which case the 3 x 3 submatrix need not be unitary).

The unitarity triangle of interest, namely V&V,*b+vcdv~+Vtd&~ = 0, is usually rescaled by dividing through by VcdV,*b, giving a triangle whose base has unit length and lies along the x axis and whose apex is at the point vcdv;F - 1 + w. Casting these relations in terms of the parameters X,A,p and q and defining p = (1 - X 2 / 2 ) p and 7 = (1 - X2/2)q , the apex of the triangle is at (p ,$ up to corrections of order X2. By dividing out Vcb we largely eliminate dependence on the parameter A, which is in any case relatively well known' ( A = 0.85 f 0.04). The sides and angles of the

VudV* -

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unitarity triangle can be expressed as

The angles a, ,B and y are also known as 4 2 , 41 and 43, respectively. Figure 1 shows the constraints on the unitarity triangle given in Ref. [l].

Figure 1. K systems.

Constraints in the p-Fj plane from measurements in the B meson and neutral

Measurements of Ivubl/lvcbl constrain the length of R, and constrain (p ,$ to lie in an annulus centered on the origin. These measurements are improving as more data and additional theoretical insights are brought to bear. The bands emanating from the point (1,O) correspond to the measurement of sin28, the result of the impressive initial success of the B-factory program. These measurements already give some of the most precise information about the unitarity triangle and are perhaps an order of magnitude

95

away from being limited by systematics. The B system also allows access to the length of Rt through measurements of Bozo oscillations, which give indirect sensitivity to and I&,l. The determination of Rt is dominated by theoretical uncertainties. Measurements of B: oscillations and of the ratio of b += dy to b += sy decays should allow improved determinations of Rt. While B: oscillations are not accessible at e+e- B factories, there are good prospects for this measurement at high energy hadron collider experiments. Measurement of the CKM-suppressed b -+ dy decays will require significantly larger data sets than are currently available.

3. B factory basics

The e+e- B factories operate at the "(4s) resonance, a quasi-bound bz state just above the threshold for production of B+B- or Bozo pairs. The width of the T(4S) is comparable to the beam energy spread of e+e- colliders, making the peak cross-section a weak function of the machine parameters. The cross-section at the peak is about 1.1 nb, to be compared with the underlying qQ(q = u, d, s, c) cross-section of - 3.5 nb. The "(4s) is expected to decay with a branching fraction of 0.5 to each of B+B- and Bozo; measurements are consistent with this expectation, but have a large uncertainty1 (f14% on the ratio of the two branching fractions). The mass difference between the T(4S) and a pair of B mesons is about 20 MeV, so no additional particles (apart from low-energy radiated photons) are produced, and the final state B mesons have one unit of orbital angular momentum and small velocity (B E 0.06) in the T(4S) rest frame.

The cross-section for b hadron production at hadron colliders is much higher-typically by a factor of 100 or more, depending on the collider energy and the acceptance in pseudo-rapidity. In addition, B: and b baryons are also produced. However, the fraction of events containing b hadrons is much lower (a few per mil) and only those events leaving a clean trigger signature are accessible. In the short term the most important B physics measurements that will be made at the hadron colliders are the B; oscillation frequency and CP asymmetries in B: decay.

3.1. Asymmetric e+e- B factories

The asymmetric B factories designed to study CP asymmetries in B decays collide low energy positiron beams (3.1-3.5 GeV) with higher energy electron beams (9.0-8.0 GeV) and give the center-of-mass of the collision a boost of By 1~ 0.5 along the beam axis. As a result the distance between the

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decay points of the two B mesons, whose lifetimes are N 1.6 ps, is typically 250 pm. This is critical in measuring CP asymmetries that arise in the interference between amplitudes for BOBo mixing and B decay, since the time integral of these CP asymmetries vanishes. The required luminosity is set by the scale of the branching fractions for Bo decay to experimentally accessible CP eigenstates and the need to determine the flavor of the other B in the event and the time difference between the two B decays. This leads to a requirement of 30 fb-'/year, or a luminosity of at least L = 3 x cm-2 s-'. The B factory detectors must provide good particle identification over the full momentum range, excellent vertex resolution, and good efficiency and resolution for charged tracks and photons.

Two B factories exceeding these minimum requirements have been operating since 1999: the Belle detector at the KEK-B accelerator at KEK and the BaBar detector at the PEP-I1 accelerator at SLAC. Both facilities have been operating well, providing unprecedented luminosities (as of February, 2003) :

KEK-B / Belle PEP-11 / BaBar L,,, ( ~ ~ ~ ~ c m - ~ s - ~ ) 8.3 4.8 best day (pb-l) 434 303 total (fb-l) 106 96

The BaBar and Belle detectors are broadly similar: each has a silicon vertex detector surrounded by a wire tracking chamber with a Helium- based gas, particle identification, a CsI(T1) calorimeter, a superconducting coil and detectors interspersed with the iron flux return to measure Kg and identify muons. They differ in their silicon detectors, where Belle uses 3 layers a t small radii (3.0-5.8 cm) while BaBar adds two layers at large radii (up to 12.7 and 14.6 cm); in each case the wire tracking device starts a few centimeters beyond the last silicon layer. The biggest difference is in the technology used for particle identification. While both detectors exploit dE/dx in the tracking chambers to identify low momentum hadrons, Belle uses a combination of time-of-flight and aerogel threshold Cherenkov counters. BaBar has a different strategy, using long quartz bars to generate Cherenkov light from passing particles and to transport it via total internal reflection to a water-filled torus where the Cherenkov angle is measured. The performance of each detector is similar in most respects.

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4. B hadron decay

The weak decay of a free b quark is completely analogous to muon decay. While there are no free quarks, this is a useful starting point for understanding B hadron decay. The B meson lifetime is relatively large (- 1.6 ps), much longer than the lighter D mesons or tau lepton, due to the smallness of IVcbl. Semileptonic decays are prominent, with branching fractions of about 10.5% each for semi-electronic and semi-muonic decays and about 2.5% for semi-tauonic decays. These decays contain a single hadronic current and are more tractable theoretically than fully hadronic final states, which make up the bulk of the B decay rate. Purely leptonic decays are helicity suppressed (less so for tau modes) and require either CKM-suppressed b += u transitions or Flavor-Changing Neutral-Currents (FCNC), forbidden at tree level in the SM, leading to branching fractions4 B(B+ += T+v,) - 6 x

The long B lifetime, along with the large top quark mass which breaks the GIM mechanism, give radiative “penguin” FCNC decays like b += sy and b += s@ branching fractions in the - range, making them accessible. These same factors result in large Bozo mixing through second order weak processes involving box diagrams with virtual W and top particles, and make rare B decays a fruitful ground for searching for physics beyond the SM.

B(Bo += T+T-) - 3 x lo-’.

4.1. Theoretical picture of B decay

The material in this subsection is covered in more detail in several excellent review article^.^ The free quark picture is a useful starting point, but the impact of the strong interactions binding the b quark in the B hadron must be addressed to achieve a quantitative understanding of B decay. Early attempts to do this involved models that gave the b quark an r.m.s. “Fermi momentum” to account for bound state effects. While these models improved the understanding of some observables, like the lepton energy spectrum in semileptonic decay, they did not provide a quantitative assessment of the theoretical uncertainties. Since the early 1990s new theoretical methods have been used based on a systematic separation of short-distance and long-distance scales through the Operator Product Expansion (OPE). The OPE formalism is used to develop effective field theories where the short distance behaviour is integrated out of the theory. A scale p is defined to separate the long- and short-distance regimes. The choice of p is in principle arbitrary, since no observables can depend on it if the calculation is carried

98

out t o all orders. In practice, p is chosen to satisfy AQCD << p << Mw. The result of integrating out the short-distance heavy particle fields is a non- local action that is then expanded in a series of local operators of increasing dimension whose (Wilson) coefficients contain the short-distance physics. Perturbative corrections (e.g. for hard gluon emission) to the short-distance physics are incorporated using renormalization-group methods.6 B decay amplitudes are expressed as

A(B + F ) = (Flffe~lB) = C cib)(FlQi(~)IB) (7) i

The Wilson coefficients Ci(p) typically include leading-log or next-to- leading-log corrections. The sum involves increasing powers of the heavy quark mass, required to offset the increasing dimensions of the non- perturbative operators. This suppression of higher-dimension operators is central to our ability to make quantitative predictions for B decays. At present only terms of order l /mi or l/mz are considered, leaving only a modest number of non-perturbative matrix elements to determine (either experimentally or through non-perturbative calculational techniques).

A major step forward in the understanding of B decays was the recognition of heavy quark symmetry. The scale AQCD - 0.2 GeV at which QCD becomes non-perturbative is small compared to the heavy quark mass mQ. As a result the gluons binding the heavy quark and light spectator are too soft to probe the quantum numbers-mass, spin, flavor-of the heavy quark. In the limit mQ + 00 the heavy quark degrees of freedom decouple completely from the light degrees of freedom, resulting in a spin-flavor SU(2lVh) symmetry, where Nh is the number of heavy quark flavorsb This symmetry has an analogue in atomic physics, where the nucleus acts as a static source of electric charge and where nuclear properties decouple from the degrees of freedom associated with the electrons; to first approximation different isotopes or nuclear spin states of an element have the same chemistry. In heavy-light systems, the heavy quark acts as a static source of color charge.

Heavy quark symmetry forms the basis of an effective field theory of QCD, namely Heavy Quark Effective Theory (HQET). The key observation is that in the heavy quark limit the velocities of the heavy quark and the hadron containing it are equal: PQ = mQv + l c , where PQ is the 4-vector of the heavy quark, w is the 4-velocity of the hadron and lc is the residual

bEffectively two, since the top quark decays before hadronizing.

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momentum, whose components are small compared to mQ. The degrees of freedom associated with energetic (O(2mQ)) fluctuations of the heavy quark field are integrated out, resulting in an effective Lagrangian

1 - s s - - Leg = h,iw. Dh, + -h,(ijZj,)2hu + -h,,olLYGp"hu + O(mQ2) (8)

2mQ 4mQ

where h,(s) = e imQu."YQ(z) is the upper 2 components of the heavy quark Dirac spinor, the lower components having been integrated out of the theory. The first term is all that remains in the limit mQ -+ 00, and is manifestly invariant under SU(2Nh). The second term is the kinetic energy operator OK for the residual motion of the heavy quark, and the third term gives the operator OG for the interaction of the heavy quark spin with the color-magnetic field. The matrix elements associated with these operators are non-perturbative, but can be related to measurable quantities.

The non-perturbative parameters at lowest order are A1 = ( & l o ~ l Q ) / 2 m ~ and A2 = - - ( Q I O G [ Q ) / ~ ~ Q . The mass of a heavy meson can be written

+ Q (mG2> (9) -A1 + 2 [ J ( J + 1) - 3 A2

mHQ = mQ +x+ 2mQ

The parameter x arises from the light quark degrees of freedom, and is defined by = limmQ (mHQ - mQ). In the heavy quark limit all systems with the same light quark degrees of freedom should have the same K. It can be verified that this gives a good description of SU(3)fl,,, breaking (m(B,)-m(Bd) 21 m(Ds) -m(Dd)). The mass splitting between the vector and pseudo-scalar mesons determines A2 to be approximately 0.12 GeV:

m2(B*) - m2(B) = 0.49 GeV2 = 4x2 + O(rn,')

m2(D*) - rn2(D) = 0.55 GeV2 = 4x2 + O(m;') (10)

(11)

4.2. Exclusive semileptonic decays and I Vet, 1 Heavy quark effective theory is clearly a powerful tool in understanding transitions between two heavy-light systems, since the light degrees of freedom don't see the change in heavy quark flavor or spin in the heavy quark limit. An area of great practical importance is the determination of IV,bl

from exclusive semileptonic decays like B + D*l+v. In the heavy quark limit the form factor for the decay can depend only on the product of 4- velocities of the initial and final mesons, w = wg . WD*. This universal form factor is known as the Isgur-Wise function7 [(w). The form of the function

100

is not specified in HQET, but its normalization is unity at the “zero-recoil” point, [(l) = 1, where the D* meson is stationary in the B meson rest frame and the light degrees of freedom are blind to the change in heavy quark properties.

One of the striking predictions of HQET is that the four independent form factors in a general P -+ V f i transition are all related to the Isgur- Wise function:

hv (W) = hAl (W) = h~~ (W) = [(W)

[(w) -+ 0 as rnQ -+ 00 I 2rnBrnD. (1 + w) (mB + rnD*)2

hA2 (w) =

where hv is the form factor for the vector current and hAl , hA2 and hA3 are the form factors associated with the axial-vector current. These relations can be tested experimentally.

The normalization of the physical form factor at zero recoil differs from unity due to QCD radiative corrections and heavy quark symmetry- breaking corrections. This leads to

where QA incorporates the QCD correction’ and the absence of a correction at order A Q C D / ~ Q is known as Luke’s t h e ~ r e m . ~ The value F(1) must be calculated using non-perturbative techniques such as Lattice QCD or QCD sum rules. These lead to the currently accepted value” of 0.91 f 0.04. This rather precise prediction can be combined with an experimental measurement of the decay rate for B + D*C+v to determine IVCbl2. The measurement is complicated by the need to extrapolate the differential decay rate dI’/dw to the point w = 1, since dr‘ldw vanishes there. A further complication comes from the fact that the transition pion from the D* -+ D decay has very low momentum in the B frame for w N 1. Nevertheless, the measured experimental rates give F(1)lVcbl = (38.3 f 1.0) x loM3 from which a precise value of lvcbl is obtained:’

lvcbl = (42.1 f 1.1 f 1.9) x (14)

Similar measurements can be made for B -+ nC+v. The theoretical situation here is less favorable, since Luke’s theorem does not prevent AQcD/mQ corrections in this case, and the experimental situation is complicated by feed-down from B -+ fj*C+v decays. The ratio of form factors

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at zero recoil can be measured and compared with predictions:

- W ) = 1.08 f 0.06 (theory) W )

= 1.08 f 0.09 (experiment)

where G(w) is the form factor in B + Dt?v decay. The tests of the HQET predictions for form factors in semileptonic B decays to charm are nearly at the point of testing the symmetry breaking terms, and are improving.

4.3. Inclusive sernileptonic decays

The OPE and HQET formalism can be used to study inclusive semileptonic decays. Bound state effects can be accounted for in a systematic expansion in terms of as and l lma. To do this, however, one must introduce a new assumption, namely that the (long distance) process of forming color singlet final state hadrons does not change the rates calculated at the quark level. This assumption goes under the name of quark-hadron duality. While it has been demonstrated to hold under certain conditions - e.g. in the cross- section for e+e- -+hadrons and in tau decays to hadrons - it also clearly breaks down in regions where the density of color-singlet final states is small or zero, e.g. for mhad < 2m,. While duality violations in inclusive rates are expected to be small, their level is hard to quantify, and they can be important when a severely restricted phase space is examined (e.g. when selecting b + u& decays by requiring that the charged lepton momentum exceeds the kinematic endpoint for leptons from b + c@ decays).

The semileptonic decay rate in the Heavy Quark Expansion (HQE) is

+ ...I (15) G$mg -xi - 9x2 r(B + = - [1+ cl* + ... + 1 9 2 ~ ~ lr 2mz

where the non-perturbative matrix elements A1 and A2 are familiar from HQET. Note the absence of a limb correction term; this allows the term in brackets to be computed to a precision of about 5%. The dependence on mi can result in large uncertainties in the theoretical prediction. These have been brought under control by using the upsilon expansion," in which (ignoring the subtleties) one-half the mass of the T(1S) is substituted for mb. The resulting theoretical expression for extracting lV&,l from the corresponding inclusive semileptonic decay width id2

(16) r(B -+ xu&) J 1.Ons-l IvUal = (3.87 f 0.10 f 0.10) x 10-~ x

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A similar expression relates iT/cbl to I'(B + Xc&):

(17) r(B + x&)

65.6ns-' lVcbl = (44.5 f 0.8 f 0.7 f 0.5) x x

Measuring the semileptonic width for b + dv transitions is straightforward; up to small corrections one just measures the semileptonic branching fractions and lifetimes of B mesons and sets rsl = &/TB. The momentum spectrum of leptons from B decay is fairly stiff, while leptons from other processes (most notably b --+ c + C decays) are softer. The formula given above can then be used to extract lVcbl with small theoretical uncertainty. Proceeding in this manner with the present experimental information' on .(€lo) = 1542 f 16 fs, T(B+) = 1674 f 18 fs and B(B + Xc&) = (10.38 f 0.32)% gives'

lVcbl = (40.4 f 0.5,,, f 0.5non--pert f 0.8,,,t) x lop3 (18)

This determination is fully consistent with the value derived from exclusive semileptonic decays.

The determination of IVub I from inclusive semileptonic decays is more challenging due to the large background from the CKM-favored b + c transitions. The first measurements of IVubl came from the endpoint of the lepton momentum spectrum, where a small fraction (- 10%) of the leptons from b + u transitions lie above the endpoint for leptons from b --+ c transitions. The experimental signal in this region is very robust, but the limited acceptance results in large theoretical uncertainties in extracting IVubl. These uncertainties arise because of limited knowledge of the so- called shape function, i.e. the distribution of the (virtual) b quark mass in the B meson, which affects the kinematic distributions of the final state particles and therefore changes the fraction fu of b + u decays above the minimum accepted lepton momentum.

One means of reducing the theoretical uncertainty is to obtain information on the shape function from other B decays. The easiest method conceptually is to examine the photon energy spectrum in the B rest frame for b + sy decays.13 Since the photon does not undergo strong interac- tactions it probes the b quark properties, with mb = 2E, at lowest order. The first moment of this spectrum is essentially the mean b quark mass (or, equivalently, x) while the second moment is essentially -XI. Simi- lar use can be made14 of the recoiling W in semileptonic b + u decays, where mb = Ew + [&I, but requires the reconstruction of the neutrino momentum. Measurements of other moments in semileptonic decays of

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both b -+ u and b -+ c (e.g. of El, mt ad...) also give information on the non-perturbative parameters Ti; and XI and can be used to constrain the range of variation that must be considered in assessing the theoretical error due to the acceptance cuts.

Another approach to reducing the theoretical uncertainty in IV,bl from inclusive semileptonic decays is to measure more than just the charged lepton. Setting aside the experimental difficulties, a measurement of the mass of the recoiling hadron allows a much greater fraction of the b -+ u final states to be accepted, namely those with invariant mass mhad < mD, thereby reducing theoretical uncertainties.15 Measuring the invariant mass of the lepton and neutrino (q2) and requiring q2 > (mB - mD)2, while having a lower acceptance than a cut on mhad, results in a similar theoretical uncertainty.14 Both of these approaches are in progress at the B factories. These approaches should yield IV,bl with uncertainties of 10% or less in the near future.

Exclusive charmless semileptonic decays ( B -+ T ~ + Y , etc.) provide an independent means of determining I V,b I. The experimental measurements of these decays are improving. At present the leading uncertainties come from theoretical calculations and models of form factors. There is an expectation that lattice QCD calculations of these form factors will eventually allow IV,b/ to be extracted with uncertainties of less than lo%, providing an independent test of the IV,b I determined from inclusive semileptonic decays.

5. B O B O oscillations

The material developed in the next two sections is covered in greater depth in several excellent Quark flavor is not conserved in weak interactions. As a result, transitions are possible between neutral mesons and their antiparticles. These transitions result in the decay eigenstates of the particle-anti-particle system being distinct from their mass eigenstates. In systems where the weak decay of the mesons is suppressed (e.g. by small CKM elements) and the A(flavor)= 2 transitions between particle and antiparticle are enhanced (due to the large top mass and favorable CKM elements) the decay eigenstates can be dramatically different from the mass eigenstates, resulting in the spectacular phenomenon of flavor oscillations. The flavor oscillations first observed in the neutral K system result in the striking lifetime difference between the two decay eigenstates and the phenomenon of regeneration. In neutral B mesons, the lifetime differences are

.reviews.

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small as is the branching fraction to eigenstates of CP. As a result, oscillations are observed by studying the time evolution of the flavor composition (b or b) of weak decays to flavor eigenstates.

The neutral B mesons form a 2-state system, with the flavor eigenstates denoted by

P O ) = (;) Po) = (;) The effective Hamiltonian, which includes the 2nd-order weak Ab = 2 transition, is diagonalized in the mass eigenbasis, obtained by solving

HIBH,L) = EH,LIBH.L) (20)

where the subscript H and L denote the “heavy” and “light” eigenstates and the effective Hamiltonian can be written as

Mi1 Mi2

where in the last line CPT symmetry is used to write M = M11 = M22

and = Fll = r22 . The values of M and r are determined by the quark masses and the strong and electromagnetic interactions. The last term induces Ab = 2 transitions and is responsible for flavor oscillations. The dispersive (Mlz) and absorptive (r12) parts correspond to virtual and real intermediate states, respectively. The time evolution of a state that is a pure Bo at t = 0 is given by

where (ignoring CP violation for the moment) lpI2 + 1qI2 = 1, M = ~ ( M H +

In the B system we always have A r << I?, since the branching fraction to flavor-neutral intermediate states (with quark content czdz or uTid2) is O(l%), and only these can contribute to Ar. The formula above simplifies in this approximation. No such constraint applies to Am/I’, since virtual intermediate states contribute. In fact, the large top quark mass breaks

ML), I‘ = $ ( r H + r L ) , Am = $(MH - ML), and A r = i ( r H - F L ) .

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the GIM mechanism that would otherwise cancel this FCNC and enhances Am.

The dominant diagrams responsible for Bozo oscillations in the SM are W-C box diagrams. While the short-distance physics in these diagrams can be calculated perturbatively, there are also non-perturbative matrix elements that enter the width. The standard OPE expression for Am i d6

where QB is a perturbative QCD correction, fB is the B meson decay constant, BE is the “bag factor”, and q can be either d or s. The term So is a known function of m?/M& that has a value of N 2.5 for the measured masses. The uncertainty in f i h B produces a - 30% uncertainty in extracting l&dl or l&,l by comparing Am, with measured values.

Many methods have been used to study Bozo oscillations. The most sensitive is the dilepton charge asymmetry17 as a function of the Bo decay time (or, in the case of the B factories, the decay time difference between the two B mesons). The current world average’ for the oscillation frequency is Amd = (0.489 f 0.008) ps-l. Improvements in calculations of f i B B are needed in order to improve the impact this measurement has on constraining the unitarity triangle.

Bf oscillations cannot be studied in T(4S) decays. The Oth-order expectation for Am, is Am, = I&s/&d12Amd N 15 ps-l, but the numerical value is not very precise due to uncertainties in the CKM elements. The large value of Am, implies very rapid oscillations and makes the measurement of Am, challenging. Note that evidence exists for Bf flavor change;” it is consistent with being maximal. However, at present there are only lower limits1 on Am, from experiments at LEP and from CDF. Similar uncertainties in f i B B arise when comparing the theoretical and measured values of Am, as for Amd. However, the theoretical uncertainty on the ratio Amd/Am, is smaller, as some of the uncertainties in the ratio (f& hBd)/( f & h B d ) cancel; this is an active area of theoretical investigation.21 A measurement of Am, will provide significant information in constraining the unitarity triangle.

6. CP violation

The CP operation takes particle into anti-particle, admitting an arbitrary (and unobservable) phase change:

CPIX) = e+2ecpIX); C P I ~ ) = e - 2 e ~ ~ ~ ~ ) (24)

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CP violation was discovered22 in KE decays to mr final states in 1964. At the time there was no known mechanism that could accommodate this observation. Such a mechanism was introduced by Kobayashi and M a s k a ~in 1973. They postulated the existence of a third generation of quarks, noting that the 3 x 3 unitary matrix describing the mixing of quark weak and mass eigenstates retains one phase that cannot be removed by rephasing the quark fields. The presence of this phase allows for CP to be violated in reactions involving two or more interfering amplitudes. The first particle of the third generation was discovered the very next year24 and the first quark of the third generation25 three years thereafter. The mechanism uncovered by Kobayashi and Maskawa in fact requires CP violation in the absence of special values of the non-trivial phase or other fine-tuning conditions, like quark mass degeneracies or the vanishing of a CKM angle.

CP violation has been observed more recently in the B ~ y ~ t eand appears to conform to the expectations of the KM picture. It remains to be determined, however, if the KM mechanism is the sole source of the CP violation seen in the K and B systems.

An invariant measure of the size of the CP violation in the CKM matrix is given by the Jarlskog invariant29

where C i j and sij are shorthand for the cosine and sine of the angle B i j , and A, X and q are the parameters of the Wolfenstein parameterization. The maximum value of J in any unitary 3 x 3 matrix is ( 6 a ) - l - 0.1; the value in the CKM matrix is - 4 x which underlies the statement that CP violation in the SM is small.

6.1. CP violation in B decay

The CP violation in the SM is the result of a phase, and is therefore only observable in processes involving interfering amplitudes. The mechanisms for generating this interference in B decays fall into three classes: CP violation in flavor mixing, CP violation in interfering decay amplitudes, and CP violation in the interference between flavor mixing and decay.

The CP violation first observed in the neutral K system arises in flavor mixing. The mass eigenstates in the K system are not quite eigenstates of CP, and can be described as having a small component with the opposite CP. This type of CP violation arises because of the interference between the on-shell and off-shell As = 2 transitions between KO and Eo. In the B

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system the smallness of Ar/r (i.e. the on-shell transition width) suppresses this source of CP violation (in contrast to the neutral K system, where ArK N - 2 A m ~ ) .

CP will be violated in BOBo mixing only to the extent that (q/pI # 1 (see eq. 22):

A manifestation of this CP violation would be an asymmetry in the semileptonic decays,

r(Bo -+ e + ~ x ) - r(Bo -+ e-vx) r(E0 -+ ~ + v x ) + r(BO -+ e-nx) ACP =

which is proportional to (1 - 1q/pI4)/(1 + lq/pI4) = S(r12/M12). In the SM this asymmetry is c?(10-4) and cannot be calculated with precision due to large hadronic uncertainties in the determination of r12.

Interference between competing decay amplitudes can also render CP violation observable in the SM. This is known as direct CP violation, and was first as a non-zero value of E' f E in neutral K decays. In direct CP violation lX~/Af l # 1, implying the decay rate for B -+ 7 is not the same as for B -+ f . All unstable particles (not just neutral mesons) admit this type of CP violation in principle. The decay rate asymmetry is

where A1 and A2 are competing decay amplitudes that lead to the same final state f , 6 is the difference between the strong interaction phases of the two amplitudes, and q5 is the difference between the weak phases (which include the CKM contribution). Once again, precise predictions of this type of CP violation are not available due to hadronic uncertainties in calculating the strong phase difference 6. It remains of interest, however, to search for decay modes where the weak phase difference q5 N 0, in which case any ACP which deviates significantly from zero is a sign of new physics.

The CP violation that arises due to the interference between Bozmixing and decay is different, in that theoretical predictions nearly free from strong interaction uncertainties are possible. The interference arises between the decay Bo -+ fcp and the sequence Bo -+ Bo -+ fcp. Clearly only those final states that are eigenstates of CP can contribute. This type of CP violation can be present even when (q/pI = 1 and X~,, /AfCP = 1.

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The quantity

- Q A7cp

XfCP = VfcP-- P AfCP

where Vfcp = fl is the CP eigenvalue, is independent of phase conventions and contains the information on CP violation. Since the interference is mediated by mixing, the CP asymmetry has a characteristic time dependence:

The coefficient of the cos A m s t term is a measure of direct CP violation (or CP violation in mixing, but this is always small in the B system). For decay modes dominated by a single decay amplitude it vanishes. The coefficient of the sin AmBt term is then a pure phase. This phase can be related to angles in the unitarity triangle with very little theoretical uncertainty. This is why the study of CP violation in neutral B decays has attracted so much attention. It's worth seeing how this comes about.

The ratio q/p is given by ,/- (ignoring the small contribution of I'12), where cx y$Vtdei(?r-28cp), so q/p = e2i(eCP+8M) is a pure phase. OM is the phase difference coming from CKM elements and Bcp is the arbitrary phase change in the CP transformation. The decay amplitudes are

giving zi,,p/AfCp = qCpe-2i(8CP+8D), where 80 is the weak phase associated with the decay. Note that the dependence on the strong phase 6 cancels in the ratio of decay amplitudes. Putting this together, Xfcp = qcpe2i(8M-8D). This clean relation holds for Bo decays to CP eigenstates that proceed via a single decay amplitude. Channels involving interfering decay amplitudes in general result in a mix of direct CP violation and CP violation in the interefence of mixing and decay, and in these cases the correspondence with unitarity triangle angles is not free from hadronic uncertainties.

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6.2. Measuring Unitarity Angles with CP Asymmetries

6.2.1. sin2,B

The “golden mode” for studying CP violation in B decays is Bo J/$Kg. In this case the decay is dominated by the tree diagram with internal W + CS emission, leading to (Ed) + EW+d + ( ~ c ) ( s d ) . This is not a flavor- neutral state at the quark level, but becomes so at the hadron level through KO mixing. For this decay one finds

(33)

Wf,,) = VCP sin 2,B (34)

with very little theoretical uncertainty. The CP eigenvalue is -1 (for Bo + J/$Xi it is +1). This decay mode is also favorable experimentally. The product branching fraction B(Bo + J/$Kg)B(J/$ + C+C-) N 5 x lov5 is well within the reach of B factories, and the final state includes a lepton pair, enabling excellent background suppression.

The experimental determination of sin 2,B involves three key elements:

0 The reconstruction of the CP eigenstate, J/$Kg. This requires good momentum and energy resolution for charged particles and photons.

0 The determination of the b quark flavor of the recoiling B meson at the time of its decay. This requires good particle identification in order to cleanly identify the charged kaons and leptons that are used to infer the b quark flavor.

0 The determination of the difference between the decay times of the B decay to the CP eigenstate and the recoiling B. This requires an asymmetric collider to boost the pair of B mesons along the beam direction and excellent vertex resolution to extract the spatial distance between the decay points of the two B mesons.

The B factories have been optimized to make this measurement. Given a sample of B decays to CP eigenstates, a determination of the flavor of the recoiling B, and the time difference between the decays, one can form the CP asymmetry

N(B0) - N(B0) = N(B0) + N(B0)

N (1 - 2w) sin28 sin AmBAt . (35)

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The asymmetry is based on the flavor assignment (Bo or Bo) of the recoiling B, w is the probability of incorrectly determinating the flavor of the recoiling B, and At is the time difference between the two B decays. One must determine the dilution (1 - 2w) in order to extract sin 2p. Since the underlying asymmetry is an oscillatory function, its amplitude is also diminished by the imperfect resolution on the decay time difference. Both of these effects (flavor mis-tagging and At resolution) can be controlled by considering a related asymmetry formed using fully reconstructed Bo decays to flavor eigenstates (like Bo + l l*-~+) in place of the CP eigenstate sample:

N(mixed) - N(unmixed) N(mixed) + N(unmixed) Amixing(At) =

21 (1 - 2w) cos A r n ~ A t (36)

The flavor eigenstate sample has much higher statistics than the CP eigenstate sample, ensuring precise determinations of w and the At resolution. In practice the dilution factor at the B factories is (1 - 2w) N 0.25.

The BaBar and Belle experiments first observed non-zero CP violation26 in 2001 and have now measured sin 2p (sin 41) with good p r e c i s i ~ n .

sin 2p = 0.719 f 0.074 f 0.035 (Belle) (37) sin 2p = 0.741 f 0.067 f 0.034 (BaBar) (38)

The systematic errors are dominated by the statistics of the auxiliary samples used to evaluate them, and should continue to fall with increasing luminosity. Figure 2 shows the CP asymmetry observed in BaBar for both the Jft+!IK; and J/t+!IK; modes. The K i mode is reconstructed by using the position of the KE interaction in the calorimeter or muon system and the known B energy to estimate the K i 4-vector and form the invariant mass of the J/t+!IK: pair. While the background is higher than for the Jft+!IKg sample, it's satisfying to see a CP asymmetry of the opposite sign!

plane (see Figure 1). The measurements of sin2P now give precise constraints in the ij -

6.2.2. sin2a

There is substantial effort at present on determination of the angle a (42). This angle is accessible in b -+ u transitions leading to uiidz final states, e.g. Bo T+x-. In contrast to the golden mode, however, there are both tree and penguin decay amplitudes that contribute appreciably to these

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-5 0

Figure 2. The distributions of At for events with recoiling B mesons tagged as Bo and Bo (a) and the CP asymmetry (b) for J/+Kg decays. The same distributions are shown in (c) and (d) for J/+KE decays. This figure is taken from Ref. [27].

-

decays, rendering the precise determination of a more difficult. The experimental situation is also less favorable for several reasons: the very small branching f r a c t i o n ~ ~ ~ y ~ ~ (B(Bo -+ 7r+7r-) N 5 x lop6); the higher backgrounds, primarily from the underlying e+e- -+ qij continuum events; and the difficulty in distinguishing Bo + 7r+7r- decays from the more numerous Bo -+ K+7r- decays. The amplitudes of the underlying penguin and tree diagrams can be ~ o n s t r a i n e d ~ ~ by measuring the branching fractions of the isospin-related channels Bo -+ 7r+7r-, Bo -+ 7r07ro and B+ -+ 7r+7ro. This is, however, challenging; at present35 only upper limits exist on B(Bo -+ 7rO.O).

Other approaches34 to limiting the uncertainty due to the penguin amplitudes have been proposed; this is an active area of investigation. In practice

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one measures the coefficients C,, and S,, of the cosine and sine terms' in eq. 30. The coefficienct of the sine term would be sin2a in the absence of penguin contributions.

The current measurements of these coefficients in BaBar and Belle differ by about 2.50, and lead to rather different interpretations on the evidence for direct CP violation in Bo -+ T+T-

S,, = +0.02 f 0.34 f 0.05 (BaBar) (39)

S,, = -1.23 f 0.41 ?:::: (Belle) (40) C,, = -0.30 f 0.25 f 0.05 (BaBar) (41)

-A,, = -0.77 f 0.27 f 0.08 (Belle) (42)

Note that the bound Sz, + C;, must be satisfied by the true values of these coefficients. The Belle data are shown in Figure 3.

6.3. CP Asymmetries in B: Decays

The B; system can also be used to study CP violation. However, B: production is suppressed relative to B: , implying smaller signals and higher backgrounds. The outlook for studying B; at threshold e+e- machines is not good. However, dedicated experiments at high energy hadron colliders are expected to contribute significantly in this area.

The presence of spectator s quark makes a different set of unitarity angles accessible in B: decays. The rapid oscillation term (AmB: - 3 0 A m p ) makes time resolved experiments difficult, but not impossible. The width difference between the B; mass eigenstates may be exploited as well.

7. Rare decays

Rare B decays offer a window on new physics. A particularly fruitful place to look for new physics is in FCNC decays, which are highly suppressed in the Standard Model. New physics can enhance these rates substantially; see Refs. [37] and [20] for overviews of this subject. The first b -+ s FCNC decays observed,38 namely b -+ sy, still provide the best limit on the mass of a charged Higgs boson. The penguin decays b -+ sy, b -+ sC+C- (C = e or p ) and b -+ SVP are areas of active investigation at the B factories. The

CThis is another unfortunate case of notational differences. BaBar and Belle use different conventions (related to the inclusion or not of the CP eigenvalue in the definition of the coefficients) resulting in CFgBar = -ABelle. 7777

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- g 60 r 40 m

v . Lo

E 20 9 w 0

g 60 2 40

- Ln

v . v)

E 20 9 Lu

0 40 30 .- ,=- 20

+E 10 0

c 5 1

D a -1

Q)

g o

- Total ,,, n+n- .... qti + Kn.

(b) q = -1

Figure 3. Distributions of Bo + T+T- events versus At for Bo tags (a) and go tags (b). The background-subtracted distributions and the asymmetry are shown in (c) and (d). This figure is taken from Ref. [36] .

CKM-suppressed modes, with s replaced by d, have not yet been observed; their measurement will allow clean determinations of the ratio I&12/I&s12.

The branching fraction for b -+ sy is now measured38 and predicted39 with good precision:

B(b + sy) = (3.3 f 0.4) x experiment (43) (44) = (3.29 f 0.33) x lop4 theory

The B factories have recently observed the first evidence for FCNC decays involving 2 penguin and W box diagrams. Belle has measured40 the inclusive decay B(b + sl+l-) = (6.lf1.4?:::)~10-~ and the combined BaBar41 and Belle42 measurements give B ( B -+ K l f l - ) = (7.6f 1.8) x These are compatible with SM expectation^.^' The sensitivity will improve with

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increasing luminosity and the forward-backward asymmetry of the lepton pairs will be measured, providing stringent constraints on new physics.

The related decay b + svV is also of interest. It is very clean theoretically, and is sensitive to all three generations. The SM rate is also higher than for b + sC+C- due to the larger couplings of neutrinos to the 2. The experimental signature, which includes at least two missing particles, makes searches for these modes also sensitive to exotic, non-interacting particles (e.g. the lightest supersymmetric particle). The best existing limit is on the mode B+ + K+vV, where BaBar has a preliminary result43 of B(B+ -+ K+vV) < 9.4 x at 90% c.1. The sensitivity of these searches is improving as data sets increase.

8. Summary

The B factory program has had a very fruitful beginning-and it is still the beginning. The next few years will bring significant advances in our knowledge of flavor physics.

CP asymmetries in B decays have been observed, are large and will be observed in many modes in the coming years. Precision studies of B decays and oscillations provide the most significant source of information on three of the four CKM parameters and are beginning to provide stringent tests of the Standard Model. The interplay of theory and experiment is vibrant and necessary in order to extract precision information on the matrix elements Ivubl and 1Vcbl and on the angles a and y of the unitarity triangle. Rare B decays offer a good window on new physics due to the large top quark mass, and the sensitivity to these decays is improving rapidly. B hadrons are also a laboratory for studying QCD at large and small scales, and a theoretical framework has been developed to make precise predictions and suggest new measurements to test the soundness of the framework.

The constraints of time have dictated an abbreviated treatment of a number of the topics covered here and have precluded the inclusion of others. The space devoted to the wealth of B physics measurements made a t non-B factory facilities has been minimal; I can only refer the interested reader to broader reviews of B physics, e.g. as given in Ref. [44].

The field of flavor physics is vibrant at the start of the 21St century. The B factories and neutrino experiments, in discovering CP violation in B decays and neutrino oscillations, have produced the most significant discoveries since the LEP/SLC program. These same two fields will probe deeper into the mysteries of flavor oscillations and CP violation throughout

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this decade. Flavor physics is becoming precision physics!

Acknowledgements

I’d like to thank the organizers of the Lake Louise Winter Institute for their kind invitation and hospitality.

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(1990).

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17. Early measurements of B: mixing are from H. Albrecht et al. (ARGUS), Phys. Lett. B 192 245 (1987); M. Artuso et al. (CLEO), Phys. Rev. Lett. 62 2233 (1989). Recent measurements of the B: oscillation frequency are in N.C. Hastings et al. (Belle), Phys. Rev. D 67:052004 (2003); B. Aubert al. (BaBar), Phys. Rev. Lett. 88:221803 (2002).

18. This is based on measurements of the average mixing parameter x at high energy colliders. See, e.g., the LEP results collected by the LEP Electroweak Working Group in Nucl. Instrum. Methods A 378 101 (1996).

19. Y. Nir, hep-ph/9911321; Y. Nir, Nucl. Phys. Proc. Suppl. 117 111-126 (2003).

20. A.J. Buras, hep-ph/0101336. 21. M. Ciuchini et al., hep-ph/0012308;

L. Lellouch and C.-J.D. Lin, hep-ph/0011086; J. Flynn and C.-J.D. Lin, hep-ph/0012154; C. Sachrajda, hep-lat/0101003.

22. J.H. Christensen et al., Phys. Rev. Lett. 13 138 (1964). 23. M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49 652 (1973). 24. M.L. Per1 et al., Phys. Rev. Lett. 35 1489 (1975). 25. J.W. Herb et al., Phys. Rev. Lett. 39 252 (1977). 26. B. Aubert et al. (BaBar) Phys. Rev. Lett. 87:091801 (2001);

K. Abe et al. (Belle) Phys. Rev. Lett. 87:091802 (2001). 27. B. Aubert et al. (BaBar) Phys. Rev. Lett. 89:201802 (2002). 28. K. Abe et al. (Belle) Phys. Rev. D 66:071102(R) (2002). 29. C. Jarlskog, et al. Phys. Rev. Lett. 55 1039 (1985); 2. Phys. C 29 491 (1985). 30. The first evidence for a non-zero value was from

G.D. Barr et al. (NA31) Phys. Lett. B 317 233 (1993); and was confirmed by A. Alavi-Harati et al. (KTEV) Phys. Rev. Lett. 83 22 (1999).

31. K. Abe et al. (Belle), Phys. Rev. Lett. 87:101801 (2001). 32. B. Aubert et al. (BaBar), Phys. Rev. Lett. 89:281802 (2002). 33. M. Gronau and D. London, Phys. Rev. Lett. 65 3381 (1990). 34. A. Snyder and H.R. Quinn, Phys. Rev. D 48 2139 (1993);

A.J. Buras and R. Fleisher, Phys. Lett. B 360 138 (1995); A.S. Dighe, M. Gronau and J. Rosner, Phys. Rev. D 54 3309 (1996); M. Beneke, G. Buchalla and I. Dunietz, Phys. Lett. B 393 132 (1997).

35. BaBar Collaboration, hep-ex/0303028, submitted to Phys. Rev. Lett. 36. Belle Collaboration, hep-ex/0301032, submitted to Phys. Rev. D. 37. For b + sy: G. DeGrassi, P. Gambino and G.F. Giudice, JHEP 0012:009

(2000); A.J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silverstrini, Nucl. Phys. B 592 55 (2000). For b + s@: A. Ali, P. Ball, L.T. Handoko and G. Hiller, Phys. Rev. D 61:074024 (2000); G. Buchalla, G. Hiller and G. Isidori, Phys. Rev. D 63:014015 (2001).

38. S. Chen et al. (CLEO), Phys. Rev. Lett. 87:251807 (2001); K. Abe et al. Phys. Lett. B 511 151 (2001);

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BaBar Collaboration, hep-ex/0207076. The values used in the text come from Ref. [l].

39. K. Chetyrkin, M. Misiak and M. M u m , Phys. Lett. B 400 206 (1997); erratum-ibid B 425 414 (1998); A.J. Buras, A. Kwiatkowski and N. Pott, Phys. Lett. B 414 157 (1997); erratum-ibid B 434 459 (1998); A.L. Kagan and M. Neubert, Ew. Phys. J. C 7 5 (1999). The values used in the text come from Ref. [l].

40. J. Kaneko et al. (Belle) Phys. Rev. Lett. 90:021801 (2003). 41. BaBar Collaboration, hep-ex/0207082. 42. K. Abe et al. (Belle) Phys. Rev. Lett. 88:021801 (2002). 43. BaBar Collaboration, hep-ex/0207069. 44. Proceedings of the Workshop on the CKM Unitarity Triangle,

http://ckm-uorkshop.ueb.cern.ch/ckm-workshop/ckm-uorkshops/Default2002.htm.

NUCLEAR ASTROPHYSICS AND NUCLEI FAR FROM STABILITY

H. SCHATZ Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, M I 48864, USA, E-mail:

schatzOnscl.msu. edu

Unstable nuclei play a critical role in a number of astrophysical scenarios and are important for our understanding of the origin of the elements. Among the most important scenarios are the r-process (Supernovae), Novae, and X-ray bursts. For these astrophysical events I review the open questions, recent developments in astronomy, and how nuclear physics, in particular experiments with radioactive beams, need to contribute to find the answers.

1. Introduction

Nuclear Astrophysics is a radpidly evolving field driven by technological advances. On one hand, a new generation of astronomical observatories produce a stream of discoveries and unprecedented quantitative data. Ex- amples include abundance observations in extremely metal poor stars by VLT, Keck, HST and others; the recent discovery of superbursts from accreting neutron stars with Beppo-SAX and RXTE; WMAP observations of the cosmic microwave background; and Chandra observations of neutron stars in X-ray binaries during the "off-state" when accretion from a companion shuts off. At the same time, advances in accelerator nuclear physics led to the construction of several radioactive beam facilities - such as the new Coupled Cyclotron Facility at Michigan State University or the ISAC facility in TRIUMF, Canada. With these facilities it is now possible to study the exotic nuclei that govern many of the astrophysical scenarios. Only with an understanding of the underlying nuclear physics we can interpret the astronomical data and hopefully come closer to answer some of the most important open questions of the field.

These open questions include the question of the origin of the heavy elements in nature. This question has recently been identified as one of the 11 most important open questions to be addressed in the context of astro

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particle physics by the Comittee for the Physics of the Universe '. It is mainly related to a lack of understanding of the rapid neutron capture process (r-process) which will be discussed in section 2. A second important question relates to the broad issue of the behaviour of matter under extreme density and temperature conditions. Here, astrophysical explosions such as Supernovae, Novae, and X-ray bursts provide unique laboratories. Observations of energy production and nucleosynthesis products can yield insights into regions of extreme conditions that are not accessible directly with conventional telescopes, provided the astronomical data and a complete understanding of the nuclear physics are at hand. The discussion of Novae in section 3 and of X-ray bursts in section 4 relates to this issue.

2. The r-process

The r-process is one of the major nucleosynthesis processes in the universe producing roughly half of all elements heavier than iron. The basic mechanism is a series of neutron captures on timescales of microseconds interspersed with ,!3 decays far from stability at neutron separations energies of a few MeV close to the neutron drip line. But where in the universe does this process occur ? Where in the universe can free neutron densities of several 100 g/cm3 be achieved and the syntheized nuclei be ejected into space ? Possible sites include (i) the neutrino-driven wind in core-collapse supernovae 2 , 3 7 4 , (ii) accretion onto and jets from a forming neutron star in core collapse supernovae 5 1 6 , and (iii) neutron star mergers 728. So far, all these scenarios have their merits and problems and the question of the site of the r process is still open.

Recently, observations of r-process elements in ultra metal poor (UMP) halo stars have shed new light on the operation of the r-process during the early history of our Galaxy and on the question of the r-process site (see Truran et al. for a recent review). These UMP halo stars formed very early in galactic history before large scale mixing of elements from various sources occurred. UMP halo stars with a strong enhancement in r-process elements therefore provide a unique glimpse of the r-process element abundance distribution produced in a single or very few r-process events. They essentially formed out of matter "polluted" by a nearby r-process events. Today these stars allow us to observe this ancient mix of elements. Abun- dances of up to 28 r-process elements ranging from strontium to uranium have now been determined in some UMP stars, with the most detailed composition information being avaliable for CS22892-052 lo. The quality

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of the observations in fact begins to rival that of the sun. Furthermore, the observation of long lived radioactive nuclei such as thorium and, more recently, uranium 1 1 t 1 2 in UMP halo stars provides important constraints on the r-process beyond lead. In addition these observations can be used to date the r-process by comparing the predicted r-process production of uranium and thorium to the ones observed today. Because UMP halo stars are among the oldest stars in the Galaxy, one also obtains lower limits for the age of the universe l3,l4?l5.

One of the important conclusions from these observations is the possibility of two distinct r-process components. The so-called strong component seems to produce mostly the heavier mass r-elements with A > 130. The abundance pattern produced by the strong component resembles the solar system abundance distribution of r-elements and shows no event to event variations. The weak component seems to be restricted to the production of several lighter r-nuclei with A < 130. The existence of a weak and a strong r-process has also been proposed based on meteoritic data pointing to different chemical evolution histories of the radioactive r-process isotopes "'I and 182Hf that were present at the time of solar system formation 16.

To address the complex open questions there is a need for more data. Most importantly one needs: (i) more observations of light r-process element abundances in metal poor stars, and (ii) much more information on the nuclear physics, in particular masses, ,B decay half-lives, neutron capture rates, fission rates and fission product distributions. For the forseeable future r-process calculations will have to rely to a large extent on theoretical predictions. Therefore, experiments are needed not only to provide direct input into r-process calculations, but also to unravel nuclear structure of neutron rich nuclei in general to allow reliable extrapolations beyond the reach of experiments.

The nuclei in the r-process path are extremely neutron rich and short lived. Fig. 1 shows, that to a large extent the r-process path lies beyond the region of nuclei for which experimental data are available. Exceptions are some nuclei around the N = 50 and N = 82 shell closures, mostly owing to pioneering experiments at ISOLDE (see Pfeiffer et al. 2001 l7 and Kratz et al. 2000 l8 for recent reviews). Recent examples include the spectroscopy of 135-137Sn l9 and measurements of decay properties of 1351n 2o and l3l>l3'Cd 'l. Other experiments with r-process nuclei include measurements in the Ti-Co region at GANIL using projectile fragmentation 22, and measurements on 135Sn at OSIRIS using fast neutron induced fission 23. Nevertheless, most nuclei in the weak r-process including particularly

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Figure 1. The classical r-process path marked with thick squares (from Schatz et al. 2002 13). Half filled and fully filled squares denote nuclides in the r-process path that are within reach for at least a half-life measurement at the new NSCL Coupled Cyclotron Facility and the proposed RIA facility, respectively. Shaded in grey are nuclides with experimentally known half-lives.

important isotopes such as the waiting point 78Ni and nuclei in the vicinity of the N = 82 shell closure for 2 < 47 have been out of reach so far. To address this problem we have begun to develop an experimental program at the new NSCL Coupled Cyclotron Facility at MSU focusing specifically on the weak r-process 24. Fig. 1 shows that most of the weak r-process path below Z x 5 0 is within reach at the NSCL. However, to reach heavier r-process nuclei which play a particularly important role for understanding of the synthesis of Uranium and Thorium, a next generation facility such as the Rare Isotope Accelerator (RIA) proposed in the US is needed.

3. Novae

Novae are thermonuclear explosions on the surface of a white dwarf accreting matter from a companion star in a close binary system 25,26,27. Once the white dwarf’s accreted surface layer reaches a critical density and temperature, nuclear reactions trigger a thermonuclear runaway. The explosive burning of hydrogen during the thermonuclear runaway and the decay of

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freshly synthesized radioactive nuclei provide the energy that leads to the observed dramatic brightening of the star and to the ejection of the accreted layer into space. Observation of the ejecta composition clearly show a significant enrichment in white dwarf matter (CO or ONeMg) mixed with freshly synthesized nuclei that can be as heavy as calcium.

Nova model calculations have been performed since the early 1970's and have been quite successful in predicting most observables. However, today two major problems remain unsolved and might indicate severe deficiencies in our understanding of novae. The first problem is the question of how and when white dwarf material is mixed into the accreted layer 2 8 7 2 9 . The second problem has been coined the "missing mass problem" 27 denoting that nova models notoriously underpredict the total mass of the ejecta by typically a factor of 10 compared to observations. Another open question is the contribution of Novae to galactic nucleosynthesis. It seems likely that Novae are the source of at least a significant fraction of 13C, 15N, and 1 7 0

found in the solar system 26. However, whether Novae contribute to the observed galactic y-ray emitter 26A1 is less clear 30731.

By comparing observed elemental abundances with calculations, constraints for the white dwarf mass and for the thickness of the accreted layer can be obtained if the nuclear processes are well understood. Even more stringent constraints could be derived from the detection of the decay y- rays from radioactive isotopes like 22Na or 7Be (See Hernanz et al. 1999 32 for a recent discussion). So far only upper limits on the y-ray flux from nearby nova ejecta have been obtained, but it is expected that y-rays will be detected with new generation y-ray observatories like the recently launched INTEGRAL.

The importance of most reaction rates in Nova is derived from qualitative arguments, but several sensitivity studies provide now a more quantitative asessment of the dependence of nucleosynthesis on present reaction rate uncertainties. These studies include an analysis of the uncertainties in the production of the y-ray emitters "Na (34), 26A1 (34), and 7Be (32), as well as the production of heavy elements such as sulfur 35. More recently a comprehensive analysis of the impact of all reaction rate uncertainties has been performed 37. These sensitivity studies are extremely important in providing guidance for future experimental work. However, they do not necessarily provide a final answer to the question of importance of a particular experiment. First of all it is difficult to estimate reaction rate uncertainties reliably, and surprises are always possible. Furthermore, sensitivity studies strongly depend on the astrophysical model and the chosen

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Figure 2. The solid lines indicate the sequence of the most important reactions during a nova explosion in the 1.35Mo nova model from 33. Thick lines mark important reactions on radioactive nuclei. If the thick line is dashed the reaction rate is important even though the dominant reaction flow does not pass through that reaction for this particular nova model and with the reaction rate used. The dashed nuclei are candidates for observable short lived y-ray emitters.

model parameters. In the end, reliable calculations need to be based on experimental data.

A particularly important question is whether there is a breakout of the hot CNO cycles during a Nova explosion via the 150(a,y) reaction (see 36 for a recent review on CNO cyles and breakout). Current Nova models and reaction rate estimates seem to indicate that nova peak temperatures are not sufficient for significant breakout. This conclusion is now on firm ground with recent experimental data providing an upper limit for the 150(a,y) rate 38. However, temperatures and densities during nova explosions can be very close to breakout conditions. Furthermore, a possible signature of breakout has been observed in Nova V838 Her 1991 39. The ejecta of this nova show a strong depletion in oxygen as well as enrichment in heavier elements such as sulfur. However, the non observation of breakout in most novae and the possible observation of breakout in Nova V838 need to be translated into limits on temperature and density and on system parameters such as mass of the accreted layer, accretion rate etc. This requires an accurate 150(a,y) reaction rate, not just a limit. Therefore, a measurement of this reaction rate, for example with a radioactive 150

beam would still be important.

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Clearly reactions on radioactive nuclei play an important role in novae. For these reactions radioactive beam experiments offer the unique opportunity to measure rates directly in inverse kinematics at the relevant low energies of the order of 0.1-1 MeV/u. For most of the important reaction rates below Na (with the exception of 150(a,7)) first attempts of direct measurements with radioactive beams have been made in pioneering experiments, mainly at Louvain-la-Neuve 41 ,42y43 ,44 and ANL 4 5 7 4 6 . More recently, the new ISAC facility reported the first direct measurement of the 21Na(p,y) reaction rate 47. However, much work remains to be done, and still higher beam intensities, for example at the planned RIA facility in the US, are needed to perform the important measurements. For the forseeable future, direct low energy measurements of reaction rates will have to be complemented with more sensitive indirect techniques like proton scattering 48, transfer reactions 49, and Coulomb breakup 50 . A complementary approach with stable beam and radioactive beam experiments with various techniques is necessary.

4. Type I X-ray bursts

X-ray bursts are, like Novae, thermonuclear flashes on the surface of a compact stellar object accreting matter from a companion star - with the main difference that the compact object is a neutron star, not a white dwarf (for a recent review see Strohmayer and Bildsten 2003 51). Because of the much stronger surface gravity of neutron stars, X-ray bursts are very different compared to Novae. Temperatures are much higher, shifting the luminosity into the X-ray band. Ignition conditions are reached much quicker reducing burst recurrence times to just hours or days. Most of the burned material is not ejected into space, but remains on the surface of the neutron star forming a layer of ashes that over time replaces the original crust of the neutron star. X-ray burst are a frequent phenomenon - there are about 50 Galactic sources known, many of them bursting at least once a day.

There are many open questions concerning X-ray bursts. To find the answers, the observations have to be interpreted with a thorough understanding of the underlying physics of the X-ray burst phenomenon, in particular the nuclear physics that directly powers the burst. One of the open issues is the source of the variation in burst timescales observed from X-ray bursters. Some bursts last only about 10 s. This can be easily understood from the timescale of radiation transport from the burning layer t o the pho-

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tosphere, which is about 10 s. However, many bursts last longer, mostly up to minutes. More recently, a new class of bursts has been discovered, the so called superbursts. Superbursts last up to 1000 times longer than ordinary X-ray bursts, they are about a factor of 1000 more energetic and their recurrence time is estimated to be of the order of years. So far, 7 superbursts have been discovered in 6 sources that otherwise show regular X-ray bursting behavior (see 52 for a summary). As we will see in the following discussion, nuclear physics plays an important role in explaining prolonged X-ray bursts.

4.1. Normal X-ray bursts

Normal type I X-ray bursts are powered either by pure helium burning or by mixed hydrogen and helium burning. The latter occurs for systems accreting from a companion star with a hydrogen rich envelope at a rate that is sufficiently high to ignite helium before all hydrogen is burned by the CNO cycle during the accretion phase. In this case, the X-ray burst ignites at densities of about lo6 g/cm3. The temperature sensitivity of the 3~ reaction triggers a thermonuclear runaway. Energy generation is greatly accelerated by breakout of the CNO cycles into the rapid proton capture process (rp process) 53 - a sequence of (qp) , (p,y) and p+ reactions.

Fig. 3 shows the full sequence of nuclear reactions powering type I x- ray bursts calculated with a one zone model coupled selfconsistently to a complete reaction network 5 5 . The endpoint of the rp process depends on the amount of hydrogen available at burst ignition, which in turn varies with the parameters of the system such as accretion rate, heat flux from the neutron star surface and composition of the accreted material. However, it has recently been pointed out that the rp process cannot proceed past a SnSbTe cycle, which forms as a consequence of the very low Q binding energies of the proton rich Te isotopes. This cycle is reached in bursts with a initial hydrogen abundance that is close to solar, and an example is shown in Fig. 3. The SnSbTe cycle prevents the synthesis of nuclei more massive than A x 106 in the rp process. This limitation could only be overcome in a multiburst rp-process where the freshly synthesized nuclei decay back to stability and are then again bombarded with protons in a second burst (the rp2 process 56).

The critical nuclear physics data for rp-process calculations are nuclear masses, p decay rates, and the rates of (p,y) and (a,p) reactions. In particular it is the interplay of masses and p decays that sets to a large extent

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Figure 3. Reaction flow time integrated over a complete x-ray burst. The inset shows the SnSbTe cycle in detail.

the path and timescale of the rp process. Over the last years radioactive beam experiments at a large number of different facilities have provided a wealth of new data on the location of the proton drip line between Ni and Te. These include experiments at LBL 57 , GANIL 58759y60, GSI 61762,63764,

ISOLDE 65166, MSU/NSCL 67968769, and ORNL 70. These experiments focused on the determination of the transition from p t o proton decay as one moves away from stability, either by measuring ,B decay rates or by obtaining lifetime limits from the nonobservation of isotopes with known production rates. Proton emitters have in most cases been identified on the basis of such lifetime limits - with the exception of lo5Sb 5 7 7 6 2 no di-

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rect proton emission has been observed in this element range. In addition these experiments provided data on the majority of p decay half-lives in the rp process, with the exception of 74Sr, 8 7 R ~ , 95996Cd. However, a major remaining uncertainty in rp process calculations is the lack of sufficiently precise proton separation energies (accuracy M kT = 80 keV needed) along the proton drip line between Ni and Te. Especially, the unknown proton separation energies of 6 5 A ~ , 66Se, 69Br, 70Kr, 73Rb, and 74Sr introduce large uncertainties in predicted burst time scales, energy generation and final composition 72. Recently a number of advanced techniques have been used to measure masses of exotic nuclei in the path of the rp process. These include time-of-flight measurements at the ESR storage ring at GSI 73 in the Ti-Mn region and ion trap experiments at ISOLTRAP 74. At the same time, new mass predictions based on Coulomb shift calculations can now provide quite reliable data for masses beyond the N = 2 line, provided the mass of the mirror nucleus is experimentally known 72.

In addition, proton capture rates and the breakout reactions of the CNO cycles - 1 5 0 ( ~ , y ) and 18Ne(a,p) - are important in rp process calculations. Experimental progress in that respect has focused on lighter nuclei up to Na as discussed in the Nova section. For heavier nuclei, progress has been made with a new generation of reaction rates calculated with a large scale shell model 75 .

A group of nuclei that play an important role in the rp process are the so called waiting point nuclei. These nuclei have particularly long lifetimes under rp-process conditions owing to long B decay half-lives and low proton capture Q-values. The reaction flow beyond Ni has to pass through exceptionally long lived waiting points such as 64Ge, 68Se and 72Kr, which prolongs the energy generation leading to long tails that can nicely explain the longer burst timescales of the order of a minute. In this picture, long bursts signal the presence of large amounts of hydrogen at ignition. Shorter burst occur for lower accretion rates when significant hydrogen burning occurs prior to burst ignition, or in systems that accrete from a hydrogen poor companion star. However, these conclusions rely on assumptions on the nuclear physics that need to be verifyed experimentally. At the same time, full multi zone X-ray burst calculations with complete reaction networks up to Sb are necessary to confirm the results and to provide accurate lightcurve predictions. First results from such a calculation have been published after this article was written. 76

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4.2. Superbursts

The rp process can explain type I bursts of up to several minutes duration within the current uncertainties of the nuclear physics. However, recently discovered superbursts can last about a factor of 1000 longer and release about a factor of 1000 more energy. Superbursts therefore clearly require a different fuel.

Recently, Cumming and Bildsten 77 proposed that the rp process ashes - a mix of carbon and heavier nuclei in the A = 64 - 106 mass range - could serve as such a fuel if the amount of carbon is sufficient to ignite. Indeed, recent network calculations with a full rp process indicate that X- ray bursts burn hydrogen completely. As a consequence the ashes contains carbon from the late time fusion of helium once hydrogen is exhausted (because of the slow 3a reaction helium burns slower than hydrogen, especially at low helium abundance). Later, Schatz et al. (2003) 78 showed that not just the carbon, but also the elements beyond nickel serve as fuel. After an initial carbon flash rises the temperature above 1-2 GK, (-y,n) photodisintegration of the somewhat neutron rich heavy nuclei (Ye = 0.43) followed by recapture of the neutrons by abundant intermediate mass nuclei (A M 64) triggers a rapid photodisintegration runaway. Peak temperatures of 7 GK are reached. During the flash carbon fuses into iron-nickel elements. At the same time, heavy elements are quickly destroyed by (r,n), (y,p), and (-y,a) reactions. The free nucleons and a particles quickly reassemble and the composition is driven into nuclear statistical equilibrium favouring mainly 64Ni and 66Ni because of the high densities. The net effect is the conversion of both, carbon and the heavy elements into nickel. Of course both generates energy as the binding energy per nucleon has its maximum around 62Ni. As a result, more than half of the superburst energy comes from the destruction of heavy nuclei. As the greater ignition depth leads to much longer burst timescales, this model can nicely explain energetics, duration, and recurrence times of superbursts (see 79 for a more popular description).

Of special importance in this scenario is the initial composition of the superburst fuel. This in turn depends sensitively on the properties of the extremely proton rich nuclei in the rp process. First of all, the amount of heavy elements and carbon in the ashes directly enters the calculations as the amount of available fuel. Furthermore, the heavy elements play an important role in increasing the electron scattering opacity and therefore decreasing the ignition depth. Finally, the conditions needed for the ignition of the photodisintegration runaway are very sensitive to the detailed

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composition of the rp process ashes. A critical role play isobar chains, where a given electron capture threshold is reached at low neutron separation energy. Then, energetic, degenerate electrons in the neutron star crust can drive the nuclei in such an isobaric chain into a nucleus with a particularly low threshold for (-y,n) photodisintegration. For example A = 97,101,103,107 are such isobaric chains. If there is significant abundance in these mass chains considerably lower temperatures are needed for the ignition of the photodisintegration runaway. On the other hand, if abundances in these mass chains are low, much larger amounts of carbon are needed to initiate photodisintegration leaving the possibility that only a subset of superbursts, depending on conditions, destroys the heavy elements. Current rp process calculations that include the Sn-Sb-Te cycle seem to produce large amounts of A = 103 material, but better nuclear physics, for example proton separation energies for Sb isotopes, are needed to reach a final conclusion.

Whether or not superbursts destroy heavy elements on the surface of accreting neutron stars has important consequences for crust properties. The high impurity of a crust made of rp process ashes leads to very low thermal and electrical conductivities. On the other hand, in systems where superbursts burn all material, the crust would consist mainly of iron-nickel group elements. This would be similar to the crust of isolated neutron stars, though the impurity is still considerably larger.

H.S. is supported by the National Science Foundation under grants PHY 0110253 (NSCL) and PHY 0072636 (Joint institute of Nuclear As- trophysics). H.S. is an Alfred P. Sloan Fellow.

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NEUTRINO PHYSICS: STATUS AND PROSPECTS

K. SCHOLBERG Massachusetts Institute of Technology,

Dept. of Physics, Cambridge, MA 02139, USA

E-mail: scholOmit.edu

This pedagogical overview will cover the current status of neutrino physics from an experimentalist's point of view, focusing primarily on oscillation studies. The evidence for neutrino oscillations will be presented, along with the prospects for further refinement of observations in each of the indicated regions of two-flavor oscillation parameter space. The next steps in oscillation physics will then be covered (under the assumption of three-flavor mixing): the quest for 013, mass hierarchy and, eventually, leptonic CP violation. Prospects for non-oscillation aspects of neutrino physics, such as kinematic tests for absolute neutrino mass and double beta decay searches, will also be discussed briefly.

1. Neutrinos and Weak Interactions

Neutrinos, the lightest of the fundamental fermions, are the neutral partners to the charged leptons. In the current picture, they come in three flavors (e , p, T ) ~ and interact only via the weak interaction. In the Standard Model of particle physics, neutrinos interact with matter in two ways: in a charged current interaction, the neutrino exchanges a charged W' boson with quarks (or leptons), producing a lepton of the same flavor as the interacting neutrino (assuming there is enough energy available to create the lepton.) In a neutral current interaction, a neutral 2 boson is exchanged; this type of interaction is flavor-blind, i .e. the rate does not depend on the flavor of neutrino (see Figure 1.)

2. Neutrino Mass and Oscillations

Neutrinos are known to be very much lighter than their charged lepton partners; direct measurements of neutrino mass yield only upper limits of

aThe T neutrino has only recently been directly detected by the DONUT experiment1.

132

133

d 9

I

W - A I

ve et-

I

2 0 A I

Figure 1. Examples of CC (left) and NC (right) neutrino interactions.

< 2 eV/c2. However, the question of neutrino mass can be probed using the oscillatory behavior of free-propagating neutrinos, which is dependent on the existence of non-zero neutrino mass.

Neutrino oscillations arise from straightforward quantum mechanics. We assume that the N neutrino flavor states luf), which participate in the weak interactions, are superpositions of the mass states Iui), and are related by the Maki-Nakagawa-Sakata (MNS) unitary mixing matrix:

For the two-flavor case, assuming relativistic neutrinos, it can easily be shown that the probability for flavor transition is given by

P(uf + ug) = 1 - I < uflug > l2 = sin2 28sin2(1.27Am2L/E), (2)

for Am2 =- m$ - m: (in eV2) and with 8 the angle of rotation. L (in km) is the distance traveled by the neutrino and E (in GeV) is its energy.

Several comments are in order:

Note that in this equation the parameters of nature that experi- menters try to measure (and theorists try to derive) are sin2 28 and Am2. L and E depend on the experimental situation. The neutrino oscillation probability depends on mass squared differences, not absolute masses.

0 In the three-flavor picture, the transition probabilities can be computed in a straightforward way. The flavor states are related to the mass states according to

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and the transition probability is given by

P(Vf + vg) =

Sfg - 4 Re(UiU,iUfjUg) sin2(1.27AmiL/E) j > i

f 2 Im(UiUgiUfjUg) sin2(2.54AmiL/E), j > i

again for L in km, E in GeV, and Am2 in eV2. The - refers to neutrinos and the + to antineutrinos.

0 For three mass states, there are only two independent Am2 values.

0 If the mass states are not nearly degenerate, one is often in a “de- coupled” regime where it is possible to describe the oscillation as effectively two-flavor, i.e. following an equation similar to 2, with effective mixing angles and mass squared differences. We will assume a two-flavor description of the mixing for most cases here.

0 “Sterile” neutrinos, v,, with no normal weak interactions, are possible in many theoretical scenarios (for instance, as an isosinglet state in a GUT.)

0 When neutrinos propagate in matter, the oscillation probability may be modified. This modification is known as the the “Mikheyev- Smirnov-Wolfenstein (MSW) effect” or simply the “matter effect”. Physically, neutrinos acquire effective masses via virtual exchange of W bosons with matter (virtual CC interactions.) For example, consider v, propagating through solar matter: electron neutrinos can exchange W’s with electrons in the medium, inducing an effective potential V = ~ G F N , , where N , is the electron density. Muon and 7-flavor neutrinos, however, can exchange virtual 2 bosons only with the matter (because there are no p’s and 7’s present.) The probability of flavor transition may be either enhanced or suppressed in a way which depends on the density of matter traversed (and on the vacuum oscillation parameters.) A description of the phenomenology of neutrino matter effects may be found in e.g. References 2,3. We will see below that matter ef-

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fects become important for the solar neutrino oscillation case, and also for future long baseline experiments.

2.1. The Experimental Game

The basic experiment to search for neutrino oscillations can be described very simply.

(1) Start with some source of neutrinos, either natural or artificial. (2) Calculate (or better yet, measure) the flavor composition and energy

(3) Let the neutrinos propagate. (4) Measure the flavor composition and energy spectrum after propa-

gation. Have the flavors and energies changed? If so, is the change described by the oscillation equation 2? And if so, what are the allowed parameters?

spectrum of neutrinos.

The signature of neutrino oscillation manifests itself in one of two ways, either by disappearance or appearance. In “disappearance’’ experiments, neutrinos appear to be lost as they propagate, because they oscillate into spme flavor with a lower interaction cross-section with matter. An example of disappearance is a solar neutrino experiment, for which v, transform into muon/tau flavor neutrinos, which are below CC interaction threshold at solar neutrino energies of a few MeV (solar v,’s do not have enough energy to create p or T leptons.) In “appearance” experiments, one directly observes neutrinos of a flavor not present in the original source. For example, one might observe T’S from v, in a beam of multi-GeV vh.

3. The Experimental Evidence

There are currently three experimental indications of neutrino oscillations. These indications are summarized in Table 1. We will now examine the current status of each of these observations.

3.1. Atmospheric Neutrinos

Atmospheric neutrinos are produced by collisions of cosmic rays (which are mostly protons) with the upper atmosphere. Neutrino energies range from about 0.1 GeV to 100 GeV. At neutrino energies X 1 GeV, for which the geomagnetic field has very little effect on the primary cosmic rays, by geometry the neutrino flux should be up-down symmetric. Although

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u source Experiments Flavors E L Am2 sensitivity (km) (eV2)

Sun Chlorine u, + uz 5-15 MeV los 10-'2 - 10-10 Gallium Water E

or - 10-3

Reactor Scintill. De + & 3-6 MeV -180 10-5 - 10-3 Cosmic ray Water E up + us 0.1-100 GeV 10 - lo5 -

showers Iron calor. UDward U

Accelerator LSND i+, + De 15-50 MeV 0.03 0.1-1

the absolute flux prediction has -15% uncertainty, the flavor ratio (about two muon neutrinos for every electron neutrino) is known quite robustly, since it depends on the well-understood decay chain T* + pf v,(~,) -+ e*ve(De)D,(v,). The experimental strategy is to observe high energy interactions of atmospheric neutrinos, tagging the flavor of the incoming neutrino by the flavor of the outgoing lepton, which can be determined from the pattern of energy loss: muons yield clean tracks, whereas high-energy electrons shower. Furthermore, the direction of the produced lepton follows the direction of the incoming neutrino, so that the angular distribution reflects the neutrino pathlength distribution.

Super-Kamiokande4, a large water Cherenkov detector in Japan, has shown a highly significant deficit of v, events from below5, with an energy and pathlength dependence as expected from equation 2 (see Figure 2.) The most recent data constrain the two-flavor v, + v, oscillation parameters to a region as shown in Figure 3. The latest results from Soudan 26 (an iron tracker) and from MACRO's7 upward-going muon sample are consistent with the Super-K data.

Super-K has also been able to shed some light on the flavors involved in the atmospheric up disappearance. Assuming a two-flavor oscillation, the missing v,'s could have oscillated into either ve, v, or v,. The oscillation cannot be pure vp -+ ve, because there is no significant excess of ue from below. In addition, the CHOOZlO and Palo Verde" experiments have ruled out disappearance of reactor oe; only small mixing to v, is allowed8. (see Section 6.1.)b

The v, + v, hypothesis is difficult to test directly. Super-K expects relatively few charged current (CC) v, interactions, and the products of such

fact, a potential small up + v, mixing is extremely interesting, as we will see in Section 6.

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Figure 2. Zenith angle distributions for Super-K’s newest 1489 day atmospheric neutrino samples, including fully-contained events (those with interaction products that do not leave the detector) and partially-contained events (events with an exiting muon), upward through-going and stopping muons (neutrinos interacting below the detector), and multiple ring events (e.g. CC and NC single and multiple pion producing events.) The points with (statistical) error bars are the data; the solid red line represents the MC prediction for no oscillation; the paler green line is the best fit for vp + v, oscillation.

interactions in the detector are nearly indistinguishable from other atmospheric neutrino events. However, recently Super-K has employed several strategies to distinguish vp + v, from vp + v,12. First, one can look for an angular distortion of high-energy neutrinos due to matter effects of sterile neutrinos propagating in the Earth: unlike vT’s, sterile neutrinos do not exchange Zo’s with matter in the Earth, resulting in an matter effect that effectively suppresses oscillation. The effect is more pronounced at higher energies. Such distortion of the high-energy event angular distribution is not observed. Second, one can look at neutral current (NC) events in the detector: if oscillation is to a sterile neutrino, the neutrinos “really disap- pear” and do not interact via NC. A NC-enriched sample of multiplering Super-K events shows no deficit of up-going NC events. Together, these measurements exclude two-flavor vp + v, at 99% C. L., for all parameters allowed by the Super-K fully-contained events12. The maximum allowed admixture of sterile neutrinos is about 20%8.

There is one more piece of evidence from Super-K suggesting that vp + v, oscillations are primarily responsible for the observed disappearance8y9. Because the energy threshold for tau production is about 3.5 GeV and only a small fraction of the atmospheric neutrino flux exceeds this energy, only about 90 v,-induced r leptons are expected in Super-K’s 1489 day sample, given the measured oscillation parameters. Tau leptons decay with a

-2 10

10 -3

-4

Figure 3. Right: allowed region in oscillation parameter space corresponding to the fit to Super-K atmospheric neutrino data (including fully-contained events, partially- contained events, and upward-going muons.)

: -

68% C.L. - 90% C.L. - 99%C.L.

very short lifetime into a variety of modes, and can be observed as energetic multi-ring events; such events are very difficult to disentangle from a large background of multi-ring CC and NC events. Nevertheless, three independent Super-K analyses which select ".r-like" events have determined excesses of up-going v, events consistent with T appearance at about the 2a level.

3.1.1. Long Baseline Experiments

The next experiments to explore atmospheric neutrino parameter space are the "long-baseline" experiments, which aim to test the atmospheric neutrino oscillation hypothesis directly with an artificial beam of neutrinos. In order to achieve sensitivity to the oscillation parameters indicated by Super- K, LIE must be such that for -1 GeV neutrinos, baselines are hundreds of kilometers. A beam is created by accelerating protons and bombarding a target to produce pions and other hadrons; pions are then focused forward with a high-current magnetic "horn" and allowed to decay in a long pipe.

138

139

The neutrino flavor composition and spectrum can be measured in a near detector before propagation to a distant far detector.

The first long-baseline experiment is the K2K (KEK to Kamioka) experiment13, which started in March 1999, and which saw the first artificial long-distance neutrinos in June 1999. K2K sends a beam of (E,) -1 GeV vP 250 km across Japan to the Super-K experiment. K2K can look for vP disappearance (the beam energy is not high enough to make significant numbers of 7's.) Preliminary K2K r e s u l t ~ ~ ~ y ~ ~ do show a deficit of observed neutrinos: 80.1+!:2, beam events in the fiducial volume are expected, based on beam-modeling and near detector measurements; however only 56 single- ring vP events were seen at Super-K. The far spectrum was also measured. The best fit oscillation parameters using both spectrum and suppression information are entirely consistent with the atmospheric results. See Fig- ure 4. Somewhat more than half of K2K data has now been taken. The beam resumed in early 2003 after repair of Super-K. The next generation long baseline experiments will be discussed in Section 5.3.

-4- l o 0 0.2 0.4 0.6 0.8 1

sin'20

Figure 4. Left: Expected beam neutrino spectrum for no oscillations (dashed line), data (points), expected spectrum with systematic error normalized to the number of observed events (boxes) and best fit to the oscillation hypothesis (solid) for the K2K 1999-2001 data sample. Right: allowed region in oscillation parameter space corresponding to K2K 1999-2001 data sample, using both suppression and spectrum.

3.2. Solar Neutrinos

The deficit of solar neutrinos was the first experimental hint of neutrino oscillations. The solar neutrino energy spectrum is well-predicted, and

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depends primarily on weak physics, being rather insensitive to solar physics. The three “classic” solar neutrino detectors (chlorine, gallium and water Cherenkov), with sensitivity a t three different energy thresholds, together observe an energy-dependent suppression which cannot be explained by any solar model (standard or non-~tandard)’~.

The observed suppression in all three experiments can be explained by neutrino oscillation at certain values of Am2 and mixing angle: see Figure 5. The “classic” allowed regions at higher values of Am2 (“small mixing angle”, “large mixing angle” and “low”) are those for which matter effects in the Sun come into play. There are also solutions at very small Am2 values for which matter effects in the sun are not involved: these are known as “vacuum” oscillation or “just-so” solutions.c Figure 5 shows the mixing angle axis plotted as tan2 0, rather than as the more conventional sin2 20, t o make evident the difference between 0 < 8 < 7r/4 and 7r/4 < 0 < ~ / 2 : these regions are not equivalent when one considers matter effects16.

Before 2000, the most precise real-time solar neutrino data came from Super-K via the elastic scattering reaction ve,z +e- + ve,z +e-, which proceeds via both CC and NC channels, with a cross-section ratio of about 1:6. In this reaction, the Cherenkov light of the scattered electron is measured. The scattered electrons point away from the direction of the sun.

Possible “smoking guns” for neutrino oscillations include a distortion from the expected shape that would be hard to explain by other than non-standard weak physics. The latest Super-K solar neutrino spectrum shows no evidence for di~tortion’~. Another “smoking gun” solar neutrino measurement is the day/night asymmetry: electron neutrinos may be regenerated in the Earth from their oscillated state for certain oscillation parameters. The latest measured Super-K day/night asymmetry is (dayY+nigit),2 = -0.021 f 0 . 0 2 0 ~ t a t - ~ , ~ ~ ~ (syst): regeneration is therefore a relatively small effect, if it is present at all. Together, the energy spectrum and daylnight observations place strong constraints on solar neutrino parameters. In particular, Figure 5 shows the Super-K results overlaid on the global flux fit parameters: large mixing angles are favored, and the small mixing angle and vacuum solutions from the global flux fit are disfavored at 95% C.L.. Global flux fit v, + v, solutions are also disfavored.

The information from Super-K served primarily to constrain parame-

da -ni ht +0.013

=The vacuum solutions are “just-so” because oscillation parameters must fine-tuned to explain suppression at exactly the Earth-Sun distance; on the other hand, because the Sun has a range of electron densities, u, suppression will result for a broader range of oscillation parameters if one assumes that matter effects are involved.

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10-5

10-l0

0.001 0.01 0.1 1 10 tan2 8

Figure 5. Solar neutrino parameter space: the shaded areas show the “classic” global flux fit solutions from chlorine, gallium and water Cherenkov experiments (from Refer- ence 16.)

ters. The true “smoking gun” for solar neutrino oscillations recently came from the Sudbury Neutrino Observatory18, a detector comprising 1 kton of DzO in Sudbury, Canada, with the unique capability to detect neutral current reactions from the breakup of deuterium, v, + d + v, +p+ n: since this reaction is flavor-blind, it measures the total active neutrino flux from the sun. Neutrons from this reaction can be detected via various methods: capture on d itself, capture on C1 ions from dissolved salt, and neutron detectors. In addition, the charged current reaction v, + d + v, + p + e- specifically tags the ve component of the solar flux. SNO also observes the same neutrino-electron elastic scattering (ES) interaction as Super-K, which proceeds via both CC and NC channels.

SNO’s recent resultslg are summarized in Figure 7, which shows the

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5 (b) NS

-4

E Q 10 -5

10

10 -7

y4 10” I O - ~ 10-l I 10 l o 2 10” 10” lo-‘ 1 10 10

Figure 6. Solar neutrino parameter space: on the left, the light grey areas show the “classic” global flux fit solutions from chlorine, gallium and the SNO experiment’s CC measurement. The darker grey shaded regions indicate Super-K’s excluded regions from spectral and day/night information (and the darkest grey regions indicate the overlap.) On the right, the light shaded areas indicate allowed regions from Super-K data alone and SSM 8B neutrino flux.

measured fluxes 4pT vs +e.d The CC measurement, which tags ve flux q5,, is represented by a vertical bar on this plot. Since the neutral current flux is flavor-blind and therefore represents a measurement of the sum of 411r and 4 e , ie. ~ N C = + +e, the NC measurement corresponds to a straight line with slope -1 on this plot. The intersection with the vertical CC line indicates the composition of the solar neutrino flux: it is approximately 113 v, and 213 vp,.. The ES reaction measures both ve and ulL,r with a known ratio, $JES = 0.154$,, + 4, for SNO, so that the ES measurement corresponds to a line on the plot with slope -110.154; it provides a consistency check. The conclusion from SNO is that solar neutrinos really are oscillating (into active neutrinos.) The solar neutrino problem is solved!

The detailed measurements from SNO incorporating observed day/night

dNote that one cannot distinguish between vp and v, at low energy since the NC interaction does not distinguish between them.

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Figure 7. Right: allowed region in oscillation parameter space after SNO 2002 results.

Left: Inferred flavor components from fluxes measured at SNO (see text.)

asymmetry and energy spectra shrink the allowed parameters down to small regions, shown in Figure 7. At 99% C.L., only the LMA region is left.

So far, SNO's NC measurement comes from capture of neutrons on d; SNO continues to run, and will provide cross-checked NC measurements using salt and helium neutron counters.

There is one more recent chapter in the solar neutrino story. Kam- LAND, a 1 kton scintillator detector at the Kamioka mine in Japan2', has investigated solar neutrino oscillation parameters using reactor neutrinos rather than solar neutrinos directly. Reactors produce Pe of few-MeV energies abundantly; assuming vacuum oscillations, the baseline required to observe oscillations with LMA parameters is about - 100 km. Note that no significant matter effects are expected at this baseline. KamLAND observes the sum of the fluxes of neutrinos from reactors in Japan and Korea, with roughly a 180 km average baseline, via the inverse beta decay reaction De + p + e++n; fie's are tagged using the coincidence between the positron and the 2.2 MeV y-ray from the captured neutron. In December 2002, the KamLAND experiment announced an observed suppression of reaction f i e consistent with LMA parameters: see Figure 8. Solar neutrino oscillations are therefore now confirmed using a completely independent source of neutrinos and experimental technique. In addition, the LMA solution is strongly indicated.

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1.2 ''I I

0.01 I I I I I I 10' 10' 10' lo4 i d

Distance 10 Reactor (m)

";lo4 P) v

"E Q -5

10

1 Od 0 0.2 0.4 0.6 0.8 1 sin220

Figure 8. Left: Ratio of measured to expected De for various experiments as a function of baseline; the point on the far right is the KamLAND result. The shaded area represents the expectation from the solar LMA solution, and the dotted line is the best fit to the oscillation hypothesis. Right: Allowed and excluded regions in oscillation parameter space for various experiments (as indicated in the legend.)

3.3. LSND

The third oscillation hint is the only "appearance" observation: the Liquid Scintillator Neutrino Detector (LSND) experiment at Los Alamos has observed an excess of Pe events2' from a beam which should contain only op, u, and up from positive pion and muon decay at rest. The result is interpreted as -20-50 MeV Pp's oscillating over a 30 m baseline. See Figure 9 for the corresponding allowed region in parameter space, which is at large Am2 and small mixing. (The large mixing angle part of this range is ruled out by reactor experiments.)

An experiment at Rutherford-Appleton Laboratories in the U. K. called KARMEN, which has roughly similar neutrino oscillation sensitivity as does LSND (although with a shorter 17.5 m baseline), does not however confirm the LSND result22. This detector expects fewer signal events than does LSND, but has a stronger background rejection due to the pulsed nature of the ISIS neutrino source. However, due to somewhat different sensitivity, KARMEN's lack of observation of Pe appearance cannot rule out all of the parameter space indicated by LSND: see Figure 9.

145

% Y lo‘

10 3

1

10-

lo-’

Figure 9. The shaded region shows the LSND allowed regions at 90% and 99% C.L.; the region to the right of the KARMEN2 line is excluded by KARMEN. Also shown are exclusions by the reactor experiments Bugey and Chooz, the NuTeV and Nomad excluded regions, and the reach of the mini-BooNE experiment (see Section 5.1.)

4. Where Do We Stand?

Now we can step back and view the big picture. Where do we stand? The current experimental picture for the three oscillation signal indications can be summarized:

0 For atmospheric neutrino parameter space: evidence from Super-K, Soudan 2 and MACRO is very strong for ufi + v,. Furthermore, Super-K’s data favor the vfi -+ v, hypothesis over the vfi -+ vs one. These oscillation parameters have been independently confirmed using the K2K beam of -1 GeV vp’s to Super-K.

0 For solar neutrino parameter space (v, -+ vz): The solar neutrino problem is now solved. While Super-K data favored large mixing via day/night and spectral measurements, SNO’s Dz 0-based NC and CC measurements have confirmed that solar neutrinos are oscillating, and have shrunk down the allowed parameter space to the LMA region using day/night and spectral measurements. Better yet, the KamLAND experiment has independently confirmed the LMA solution using reactor fie’s. Oscillation to sterile neutrinos is disfavored.

1 46

0 The LSND indication of Yfl 3 V , still stands; KARMEN does not rule out all of LSND’s allowed parameters.

N-1 o2 3 Y

“E 4 10

Atmospheric 1 o-2 v +VT P

1 o - ~

1 o-6

1 o-8

1 o-’O

Solar Lou

Solar Vacuui

1 o - ~ 1 o 2 lo-’ 1 sin*(20)

Figure 10. Oscillation parameter space showing all three indications of oscillation, in the two-flavor mixing approximation. At high Am2, the parameters allowed by LSND are shown by dotted lines, and the part not excluded by Karmen is shown as a solid region. Allowed atmospheric neutrino parameters are shown at large mixing and Am2 of about 2.5 x eV2. Also shown by dotted lines are the “classic” solar neutrino solutions at small Am2: “small mixing angle” (SMA), “large mixing angle” (LMA), and “low”, which all involve matter effects in the sun, and the vacuum solutions at very small Am2. With new information from SNO and KamLAND, only the LMA solution is now allowed, as indicated by the solid region at about 4.5 x eV2.

What do these data mean? There is an obvious problem. Under the assumption of three generations of massive neutrinos, there are only two independent values of Am:j : we must have Am:, = Am:, + Am;, . How- ever, we have three measurements which give Am% values of three different

147

orders of magnitude. So, if each hint represents two-flavor mixing, then something must be wrong. All data cannot be satisfactorily fit assuming three-flavor oscillations. One way to wriggle out of this difficulty is to introduce another degree of freedom in the form of a sterile neutrino (or neutrinos) or else invoke some exotic solution (e.g. CPT ~ i o l a t i o n ~ ~ . ) (We cannot introduce another active neutrino, due to the Zo width measurements from LEP, which constrain the number of light active neutrinos to be three23: any new light neutrino must be sterile.) Although pure mixing into u, is now disfavored by solar and atmospheric neutrino results, a sterile neutrino is still barely viable as part of some four-flavor mixing24. Of course, it is also possible that some of the data are wrong or misinterpreted. Clearly, we need more experiments to clarify the situation.

5. What’s Next for Two-flavor Oscillations?

So what’s next? First, let’s consider the next experiments for each of the interesting regions of two-flavor parameter space.

5.1. LSND Neutrino Parameter Space

The next experiment to investigate the LSND parameter space will be BooNE (Booster Neutrino Experiment.) This will look at N 1 GeV neutrinos from the 8 GeV booster at Fermilab, at a baseline of about 500 m (with a second experiment planned at longer baseline if an oscillation signal is seen.) This experiment is primarily designed to test up + Y, at about the same LIE as LSND. Since the neutrino energy is higher, and the backgrounds are different, systematics will presumably be different from those at LSND. BooNE, which started in 2002, expects to cover all of LSND parameter space26 (see Figure 9.) If a signal is found, the BooNE collaboration plans to build another detector at a longer baseline to further test the oscillation hypothesis.

5.2. Solar Neutrino Parameter Space

Now that the latest results from SNO and KamLAND have squeezed the allowed solar mixing parameters down to the LMA region, solar neutrino physics is entering a precision measurement era. Over the next few years, we expect to have cross-checks of NC measurements from SNO, using different neutron detection techniques (salt, NCDs.) From KamLAND we expect better precision from improved statistics and systematics; KamLAND

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will also attempt to measure the solar neutrino flux directly. Borexino, a planned 300 ton scintillator experiment at the Gran Sasso Laboratory in Italy27 with very low radioactive background, hopes to measure the solar 7Be line at 0.86 MeV.

The true frontier for solar neutrino experiments is the real-time, spectral measurement of the flux of neutrinos below 0.4 MeV produced by pp reactions in the sun, which are responsible for most of the solar energy generation. The pp flux is precisely known, which will aid in precision measurements of mixing parameters; in addition if the total pp flux is well- known, measurement of the active component will help constrain a possible sterile admixture. The pp flux is also a new window on solar energy generation. Because the pp flux is very large, one can build relatively small (tens to hundreds of tons) detectors and still expect a reasonable rate of neutrino interactions. The challenge is to achieve low background at low energy threshold. There are a number of innovative new solar neutrino experiments aiming to look at the very low energy pp solar among them LENS, Heron, solar-TPC and CLEAN.

5.3. Atmospheric Neutrino Parameter Space

Two-flavor oscillation studies at atmospheric neutrino parameters has also entered a precision measurement era.

The K2K experiment will continue, now that Super-K has been refurbished to 47% of its original number of inner detector phototubes after the accident of November 2001. The results published so far represent about half of the total number of protons on target for the neutrino beam; the next few years will see both systematic and statistical precision improvements in mixing parameter measurements.

The next set of long baseline experiments to explore atmospheric oscillation parameter space have -730 km baselines and will start in a few years. The NuMi beamline3’ will send a vp beam from Fermilab to Soudan, with a beam energy of 3 - 8 GeV, and a baseline of 735 km. The far detector, MINOS2’ is a magnetic iron tracker. A primary goal is to attain 10% precision on 2-3 mixing parameters Am;, and sin2 2823.

CNGS (Cern Neutrinos to Gran sass^)^^ is a -20 GeV vp beam from CERN to the Gran Sasso 730 km away. The two planned CNGS detectors, OPERA32 and I ~ a r u s ~ ~ , are focused on an explicit vT appearance search. Because when T’S decay they make tracks only about 1 mm long, both detectors are fine-grained imagers. Icarus is a liquid argon time projection

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chamber, and OPERA is a hybrid emulsion/scintillator detector. Both experiments expect a few dozen r events over several years of running.

6. Beyond Two-Flavor Oscillations

The previous section discussed the future of neutrino oscillation studies in the context of two-flavor oscillations. As noted in section 2, however, this is an approximation valid for well-separated mass states, which appears to be the case. However a full description requires three flavors.

In the following, we will assume that a “standard” three-flavor picture is valid. If mini-BooNE confirms the LSND effect, we will have to rethink our picture, and our goals.

In this “standard” picture, neutrino mixing can be described by six parameters: two independent Am:j (Amf2, Amg3) , three mixing angles (1312, 823, &3), and a CP violating phase 6.“ The mixing matrix U of equation 2 can be written as a product of three Euler-like rotations, each described by one of the mixing angles:

-512 c12 0 (4) 0 0 1

where “s7’ represents sine of the mixing angle and “c” represents cosine. The “1-2” matrix describes solar mixing; the “2-3” matrix describes at-

mospheric neutrino mixing. The “1-3” or “e3” mixing is known to be small; 013 may be zero. The mass-squared difference Am;, - 2 x eV2 describes the atmospheric mixing, and Am?, w 4.5 x eV2 describes solar mixing. Neutrino oscillation experiments tell us only about mass-squared differences; the absolute mass scale is known only to be less than about 2 eV. It is also as yet unknown whether the mass hierachy is “normal” , i. e. the solar mixing is described by two lighter states, or “inverted”, i.e. the solar mixing is described by two heavier states (see Figure 11.)

The remaining questions can be addressed by neutrino oscillation experiments are:

0 Is Ue3 non-zero? 0 Is the hierarchy normal or inverted?

eMajorana phases, which cannot be measured in oscillation experiments and in general are very difficult to observe 34, will not be considered here.

150

"Normal" hierarchy "Inverted" hierarchy

Figure 11. Normal and inverted hierarchies in the three-flavor picture, with mass- squared values of the three states indicated vertically, and possible flavor composition of the mass states indicated by the horizontal divisions.

Is 2-3 mixing maximal, or just large? 0 Is the CP-violating phase non-zero?

6.1. The Next Step: e3 Mixing

The next question which can be approached experimentally is that of e3 mixing. A consequence of a non-zero Ue3 matrix element will be a small appearance of v, in beam of up: for Am;, >> Am:, (as is the case), and for E, - LArn;,, ignoring matter effects we find

P(vp + v,) = sin2 2OI3 sin2 623 sin2(1.27Arni3L/E). (5)

This expression illustrates that 013 manifests itself in the amplitude of an oscillation with 2-3-like parameters. Since v, appearance has never been observed at these parameters, this amplitude (and hence 013) must be small. The best limits so far, shown in Figure 12, come from a reactor experiment, CHOOZ, which observed no disappearance of reactor fie.f. The on-axis long baseline experiments mentioned in section 3.1.1 can likely improve this limit by a factor of approximately five. To do better than this is a difficult job: since the modulation may be parts per thousand or smaller, one needs both good statistics and low background data. The primary sources of background for a long baseline experiment are: intrinsic beam v,

'In the literature one finds limits and sensitivities to this mixing angle variously expressed in terms of 813 (in radians or degrees), sin813, sin2 813, sin2 2813, sin2 28,,, IUe31, or IUe3I2; no convention has yet emerged. For Am:2 << Ami3 N Am:,, sin228,, sin22813sin2&3 is the measured u, appearance amplitude. lUe31 = sin&, and for 823 N s/4 and 813 small, it follows that sin2 28,, N a sin2 2813 N 2 sin2 813.

151

1 90% C.L. sensitivities 10

10

10

10

Figure 12. Expected sensitivity to sin2 2813 with J-PARCnu, for various beam configurations (a 2 O off-axis configuration, labeled OAB 2deg on the plot, has been selected.) The CHOOZ excluded region for De disappearance is shown for comparison. NuMi off- axis and new reactor experiments have comparable sensitivity.

contamination, misidentified NC resonant 7ro production (since 7ro decay to y-rays which make electron-like showers), and other misidentified particles.

6.1.1. Off-Axis Beams

A promising next step for measurement of d13 (assuming it is large enough to be measured) is an off-axis detector at a long baseline neutrino beam. An experiment placed a few degrees off axis has some kinematic advantages. Because two-body pion decay kinematics imply that neutrino energy becomes relatively independent of pion energy off-axis, the neutrino spectrum becomes more sharply peaked. Therefore an off-axis siting is favorable for background reduction and oscillation fits, in spite of the reduction in Y flux.

There are two major long-baseline off-axis detector projects currently under consideration. The first of these is J - P A R C ~ U ~ ~ , comprising a high power (0.77 MW) beam from the J-PARC facility in Japan (currently under construction.) The far detector, 2" off-axis, will be a fully refurbished

152

$ 45

t 20 u 15 u 10

5 0

NUMl Low Energy Conf. L=735 Km - R=okm - R=10 km

0 2 4 6 8 1 0 1 2 1 4 E

2 120

5 80

* 20

100 R=O km b

8 60 5 40

0

*

0 2 4 6 8 1 0 1 2 1 4

Figure 13. medium-energy NuMI beams, from Reference 35.

Expected CC interaction spectra for various off-axis locations for low and

Super-K at 295 km. The second off-axis proposal37, for the US., is to exploit the NuMi beam which will exist for MINOS, and build a new detector off-axis at a distance of 700-900 km. Various detector technologies and sites are under discussion. Sensitivity to 613 for both possibilities will be roughly a factor of 10-20 better than the CHOOZ limit.

6.1.2. Reactor Experiments

Another possibility currently under consideration by groups in Russia, Japan and the US. is an upgraded reactor experiment employing the same strategy as CHOOZ, i.e. search for disappearance of F e 3 8 . The challenge for this type of experiment is reduction of systematics to the level where a few percent or smaller modulation is evident. Multiple detectors may help to achieve this.

153

6.2. Leptonic CP Violation and Mass Hierarchy

The long-term goal of long baseline oscillation experiments in the observation of CP violation in the lepton sector. The basic idea is to measure a difference between vp -+ v, and Dp + De transition probabilities. However, it is not simple to extract a CP violating phase from the measurements: transition rates depend on all MNS matrix parameters, and in addition are affected by the presence of matter.

Following the analysis of Reference 39: the approximate transition probabilities for neutrinos and antineutrinos (assuming 813, A12L and A12/A13 are all small) are:

where - J = ~ 1 3 sin 2012 sin 2823 sin 2&3, (7)

Am?. L is the baseline, Aij &, B, = JA F A131, and A is the matter parameter A = f i G F N e , where GF is the Fermi constant and N , is the electron density of the matter traversed. The upper sign in f refers to neutrinos and the lower to antineutrinos. The first two terms are the “non- CP” terms and the last term depends on the CP-violating phase.

A few observations about observability of leptonic CP violation may be made based on this expression:

0 The fact that sin2 2812 is large, as recently indicated by SNO and KamLAND, is good news: the CP term is proportional to sin2012.

0 The CP terms are proportional to sin28I3; therefore a very small value of 813 will mean that CP violation will be very difficult to observe.

0 Precision measurements of all parameters will be necessary for measurement of CP observables!

0 Matter effects cause a fake asymmetry between neutrinos and antineutrinos, as indicated by the matter terms (see Figure 14 from

154

Reference 35.) This may be considered a blessing rather than a curse, because the sign of the neutrino/antineutrino asymmetry depends on the sign of Am2. In other words, one can learn about the mass hierarchy by measuring the asymmetry. Observation of matter effects requires relatively long baselines (typically more than 500 km, depending on parameters.) Parameter ambiguities from various sources are intrinsic to these equations, and a single measurement will not suffice to measure both 6 and 1313 (and matter effects.) For instance, consider Fig- ure 15 drawn from Reference 40, which shows probability of transition for antineutrinos versus probability of transition for neutrinos (the axes represent the observables.) For a given value of sin2 M I 3 , one can draw an ellipse corresponding to different values of 6; this ellipse is shifted for different hierarchies via the matter effect. In consequence, one must make multiple measurements with different experimental parameters in order to resolve the ambiguities. Some of these issues are explored in e.g. References 40,41.

Figure 14. Transition probabilities for neutrinos (green, top curve) and anti-neutrinos (blue, bottom curve) in matter and vacuum (red, middle curve) as function of the distance for 2 GeV, Am:3 = 3 x eV2 (normal hierarchy), 023 = n/4, Am:, = 1 X lom4 eV2, 023 = s/6, IU,3l2 = 0.04, and 6 = 0. Figure from Reference 35.

Assuming that 813 is large enough for there to be some hope of observing leptonic CP violation, the obvious strategy is an upgraded long baseline experiment, perhaps as a “Phase 11” of an off-axis program, or perhaps as an on-axis detector program such as the proposed broad-band beam from Brookhaven4’. Very large detectors (e.g. the 1 Mton Hyper-K detector) and upgraded “superbeams” have been proposed36>42>43>44. As mentioned above, multiple measurements with differing energies and/or baselines, with

155

K

v,, --t ue E,=1.4 GeV L=732 km

K

!i

3L

1 <P(v)> %

XL n/2 e 3n/Z

1.25 “ “ ‘ “ “ “ ‘ ‘ L “ ‘ l l l “ l l l ’

1.25 1.50 1.75 2.00 2.25 2.50 2.75 <P(v)> %

Figure 15. The T (CP) trajectory diagrams (ellipses) in the plane P(v, t ve) versus P(ve t v,) (P(Dp -+ 0,)) for an average neutrino energy (spread 20%) and baseline of (a) 1.4 GeV and 732 km (NUMI/MINOS) and (b) 1.0 GeV and 295 km (J-PARCnu.) The ellipses labeled with a T and CP are in matter with a density times electron fraction given by Y e p = 1.5 g cmP3 whereas those ellipses labeled V are in vacuum where the T and CP trajectories are identical. The plus or minus indicates the sign of Am:, . The mixing parameters are fixed to be IAmg,I = 3 x eV2, sin2 2823 = 1.0, Amgl = +5 x eV2, sin2 2812 = 0.8 and sin2 2813 = 0.05. The marks on the CP and T ellipses are the points where the CP or T violating phase 6 = ( 0 , 1 , 2 , 3 ) ~ / 2 as indicated. See Reference 40 for details.

both neutrinos and antineutrinos will be necessary for full characterization of the parameters.

More ambitious alternatives to a traditional proton-induced neutrino su- perbeam have been proposed. For instance a muon storage ring “neutrino factory” would produce copious, and well-understood, 20-50 GeV neutrinos from muon decay4‘. Detectors at 3000-7000 km could explore matter effects. However this idea is for the rather distant future due to high cost and technical difficulties to be overcome. Other interesting ideas include a “beta-beam” of radioactive ions which could provide a high flux of Y,’s46147.

7. Non-Oscillation Neutrino Physics

So far this review has focused on neutrino oscillation studies. However, oscillation physics hardly comprises all of neutrino physics. Perhaps the two most compelling experimental questions that cannot be answered by oscillation experiments are:

0 What is the absolute mass scale? We do not know whether the

156

masses are hierarchical or degenerate. This question is fundamental, and additionally has profound consequences for cosmology47.

0 Are neutrinos Majorana or Dirac? In other words, are they their own antiparticles, described by a two-component spinor, or described by a 4-component Weyl spinor? The answer to this question has tremendous implications for the construction of theory describing neutrino masses. For instance, the “see-saw” mechanisms for neutrino mass generation require the neutrino to be Majorana.

In the following sections I will very briefly review experiments which aim to answer some, or both, of these questions. In lieu of detailed discussion, I will point to comprehensive reviews where possible.

7.1. Kinematic Neutrino Mass Experiments

As noted above, neutrino oscillation measurements say nothing about absolute masses of the mass states. The idea behind kinematic neutrino mass searches is simple: look for missing energy. The traditional tritium beta decay spectrum endpoint experiments now have limits for absolute Ve mass from the Mainz and Troitsk experiments of 6 3 eV48, and there are some prospects for improvement down to the sub-eV level by the Katrin4’ experiment. Some new techniques are under consideration, The vp and v, mass limits are currently 190 keV51 and 15.5 MeV52 respectively; however improving these direct vp and v, measurements seems less compelling if information about differences between the mass states is available from oscillation experiments.

7 . 2 . Double Beta Decay

Another way of getting at absolute neutrino mass, and, in one fell swoop, determine that the neutrino is Majorana, is to discover neutrinoless double beta decay, ( N , 2) + ( N - 2 , 2 + 2 ) + e p + e - . Such a decay is only possible if the neutrino has mass, and is Majorana, as illustrated in Figure 16. The current 90% confidence level lowest mass limits from non-observation of double beta decay are (mu) = ICU&m,,jI < 0.35 eV48 (note dependence of these limits on the matrix elements.) The current best limits are from 76Ge experiments. Many new double beta decay search experiments are planned and under construction, some employing novel techniques. It appears challenging but not impossible to push the limits down to -0.02 eV53.

too

157

d 21

\

/

/ e

d 21

Figure 16. neutrino to be its own antiparticle.

Underlying process of neutrino-less double beta decay, which requires the

7.3. Neutrino Magnetic Moment

A non-zero non-transition magnetic moment would imply that neutrinos are Dirac and not Majorana. The best limits on neutrino magnetic moment4*, in the range 1 0 - l 2 p ~ , are astrophysical. The current best laboratory limit, pve < 1.0 x 1 0 - l o p ~ , is from the MUNU e ~ p e r i m e n t ~ ~ , which measures low energy elastic scattering of reactor fie on electrons.

7.4. Supernova Neutrinos

A supernova is a “source of opportunity” for neutrino physics: we can expect an enormous burst of neutrinos of all flavors from a core collapse in our Galaxy about once every 30 years. Many of the large neutrino experiments - Super-K, SNO, Borexino, KamLAND, LVD and AMANDA, and BooNE - are sensitive55 to a burst of supernova neutrinos. Most of these are water or scintillator-based and are primarily sensitive to V e . In addition to bringing new understanding of stellar core collapse processes, a Galactic supernova would be a tremendous opportunity for neutrino physics. We may be able to extract absolute mass information from time-of-flight-related measurements, although such information, in the best case, may be only marginally better than the best kinematic (and cosmological) limits56. Potentially more promising is the information about mixing parameters (613 and mass hierarchy) that may be inferred from spectra and time-dependence of the different flavor components of the matter-induced flavor transitions in the stellar material, and also in the Earth, may cause inversion of the expected hierarchy of temperatures (&,p,vr,pp,fi7 > EDe > Eve) for some mixing parameters and conditions. Therefore detectors with sensitivity to

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158

flavors other than De are highly desirable. The relic supernova neutrinos (neutrinos from past supernovae) have

not yet been observed; best limits so far come from Super-Kamiokande5*.

7.5 . Cosmology

Neutrinos are important in cosmology59, and play an significant role in big-bang nucleosynthesis and possibly “leptogenesis” , the process by which the matter-antimatter asymmetry of the universe was generated. Ultra low energy (1.95 K) big-bang relic neutrinos are expected to permeate the universe with a number density of 113 cm-3 per family. The relic neutrinos must make up some component of the dark matter, although the fraction is now thought to be small, for consistency with galactic structure formation. Direct detection of these big bang relic neutrinos remains an experimental challenge60. However, recent advances in “precision cosmology” 47761 are starting to provide quite strong constraints on the properties of neutrinos. The latest cosmic microwave background (CMB) anisotropy data from the WMAP satellite, combined with other CMB experiment data, and other data such as the 2dF Galaxy Redshift Survey, constrain the sum of absolute masses of the neutrino states to be less than -2 eV (depending on assumptions)62. These results now rival laboratory kinematic limits, and constrain scenarios involving sterile neutrinos63. There are even prospects for attaining sensitivity to neutrino masses as low as 0.1 eV via precision cosmological measurements (e.g Reference 64 .)

7.6. Neutrino Astrophysics

Very large area long string water Cherenkov detectors (AMANDA, Baikal, Antares, Nestor and the next-generation kilometer-scale IceCube) in ice and water are embarking on a new era of high energy neutrino a s t r ~ n o m“Cosmic particle accelerators” such as active galactic nuclei and the cata- clysmic events that produce gamma-ray bursters, are expected to produce - PeV neutrinos, visible in these detectors as upward-going events. Ex- otic astrophysical sources that produce ultra-high-energy neutrinos may be associated with the highest energy cosmic rays, too. In fact, detectors designed primarily to explore ultra-high-energy cosmic ray air showers will have sensitivity to neutrino-induced “earth-skimming” horizontal air showed6. Because the Earth starts to become opaque, via CC interactions, to vP and ve at a few hundred TeV, and v,’s LLregenerate77 as the CC-induced 7’s decay, the flavor content of the flux (and the effect of oscil-

1 59

lations) can be explored by looking at the angular distribution of observed events. From these neutrinos, we may learn about the physical mechanisms behind the ultra-high-energy sources, Measurement of the relative timing between neutrinos and photons from the same source will test special rela- tivity and the weak equivalence principle.

8. Summary

It is now quite certain that neutrinos have mass and mix: atmospheric and solar oscillation signals are now multiply confirmed and parameters are quite well constrained. The LSND observation does not fit in to the three-flavor picture; we await BooNE to confirm or refute it. If BooNE confirms the LSND appearance observation, we will have to begin exploring the possibilities required to explain it. If not, and the standard three-flavor scenario holds, the next steps for neutrino oscillation experiments are clear: search for non-zero 1313, determine the mass hierarchy and ultimately, if parameters are favorable, go for leptonic CP violation. On the non-oscillation front, absolute mass can be approached via kinematic experiments and double beta decay, the latter also promising insight into the Majorana- vs-Dirac question. Precision cosmology is also making headway towards understanding of neutrinos. Knowledge of these parameters is essential for full understanding of matter-antimatter asymmetry of the universe, as well as a full description of the fundamental particles and their interactions. Although this last decade will be a hard act to follow for excitement in neutrino physics, the next decade promises yet more entertainment.

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SEMILEPTONIC B DECAYS AT LEP: EXTRACTION OF VCB AND B-+ D** 1~

PEDRO AMARAL* High Energy Physics, University of Chicago,

5640 S. Ellis Ave, Chicago, IL 60637-1433, USA

E-mail:[email protected]. edu

The extraction of the CKM matrix element V& using the semileptonic decays B + D*+eF at LEP is reviewed. The major systematic error comes from the background process + D**OeF. Measurements of + D**'eV performed at LEP are reviewed, with emphasis on a new OPAL result.

-4

1. Introduction: B" + D*+1F at LEP

The CKM matrix element v c b is one of the fundamental parameters of the Standard Model, and can be extracted using semileptonic B decays. In these, the leptonic current offers a clean experimental signature and its theoretical modelling is well understood. The advances in Heavy Quark Effective Theory (HQET) now provide a solid theoretical framework to study the hadronic current. The high boost at the Zo pole at the LEP experiments provides some distinct advantages to study these decays: the existence of displaced vertices and some theoretical important simplifica- tions, as compared to the T(4S) experiments. The experimental challenge, is to correctly identify the relevant tracks in a very narrow jet.

As of early 2003 [I, 21 the best measurements of v c b still come from the LEP experiments, namely from studying the decay B + D*+CV a

followed by D*+ -+ Don+. This is achieved by measuring the differential rate as a function of w (the product of four-velocities of the B and D*+)

-0

4

*Work partially supported by grant PRAXIS/BD/11460/97, FCT, Portugal. &Here, and throughout this paper, B refers to the Bo and B- mesons, and charge conjugate modes and reactions are always implied. Also, e refers to both electrons and muons.

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and extrapolating to w + 1. Fig. 1 shows the w spectrum as reconstructed by the OPAL experiment [3], with the superimposed likelihood fit. The major background source are resonant decays B -+ D**O CF, where D** are the orbitally excited charm mesons.

300

200

100

1 1.1 1.2 1.3 1.4 1.5

. ".." 0 Bo + D'Tv

resonant bgd.

reconstructedi

Figure 1. OPAL Distributions of reconstructed w for (a) C opposite sign to D*+ and (b) same sign C and D*+ events with Am = m(D*+) - m(Do) < 0.17GeV. The data are shown by the points with error bars and the expectation from the fit result by the histograms. The contributions from signal B D*+C-D, resonant and combinatorial backgrounds are indicated.

-0

Hence, the systematics in the measured value of Vcb are dominated by the theoretical uncertainties in the rate and shape of the B + D**OCF process. These are predicted using HQET expansions with several free parameters, that can be constrained [l, 21 using experimental input, namely the ratio of branching ratios b**:

where D1 and Df are the narrow orbitally excited charm mesons.

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2. D** orbitally excited charm mesons

These are the orbitally excited L = l bound states of a charm and a light (u,d) quark. In the Heavy Quark limit, parity and angular momentum predict four neutral (and four charged) states:

0 The D1 and DI are narrow as they can decay only via D-wave. Their existence is well established, with masses of 2420 and 2460 MeV and widths of N 20 MeV [l].

0 There are also two predicted broad states (as they should decay only via S-wave), but despite several claims, their existence and properties have not yet been firmly established [l]. Data from the B-factories might soon change this [4].

There can also be non-resonant decays constitute a significant part of the inclusive semileptonic width [5, 61.

+ D*+n-C-V that apparently

I v t ’

Figure 2. Event topology for a semileptonic B decay into a D**O l - D , Dtr0 + D*+x-, D*+ + Do,+, Do + K 37r, with the 3 reconstructed vertices shown.

3. B 3 D**O t F at LEP - mass resonance analysis

The analysis is similar to B” + D*+Cn, but one tries to find the extra n coming from the D**O decay. To distinguish it from the other n’s we label it n**. The mass difference Am** = m(D**’) - m(D*+) is reconstructed and one looks for the D1 and D; narrow resonances at their know masses. The

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exclusive reconstruction of the full decay chain D**' C - V , D**' -+ D*+7r-,

D*+ -+ DOT+, Do -+ K37r or Do -+ KT, is necessary in order to have good Am** mass resolution and to fight background '. The culprit is then to correctly identify 7 (or 5) tracks: the lepton l , the x,1,, coming from the D*+ decay, the Kaon and the (three or one) 7r's from the Do decay and most importantly the T** . To achieve this, the three separate vertices (primary vertex and the ones corresponding to the B and Do decay) of the event need to be reconstructed. This is shown in Fig. 2. The vertexing and tracking capabilities using silicon detectors are crucial, in order to separate true 7r**'s coming from D** meson decays, and 7r's from b quark fragmentation. A mass resonance analysis has already been performed at LEP by ALEPH [5] and OPAL [7], the latter using only less than half of the data collected by OPAL at the Zo resonance.

4. OPAL new result on B -+ D**O

The OPAL collaboration recently presented a new result [8], using the full Zo data set and better analysis techniques. It confirmed the results of ALEPH [5] in the D**' -+ D*+7r- mode, finding evidence of decays into the DY state, with a product branching ratio:

BR ( b -+ B) x BR (B -+ DY f T G X ) x BR (DY -+ D*+7r-) =

(2.64 f 0.79 f 0.39) x

where the first error is statistical and the second systematic. This is consistent with the value measured by ALEPH [5]:

BR ( b -+ B) x BR (B -+ Dy !-ox) x BR (Dy -+ D*+7r-) =

(1.68 f 0.38 f 0.29) x

No evidence was found for decays into the D; state and a 95% CL was set. The Am** mass spectra measured by OPAL is shown in Fig. 3. We note the complementarity between the T(4S) results, where theoretical uncertainties of the 7r** energy spectra dominate the systematic uncertainties. This is almost inexistent at LEP, due to the high boost of the decaying B mesons in Zo events.

The angular information of the D** decays was also analysed by OPAL to confirm the presence of the DY state and absence of the DfO. In the Heavy Quark limit, DI should decay according to (1/4)(1+ 3 cos2 a) whereas D;

bALEPH [5] also uses the Do decays into Ksmr and K7rr0.

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OPAL D0+Kx and K3x D, events = 28.1 f 8.6

I 5 E f 25

B 20

15

10

5

0

Amm*(GeV)

Figure 3. OPAL Am** distribution for semileptonic B decays into D**O l -0 , D**O -+ D*+a-, D*+ + DOT+, and Do + K 3 x combined. The superimposed lines show the overall fit and the background fitted shape. The expected positions of the DY and DS0 are indicated by the arrows.

decays have a distribution (3/4)(1-cos2 a). Here a is the angle between the T** and the slow pion 7r,lOw as measured in the D*+ restframe. Therefore, the DT mass peak should be enhanced for larger values of I cos aI, and for D;*, for small values of I cos (YI. The angular information present in OPAL data indeed shows this trend, as shown in Fig. 4.

5. Conclusions

The LEP analysis of semileptonic B decays are by now very "mature". Still, some new or updated analysis have been performed to attempt to extract every bit of info from the good old LEP data. A new OPAL result on B+ D**O L v was reported.

Acknowledgments

The author thanks the organizers of this most interesting and educational conference. His participation was made possible with the support of CITA.

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8 50 ' 40

30

20

10

0

&

% 20 E 17.5

15 $ 12.5

2.5 0

0 0.2 0.4 0.6 0.8 1

Icos(a)l D D '

1'1

Icos(a)l > 0.5

0.2 0.4 0.6 0.8 1

50

40

30

20

10

0

20 17.5

15 12.5

10 7.5

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OPAL 0.6 <Am*: < 1.1 GeV

0 0.2 0.4 0.6 0.8 1

Icos(a)l D D '

1'1

0.2 0.4 0.6 0.8 1

Am** (GeV) Am** (GeV)

Figure 4. OPAL Distributions dependent on the decay angle a: a) Icos(a)l for the combined Do + K s and Do + K 3 s data and Monte Carlo in the 0.35 < Am** < 0.55 GeV signal band; b) complementary events to a) in the 0.14 < Am** < 0.3 and 0.6 < Am** < 1.1 GeV sidebands; c) Am** data distributions for Do + K s and Do + K 37r combined data in the Icos(a)l > 0.5 region (expected to enhance the D1 signal); d) complementary events to c) for I cos(a)l < 0.5 (expected to suppress the D1 signal). The expected positions of the D1 and Df are indicated by arrows.

References 1. 2.

3. 4.

5. 6. 7. 8.

The Review of Particle Physics, K. Hagiwara et al., Phys. Rev. D66 (2002). R. Hawkings, Nucl. Instr. and Meth. A462 126 (2001); M. Artuso and E. Barberio, hep-ph/0205163. OPAL Collaboration, G. Abbiendi et al., Phys. Lett. B482 15- (2000). P. Krokovny, BELLE Collaboration, Contributed talk to ICHEP2002, Ams- terdam. ALEPH Collaboration, D. Buskulic et al., 2. Phys. C73 601 (1997). DELPHI Collaboration, P. Abreu et al., Phys. Lett. B457 407 (2000). OPAL Collaboration, R. Akers et al., 2. Phys. C67 57 (1995). OPAL Collaboration, G. Abbiendi et al., CERN-EP/2002-094, submitted to Eur. Phys. C, hep-ex/0301018.

B PHYSICS AT CDF

K. ANIKEEV* MIT, Fermilab - CDF - MS#318

Batavia, IL 6U51U-U5OU E-mail: [email protected]

B physics is at the core of the CDF agenda for Run 11. With the Tevatron performance gradually improving, samples of data corresponding to about 70 pb-l are now available. Due to improved detector capabilities these data already allow one to improve a number of Run I results, as well as perform a series of new measurements. We present an overview of the current state of B physics at CDF.

1. Introduction

The CDF detector has been upgraded to match the physics goals' and to take full advantage of the improved Tevatron performance. Unlike the B factories, B hadrons produced at the Tevatron are not limited to B+ and Bo, but also include heavier species such as B,, Ab, Eb , etc. These latter ones are at the focus of the CDF Run I1 B physics program. Measurements of mixing and the width difference between CP eigenstates in the B, system, CKM measurements in B, + J/$~q5 and B + h+h-, measurements of masses and lifetimes of B,, B,, and are just the beginning of the list of exciting results that are expected from Run 11.'

2. Triggers and Data Samples

An abundant program is enabled by the Tevatron's high CM energy of fi = 1.96 TeV and b production cross-section of the order of 0.1 mb. The cross- section for background processes is also very large, about 75 mb, therefore a carefully designed triggering scheme is needed. B physics at CDF relies on three major triggers. These are discussed in the following sections along with the respective data samples and the first Run I1 results extracted from them.

*On behalf of the CDF collaboration

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2.1. Di-muon Trigger. J/q5 Sample

The di-muon trigger requires two oppositely charged muons with p~ > 1.5GeV/c in the pseudo-rapidity region 1171 < 0.6 or one muon in this 17 range and the other one in the 0.6 < 1171 < 1.0 range with p~ > 2.2 GeV/c. Most of the di-muons come from J / $ decays, but $' and 'Y contribution is also significant. Due to the lower p~ threshold and the increased detector acceptance, the J / $ yield is up from 2.5nb in Run I to 7.6nb in Run 11.

550K 619. cands.

d 2

1

2.0 1.0 1.1 1.2 3.1 (p+pl mass, GeVlc'

f f , , , <j ,:.*> , , , 1 1

2.0 1.0 1.1 1.2 3.1 (p+pl mass, GeVlc'

Figure 1. decay length and mass (inlay) distribution with fit results overlaid for B+ + J /$JK+.

(a) Sample of J / $ candidates after typical quality cuts are applied. (b) Proper

A clean J / $ sample (Fig. la) is crucial for detector understanding, but it is also a basis for a number of important physics measurements. Ten to 35% of these J /$s , depending on p ~ , are coming from B decays, such as B+ + J / $ K + , Bo + J/$K*O, B, + J/$+, and A! + J /$Ao . One can determine the average B lifetime using J / $ vertices for the transverse decay length measurement and correct p T ( J / $ ) by a Monte-Carlo K-factor for the proper decay length extraction. Using a sample of 18 pb-', we measured C T B ~ ~ ~ , , = 458 f lo(stat.) f l l(syst.) pm, which is in good agreement with the PDG value of 469 f 4pm. This large statistics measurement serves as a benchmark of the detector lifetime measuring capabilities.

In the exclusively reconstructed modes mentioned above, one can extract both the mass and the lifetime of the B hadrons. We use a simultane- ous maximum likelihood fit to the mass and lifetime distributions (Fig. lb) to extract the latter. The lifetimes we measure using 72 pb-l of data are:

TB+ = 1.57 f 0.07 (stat.) f O.O2(syst.) PS

TBO = 1.42 f 0.09 (stat.) f 0 . 0 2 ( ~ y ~ t . ) PS

TB, = 1.26 f 0.20 (stat.) f 0.02(syst.) ps

In measuring masses one has to account for energy lost by tracks in the material of the detector. One of the difficulties is that the GEANT material map for a detector as complicated as CDF cannot be absolutely complete

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and accurate. Precise knowledge of the magnetic field is also required. We perform a material and magnetic field calibration using J / $ (Fig. 2a) and cross-check on T which comfortably covers the range of expected B masses. Given the current level of statistics and our understanding of systematic

d

H

Figure 2. (a) Material and magnetic field calibration using J / $ . (b) Mass distribution of the B, -+ J / $ 4 candidates with typical cuts (including L,, > 100pm) applied.

effects, we expect the world best mass measurements for B, (Fig. 2b) and Ab in the near term future.

2.2. Displaced Track + Lepton Trigger. 1 f D Sample

The displaced track + lepton trigger requires a muon or an electron with p~ > 4 GeV/c and a track with p~ > 2 GeV/c and impact parameter w.r.t. beam line, do, satisfying 120pm < do < lmm.3 The data sample obtained via this trigger is rich in semi-leptonic B decays and is called 1 + D sample.

There are two major uses of 1 + D sample. The first one is development of flavor A tagger is a tool, which determines the flavor of b quarks at production ( b or 5). Such tools are necessary ingredients for any flavor asymmetry analysis, but they are intrinsically imperfect. Each tagger is characterized by two quantities: the efficiency 6, and the dilution D = 1-2w, where w is the mis-tag probability. The error on the asymmetry scales as l / a , thus maximizing e l l 2 is a very important task. Most of the asymmetry measurements will be done in the TTT sample (Sec. 2.3), therefore 1 + D is unbiased high statistics sample for tagger optimization.

The other extremely important use of the 1 + D sample is for measuring lifetimes of B hadrons in their semi-leptonic decays. A clear benefit of this method is large statistics, which is even more important for rare species, such as B, and Ab. The complication of the analysis comes from a non- trivial trigger efficiency w.r.t. the proper decay length resulting from the impact parameter cut described above. CDF uses a realistic Monte-Carlo, that implements all running conditions and weights events by integrated

taggers.

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B+-+Dol+X 1 2928 f 65

luminosity, to unfold the trigger efficiency from the lifetime measurements.

N 12K

CDFRunII Pmliminary,L=72 f 4 p b "

914f89 sig. cands. --587+44 rg. Cands. ,.- m - -1

k

Bo -+ D-l+X B, -+ D;l+X A(, + AZ1-X

(Km) mass, GeVlc' (pKn) mass, GeV/c'

Figure 3. D-l+X. (b) A$ candidates from semi-inclusive reconstruction of A t -+ Ag1-X. The shaded histogram shows the same after particle ID (using time of flight and dE/dx information) is required on the proton from A, decay.

(a) D- candidates from semi-inclusive reconstruction of Bo

1997 f 65 N 6.2K 220 f 21 N 600 197 f 25 N 600

Figure 3 shows the mass spectrum of D- candidates from semi-inclusive reconstruction of Bo + D-Z+X and the mass spectrum of A: candidates from A: + AZZ-X. The Run I1 yields are compared to those from Run I in Table 1. Already at this time CDF has by far the largest in the world samples of semi-inclusively reconstructed B, and Ab.

Table 1. Yield comparison for semi-inclusively reconstructed B hadrons.

2.3. Displaced Vertex + High p~ Tracks Trigger. TTT Sample

The Two Track Trigger (TTT) data sample is collected using a trigger which requires displaced high p~ tracks (as described in the beginning of Sec. 2.2) and a secondary vertex. In reality TTT is a combination of triggers with one path optimized for two-body decays like B + hth; and the other one optimized for multi-body decays like B(,) + D(s)(3)7r. Before this trigger came into existence the only way to control backgrounds in b production was to require leptons, which limited the variety of analyses one could do.

The advent of the TTT has enriched the B program, but it has also opened up charm physics at CDF. In fact, high statistics charm signals were used to understand/tune the trigger. In the process of doing so a number of charm results have been obtained. Using only 10pb-I of data, CDF

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measured the ratios of the branching fraction of the Cabbibo-suppressed decays Do + K K , TT to that of the Cabbibo-favored decay Do + KT:

= 11.17 f 0.48(stat.) f 0.98(syst.)% B ~ ( D O - + K+K-) B r ( D O t K - n + )

Br(Do +T+K-) = 3.37 f O.aO(stat.) f O.lG(syst.)% Br(Do t K - d )

With more integrated luminosity CDF has obtained significant samples of D*-tagged Do and decaying into K K and TT (Fig. 4). These will

Id COF ~ u n II Preliminary, L = BS + 4 pb ' 83Mf-140 619 cands

t ++t+

tt '+

3 3:: Do+K*K

'S 8 -

a : + t (I I 4- H + E

+ 2- *** *-

--*-*--

Pm' ' ' ldl ' ' ' ' 128 ' ' ' ' 116 ' ' ' ' 1 W (KK) mass, GeV/c2

Id COF Run I1 Preliminary, L = BS + 4 pb -' 83Mf-140 6ig. cands. 2 D'+K*K

ldl 128 116 1.W PL' ' ' ' ' ' ' ' ' ' ' ' ' ' ' '

(KK) mass, GeV/c2

COFRun IIPrelmlmry,L=e5 f 4 p b "

3697m sq can&

t'. + + + 1- 4 2 - A + I3

1 + ++-+ +:---

+;

1- + -t +

f i 2 ' ' lM 116 ?16 " ' ' ' ' ' ' ' '

(un) mass, GeVlc 0

Figure 4. Do candidates reconstructed in their decays to: (a) K K , (b) mr.

allow us to substantially improve the precision of the above quoted ratio measurements, as well as measure direct CP asymmetry, which, if found to be above 1%, would strongly suggest physics beyond the Standard Model.

Another exciting result we obtained from the TTT sample is the measurement of the mass difference between D$ and D+, which are reconstructed in their decay mode to $T (Fig. 5a). Common selection and decay kinematics make the systematic uncertainty of this measurement very small. We find4 mot -mD+ = 99.41f0.38(stat.)f0.2l(syst.) MeV/c2, which agrees with the world average and has a similar precision.

(KKn) mass, GeVlc'

Figure 5. Invariant mam distributoion: (a) 06, 3 &r+, (b) B t hh.

Hadronic two body decays Bo + TT, K+T-, and B, + K K , K+n- will allow us to measure the CKM angle y. Although these decays have

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very small branching fractions, CDF has already observed a significant number of them, as shown in Fig. 5b. The width of the mass peak is larger than the detector mass resolution because the peak is a composition of 4 decay modes. A technique to statistically separate these contributions using particle identification with dE/dx is holding promise.

The branching fraction of the decay B(,) -+ D(,)T is a couple of orders of magnitude higher. In 65 pb-l of data we observe about 500 Bo + D-T+ candidates (Fig. 6a) and about 40 B, + D ; d candidates (Fig. 6b). At

CDF Run II Preliminary, L= 65 * 4 p b '

D' yield 505+44 cands.

4 . e ' ' ' CB ' ' ' ' 5.0 I ' " 5 1 " " 5.4 I ' ' ' sd (Kxm) mass, GeV/c2

Figure 6. Invariant mass distribution: (a) Bo + D(*)-?r+, (b) B, -+ D!i*)-?r+.

present time we pursue the measurement of the ratio of the branching fractions of the two decays, while eventually B, + D;T+ as well as B, -+ D;T+T+T- will be used to measure B, mixing.

3. Conclusions

The upgraded CDF detector is back in operation and has accumulated in excess of 70pb-' of data. Though detector understanding is an ongoing process, the CDF collaboration is clearly in a phase where competitive analyses can be done. The majority of the detector systems perform according to or close to the specifications. CDF has already made a number of interesting B physics measurements with Run I1 data, but many more will surface given more time and/or increase in total integrated luminosity.

Acknowledgment

Participation at the Lake Louise Winter Institute was made possible with support from the Canadian Institute for Theoretical Astrophysics (CITA) .

References 1. The CDF I1 Collaboration, The CDF I1 Detector. Technical Design

Report, FERMILAB-Pub-96/390-E (1996)

1 74

2. K. Anikeev et al., B Physics at the Tevatron: Run I1 and Beyond, FERMILAB-Pub-01/197 (2001)

3. W. Ashmanskas et al., NIM A 501, page 201-206 (2003) 4. The CDF I1 Collaboration, Measurement of Mass Difference m + -

m D + at CDF I1 , submitted to Phys. Rev. D.

TRIPLE AND QUARTIC GAUGE COUPLINGS AT LEP2

IAN BAILEY Department of Physics and Astronomy,

University of Victoria, Victoria, BC, V8 W 3P6, CANADA

E-mail: ian.baileyOcern.ch

The search for anomalous couplings between electro-weak gauge bosons at LEP2 is briefly reviewed and a selection of preliminary limits obtained by the four LEP experiments is presented. All results are consistent with Standard Model expectations.

1. Introduction

The non-Abelian, SU(2) x U(l), group structure of the Standard Model requires tree-level interactions between the electro-weak gauge bosons. Only the minimal set of couplings necessary to ensure gauge invariance is contained in the Standard Model Lagrangian. Additional tree-level couplings between gauge bosons can be introduced whilst preserving the gauge symmetry if we allow the Lagrangian to be non-renormalisable2. Such “anomalous couplings” are possible manifestations of new physics operating at a high energy scale in the electro-weak sector, e.g. sub-structure of the W bosons or loop corrections due to the exchange of super-symmetric particles.

Precision measurements from low-energy LEP data and other sources have been used to place model-dependent limits on anomalous couplings3. In recent years these constraints have been supplemented by direct measurements of the gauge boson interactions made by the detector collaborations based at both the Tevatron4 and LEP5 colliders. This paper summarises the latest combined results from the LEP detector collaborations using data gathered during the period 1996 to 2000 (LEP2).

Table 1 shows all possible combinations of three and four electro-weak gauge bosons which can interact through anomalous couplings (only electric charge conservation has been assumed). Couplings involving W bosons are referred to as “charged” whilst those involving only Z bosons and photons are referred to as “neutral”. Whereas all of the charged couplings

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have a tree-level Standard Model contribution, the neutral couplings are entirely absent at tree-level in the Standard Model. Eleven of the fifteen combinations in the table are kinematically accessible at LEP2 energies, but this review omits neutral triple gauge couplings6 and combinations which contain less than two massive bosons7.

Table 1. Combinations of electro-weak gauge bosons whose interactions have anomalous triple gauge coupling (TGC) or quartic gauge coupling (QGC) dependence. Combinations in parentheses are not measured at LEPP.

The remaining five combinations are discussed in the following sections. LEP combined results for charged triple gauge couplings (TGC) are presented in section 2. Results for quartic gauge couplings (QGC) are presented in section 3. Section 4 concludes the paper with a brief summary.

2. Charged Triple Gauge Coupling

The most general Lorentz invariant and U ( l ) e m symmetric WWy coupling is described by seven energy-dependent parameters8. The number of parameters is consistent with the general observation that a particle with a spin of J can have no more than 6 J + 1 electromagnetic form factorsg. An additional seven parameters are needed to describe the WWZ coupling. Imposing charge conjugation and parity symmetries and setting the charge of the W boson to its Standard Model value reduces the fourteen parameters to five {K, , K Z , A,, Az, g:}. Their Standard Model values are gf = K, = KZ = 1 and A, = AZ = 0.

Several ways to motivate constraints amongst the parameters can be found in the literaturelo. The two constraints used for the LEP combination (equations 1 and 2) are derived assuming that the Higgs boson is light (consistent with unitarity constraints) and that the energy scale of the new physics responsible for the anomalous couplings is of the order of 1 TeV or higher.

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(1) K.Z = g1 - (K., - 1) tan2 Ow

Az = A, (2)

Z

The set of free parameters extracted from the LEP data is chosen to be

Data from W-pair production (e+e- -+ W+W- ), single W production (e+e- -+ WeYe) and single photon production (e+e- -+ yveYe) are used in the analysis. The TGC dependent tree-level Feynman diagrams for each of these three processes are shown in figure 1. The most statistically signifi-

{g?, K.7 m d A,>.

Figure 1. dots).

Feynman diagrams containing charged TGC vertices (denoted by the black

cant is W-pair production; approximately 10,000 of these events were gathered by each LEP experiment. Anomalous values of the TGC parameters are constrained by measurements of the total cross-section, the differential cross-section with respect to the W production angle and the angular distributions of the W decay products in the W rest frame. The total and differential cross-sections are also sensitive to electro-weak loop effects which are included in LEP Monte Carlo simulations up to O(aem). Uncertainty in the effect of the missing higher order loop corrections is the dominant systematic error in the preliminary TGC parameter measurements. Con- tinuing studies are expected to lead to reductions in the systematic error for future LEP results'. From the cross-sections and angular distributions, the LEP collaborations use a variety of optimal observable and unbinned likelihood fit methods to extract values of the TGC parameters.

At LEP centre-of-mass energies, the Standard Model cross-section for single W production is an order of magnitude less than that for W-pair

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production. The purity of the event selection is also low due to the mis- reconstruction of semi-leptonic final states from W-pair events. Single photon production has a slightly higher cross-section than the single W production, but the Standard Model cross-section is dominated by radiative return to the Z peak which dilutes any effect due to anomalous couplings. Despite these limitations, useful information can be extracted from the measured event rates of both processes and from the energy spectrum and angular distribution of the photon in the single photon events.

The current preliminary results from the individual detector collaborations at LEP are shown in table 2. Also shown are the combined results obtained using a likelihood fit procedure designed to take into account asymmetries in the likelihood curves and the correlations between the systematic errors. The fitting procedure is repeated for each parameter individually, where the two parameters not being measured are set to their Standard Model values. Some collaborations have yet to include their full data set in these results.

Table 2. Preliminary measurements of charged TGC parameters from the individual LEP detector collaborations and the combined result. The errors include both the statistical and systematic effects.

\ ALEPH 1 DELPHI 1 L3 I OPAL \I LEP I

I I I I I

3. Quartic Gauge Coupling

Using similar considerations to those in section 2, five parameters are sufficient to describe the anomalous QGCs at LEP. Of these, two describe the WWyy vertex ( a y , a y ) , two describe the ZZyy vertex (ag,a:) and one CP violating coupling describes the WWZy vertex (an). The Standard Model tree-level contribution to all of these parameters is negligible at LEP energies.

The final states used in the LEP QGC analyses are WWy, Zyy and vvyy. The tree-level Feynman diagrams dependent on the QGC parameters are shown in figure 2.

The vvyy final state, where two acoplanar isolated photons are reconstructed in the detector, has contributions from both the WWyy and ZZyy

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Figure 2. Feynman diagrams containing QGC vertices (denoted by the black dot).

processes. The recoil mass of the observed photons tends to peak at the mass of the Z boson due to the Standard Model double radiative return. This peak is enhanced for anomalous values of uf or u:. Anomalous values of u r or u," tend to generate more events in the low recoil mass region.

The WWyy and WWZy vertices contribute to the WWy final state where a hard isolated photon is required in addition to the hadronic or leptonic decay products of the W bosons. Limits on a, are set using the measured total cross-section.

The current 95% confidence limits on the charged QGCs are shown in table 3. The LEP combined limits have not yet been completed. The limits on the neutral QGCs are shown in table 4.

Table 3. Preliminary 95% confidence limits on the charged quartic gauge coupling parameters. A is the energy scale of the new physics.

Table 4. Preliminary 95% confidence limits on the neutral quartic gauge coupling parameters. A is the energy scale of the new physics.

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4. Conclusions

All current LEP gauge coupling measurements are consistent with Standard Model predictions. Full details of the LEP combined measurements and references to the papers of the individual collaborations can be found in the LEP electro-weak working group report5. Final gauge coupling results from LEP are expected to be ready for publication in the near future.

Acknowledgments

The author’s participation at the Lake Louise Winter Institute was made possible with the support of the Canadian Institute for Theoretical Astro- physics (CITA) .

References 1. M. Beccaria, F.M. Renard and C. Verzegnassi, preprint hep-ph/0304175vl,

17th April 2003. 2. G.J. Gounaris and F.M. Renard, Z. Phys. C59 (1993) 133. 3. M. Beccaria, F.M. Renard, S. Spagnolo and C. Verzegnassi, Phys. Lett. B448

(1999) 129; S. Alam, S. Dawson and R. Szalapski, Phys. Rev. D57 (1998) 1577.

4. B. Abbott, et al. , Phys. Rev. D62 (2000) 052005. 5. D. Abbaneo, et al. , CERN-EP-2002-091. 6. G.J. Gounaris, J. Layssac and F.M. Renard, Phys. Rev. D62 (2000) 073013. 7. M. Baillargeon, F. Boudjema, E. Chopin and V. Lafage, Z. Phys. C71 (1996)

431. 8. K. Hagiwara, R.D. Peccei, D. Zeppenfeld and K. Hikasa, Nucl. Phys. B282

(1987) 253. 9. F. Boudjema and C. Hamzaoui, Phys. Rev. D43 (1991) 3748. 10. Physics at LEP2, edited by G. Altarelli, T. Sjostrand and F.Zwirner, CERN

96-01 Vol. 1, 525.

RECENT RESULTS ON NEW PHENOMENA FROM DO

F. BEAUDETTE* Laboratoire de 1 'Acce'le'rateur Line'aire,

BP38, 91898 ORSAY cedex, France E-mail: beaudettOlal.in2p3.fr

The New Phenomena searches in proton-antiproton collisions at a center-of-mass energy of 2TeV with 10pb-' data collected between January and June 2002 in the upgraded DO detector at the TeVatron are described.

Between 1992 and 1996, about 110 pb-' have been collected in DO and CDF, the two TeVatron detectors. At that time, the center-of-mass energy of the proton-antiproton collisions was 1.8 TeV. The energy of the collisions has been increased up to 2TeV which leads to a 30% increase of most cross-sections. Moreover, an increased luminosity and two upgraded detectors will make from the TeVatron a place of major interest for the search of new particles.

1. Search for Large Extra Dimensions

In some string theories, the Planck scale, Ms, is lowered down at the TeV scale, and can be thus probed in colliders. In such theories, the Standard Model particles are confined on a 3-dimension brane whereas the gravity propagates in other dimensions. These theories can be tested by looking for the effect of virtual graviton exchange in fermion or boson pair production (see Fig. 1).

Presently, two channels are studied: the combined di-electrons and di- photons channels and the di-muon channel. Two variables yield optimum sensitivity to the constributions from extra-dimensions: the invariant mass of the lepton/boson pair and cos8* where 8* is the scattering angle in the rest frame.

'for the DO collaboration.

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182

2

+ 2

Figure 1. dimensions.

Feynman diagrams for dilepton production in the presence of large extra

1.1. Di-electromagnetic channel

The signal selection consists in requiring two electrons or photons with a tranverse energy greater than 25GeV/c, with at least one of them being central. No requirement on a track match is made. A small missing transverse energy is also required. The electromagnetic triggers used in this analysis are fully efficient on the selected signal. About 10pb-l of integrated luminosity are used.

The main backgrounds are the Drell-Yan events, direct photon production and electron or photon mis-identification. The first two backgrounds are estimated with similated events, whereas the last one is deduced from the data. Its shape is determined by imposing anti quality cuts on the electromagnetic objects, the normalization is obtained by comparing the invariant mass spectrum of the two electromagnetic objects in the data and with the sum of all backgrounds in the low mass region where the signal is not expected to show up.

D0 Run 2 Preliminary

Figure 2. The di-electromagnetic mass us. COSP. Top left: standard model background; top right: data; bottom left ED signal plus SM background; bottom right: instrumental background.

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The comparaison of the distributions presented in Fig. 2 allows to set a limit on the Planck Scale in the Giudice-Rattazzi-Wells’ formalism of 0.92 TeV, with about 10 pb-l. The Run 1 with twelve times this integrated luminosity excluded M s < 1.2 TeV.

1.2. Di-muon channel

For the first time at a hadron collider, a similar analysis requiring two muons in the final state is carried out. A di-muon trigger is used, and the timing of the hits in the muon scintillators is crucial to remove cosmic muons faking di-muon events. The two muons are required to be away from jets to avoid the heavy flavors background. With 4.5pb-l of integrated luminosity, values of M s lower than 0.50 TeV are excluded.

2. R-parity violating Supersymmetry (SUSY) in the di-electron+jets channel

At the TeVatron, the supersymmetric partners of the quarks, the squarks, are produced by pairs in quarks annihilation or gluon fusion. Lightest Supersymmetric Particles (LSP) are produced when they decay. In R- parity violating SUSY models, the LSP is not stable. In this analysis, only the Yukawa Xij, coupling is considered. As a result, the LSP decay gives an electron and jets. The final state has a high jet multiplicity and two isolated leptons. Since the neutralino is a Majorana particle, the two leptons can be like-sign; in this case the standard model background is minimal.

The analysis requires two electrons with p~ > 15GeV/c and p~ > 10 GeV/c, and one of them being central. Both electrons must be far from each other, and away from jets. Only jets with p~ > 20GeV and 171 <2.6 are considered.

The dominant background are standard model processes with wrong charge assignment and electron misidenification. In lOpb-l, ten events are observed, none of them having a jet multiplicity higher than 2. This is compatible with the standard model expectations.

3. SUSY search in the tri-lepton channel

The tri-lepton final state, the lepton being an electron or a muon, may turn out to be the golden channel for SUSY discovery at the TeVatron. This final state can be obtained in R-parity violating models or in non-violating models with chargino-neutralino production. The main difference between the two channels being the jet multiplicity, much higher in the former.

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At least two electrons are required with p~ >15 GeVlc and 30 GeV/c . The third lepton can be an electron or a muon. All leptons must be far one from the other; to reduce the heavy flavors semi-leptonic background, the muon, if any, has to be away from the jets. The main source of backgrounds are y* -+ ee plus a radiated photon and the fake electrons in ee+jets or ep+jets events. About 5pb-’ are used in both channels, 2(1) events are observed with an estimated background of 1.9&0.4(0.9&0.2) in the eee(eep) channel. The only eep candidate, which is compatible with a Z + ee event with an additional muon, is represented in Fig. 3.

ETacale 38 GeV

X

77 = -0.92 cp = 2.59

no track match no track match charge = -1 ~ ~~~

melez = 88.9 GeV/c2 MET = 11.9 GeV

Figure 3. (a) 5 - y view (b), T - ‘p view (c) and properties of the eep candidate.

4. Gauge mediated SUSY breaking in di-photon channels

The phenomelogy of the Gauge mediated SUSY breaking (GMSB) models is very different than the gravity mediated SUSY breaking models. In the theoretical framework used in this analysis, the gravitino is the LSP and the neutralino is supposed to be the next LSP; the lifetime of the latter is not fixed by the model and it is assumed that it decays well inside the detector into a photon and a gravitino. As a result, an inclusive search for events with two photons and missing transverse energy is carried out.

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The analysis logically requires two photons with a p~ >20GeV, and a missing transverse energy in excess of 35 GeV. To avoid mismeasurements, the missing transverse energy must not be aligned with a jet.

The direct photons or the jets faking photons in QCD events constitute a background if a fake missing tranverse energy is measured. Weak interaction backgrounds such as Wy + evy are highly suppressed by requiring no track match.

The QCD background is estimated from the data assuming that the ratio of number of QCD events over fake yy events does not depend on the missing transverse energy. The normalization is obtained in the low missing transverse energy region.

Missing Transverse Energy, GeV

Figure 4. is the sum of all backgrounds as obtained from data (QCD, Drell-Yan and e -+ y).

Missing tranverse energy for yy. Points with errors are data, the histogram

Since the number of observed events agree with the standard model expectations, as it can be observed in Fig. 4, a model-independant limit on the di-photon production cross-section, within the acceptance of the analysis, can be set with 9 pb-l:

(T < 0.9pb at 95% confidence level.

5. First generation leptoquarks

The leptoquarks (LQ) are hypothesized particles coupled to quarks and leptons, carrying both lepton and color quantum numbers. They are predicted in many Grand Unification extensions of the standard model. Limits from flavor-changing neutral currents imply that LQ couple only within a single generation. Only the first generation of LQ is studied here. As a result

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only the coupling to e , v and u,d quarks are considered. At the TeVatron the pair production of LQ through gluon splitting is the dominant process.

The final state consists in two isolated electrons and two jets. To avoid the Z j j e e j j background, a veto on the Z mass region is applied. The scalar sum of the two electrons and the two jets transverse energy, ST yields an optimum sensitivity to the LQ signal.

m

Figure 5. (a) ST distribution of e e j j events from data compared to background, after applying a 2-veto cut; (b) the 95% C.L limits on the cross section times branching ratio as a function of the LQ mass.

No excess is observed ; assuming a branching ratio of LQ-+ e j equal to 1, a mass limit of 113GeV/c2 is deduced with 8pb-' (see Fig. 5) .

6. Conclusions

Some of the very first analysis based on 10 pb-' have been summarized. A total integrated luminosity equivalent to Run 1 should be reached before summer 03.

Acknowledgements

The author's participation in the Lake Louise Winter Institute was made possible with the support of the Canadian Institute for Theoretical Astro- physics (CITA) .

References 1. G. Giudice, R. Rattazzi, and J. Wells, Nucl. Phys. B544, 3 (1999), and

revised version hep-ph/9811291.

SEARCH FOR A FOURTH GENERATION b’-QUARK AT THE DELPHI EXPERIMENT AT LEP

N. CASTRO LIP, Av. Elias Garcia, 14 - 1 2 ,

P1100-149 Lisboa, Portugal E-mail: Nuno. CastroOcern.ch

A search for double production of fourth generation b’-quarks was performed using data taken by the DELPHI detector at LEP-11. The analysed data were collected at a centre-of-mass energy ranging from 200 to 209 GeV, corresponding to an integrated luminosity of about 344 pb-l. No evidence for a signal was found. Prelim- inary upper limits on ue+,-+b,g x ( B R b , + b Z ) 2 and U,+,-+b,@ x (BRb,.+cw)2 were obtained at 95% confidence level for b’ masses around 100 GeV/c2.

1. Introduction

The Standard Model (SM) is in excellent agreement with experimental data’, although there are many unanswered questions. Among other parameters, the number of fermion generations and their mass spectrum are not explained by the SM. Evidence for a three generations structure of nature comes from the measurement of the the 2 decay widths’, which establishes the number of light (m < mz/2) neutrino species, N, = 2.9841 f 0.0083. This evidence is consistent with the fit to the electroweak data with three generations, which seems to describe very well the data. Nevertheless, it is also true that when one extra heavy generation is assumed, the fit is as good as the first one2. Moreover, extra generations of fermions are predicted in several SM extentions3.

A fourth generation of fermions can be included in the SM by adding to the known fermionic spectrum a heavy family with the same quantum numbers. In the quark sector, an up quark, t’, and a down quark, b’, are included4.

If kinematically allowed, the b‘ may decay via charged currents (CC), b’ + UW, with U = t’,t,c,u, or via flavour changing neutral currents (FCNC), b’ + b X , with X = Z,H,y ,g . In the SM, FCNC are absent at tree level, but can naturally appear at one-loop level, due to Cabbibo-

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Kobayashi-Maskawa (CKM) mixing. If the b’ is lighter than both the t’ and the t , the CC decays b’ + t’W

and b’ -+ tW are kinematically forbidden. The widths of the CC and FCNC b‘ decays depend mainly on the CKM matrix elements and on the b’ and t’ masses. In particular, for m z < mbt < m H , the b’ -i CW and b’ + bZ decays are expected to be dominant5.

At LEP-I, all the experiments searched for the double production of b’-quarks (e+e- + b’&), giving a mass limit for the b’ close to half of the Z mass6. In the TEVATRON both the DO and the CDF experiments searched for double b’ production. Mass limits were obtained assuming values for the branching ratios (BR) of the studied b’ decays. DO7 found a limit of 128 GeV/c2 assuming BRbt+,W = 1 and CDF’ shows that, for

At LEP-11, DELPHI searched for the double production of b’-quarks BRbt+bz = 1, mbi > 199 GeV/c2.

with mbt N 100 GeV/c2, in both CC and FCNC decays.

2. Data samples and event generators

The analysed data were collected with the DELPHI detectorg during the 1999 and 2000 LEP-I1 runs at fi = 200-209 GeV and correspond to a total luminosity of 344 pb-l.

The main background from known SM processes is expected to be W W , qQ and 22. All the four-fermion final states (both WW and 22) were generated with WPHACTl’, while the qq(y) final state processes were generated with KK2Fl1. Signal samples were generated with PYTHIA 6.2001’. The generated signal and background events were passed through the detailed simulation of the DELPHI detectorg and then processed with the same reconstruction and analysis programs as the real data.

3. Analyses description

The b‘ pair production has been searched for in both the FCNC (b‘ + bZ) and CC (b’ -+ cW) decay channels.

The topologies in which one of the Z bosons decays invisibly and the other decays into quarks or leptons (e+e- + bZbZ + bbvvqq, bbvvll) were studied in the FCNC decay channel. These final states are characterized by the presence of a pair of low energy b jets, missing mass of about 90 GeV/c2 and a pair of energetic leptons or jets.

In the CC decay channel, the topology in which one of the W dcays hadronically and the other decays leptonically was analysed (e+e-

1 89

CWCW + ccqqlv). The signature of this topology is two low energy jets, two energetic jets, an energetic lepton and missing energy.

All the events were forced into two and four jets using the Durham jet algorithm13.

3.1. FCNC bbuull topology search

A sequential cut analysis was performed for this topology. Event preselection was made by requiring the presence of two leptons with polar angles (defined with respect to the beam pipe direction) above 30" and below 150". The angle between the two leptons had to be, at least, 30". Events were also divided into three samples:

(1) electrons (e sample): with two well identified electrons; (2) muons (p sample): with two well identified muons; (3) leptons with non-identified flavour (no-id sample): with two non-

identified leptons or with two leptons identified with different flavours.

The number of selected data candidates (and SM expectations) at this selection level were: 15 (15.5 f 1.3) in the e sample, 21 (25.5 f 1.4) in the p sample and 140 (148.4 f 3.1) in the no-id sample. The signal efficiencies, E , were 15.8%~~ 27% and 11.4%, respectively. In order to obtain the overall signal efficiency, these E must be convoluted with the BRZZ-tvvl l (which is about 4%).

Further selection was performed by requiring the angle between the two electrons to be greater than loo", 125' and 140" for the e , p and no-id samples, respectively. The recoil mass against the two jets was required to be greater than 160 GeV/c2 for the e sample and the missing energy had to be greater than 40 GeV in the p sample. In the no-id sample, the missing energy was required to be above 80 GeV. Also, in this sample, the missing momentum had to be below half of the missing energy. In total, 2 data events (4.2 f 1.1 expected from SM) were selected, for a signal efficiency of 49%. The data candidates belong to the p and no-id samples.

3.2. FCNC bbuuqq topology search

A probabilistic analysis was adopted for this topology. At the preselection level, accepted events were required to have a four jet structure. The Fox- Wolfram normalized momenta sum14 (hl+h3) and (h2+h4) had to be below 0.5 and 1.2, respectively. Also, the polar angle of the missing momentum

190

was required to be above 20" and below 160". A fit imposing energy- momentum conservation was additionaly performed and the (background like) events having X'1n.d.f. < 6 were rejected. After the preselection level, 116 data candidates (107.5 f 3.6 expected from SM) were found, for a signal efficiency of 44.8% (this efficiency must be convoluted with BRZZ+.Yuqq - 28% in order to obtain the overall efficiency).

A signal likelihood, Ls, and a background likelihood, LB, were constructed using probability density functions based on the following variables:

0 AZZ, x min(sin Oql , sin O q 2 ) , where A!& is the acoplanarity (defined in the plane transverse to the beam) and Opl,q2 are the polar angles of the jets (with the events forced into two jets");

0 the event sphericity; 0 the missing mass; 0 the angle between the two jets that best reconstruct the W mass.

The discriminant variable was defined as ln(Ls/LB) for data, SM expectation and signal and can be seen in figure la.

3.3. CC ccqqlu topology search

As for the bbvvqq search, a probabilistic analysis was performed for this topology. Events were divided into three samples: electron sample, muon sample and non-identified lepton flavour sample.

Events were preselected by requiring the polar angle of the lepton to be above 25' and below 155" and the lepton momentum to be above 10 GeV/c. At this level 224 data events (226.5f3.1 expected from SM) were selected in the electron sample, 240 data events (239.1f3 from SM) in the muon sample and 141 data events (144.4f2.7 from SM) in the no-id sample. Signal efficiencies were 14.0%, 17.6% and 5.7% for the electron, muon and no-id samples, respectively. The overall efficiencies can be obtained by the convolution of these values with the BRww+qqzu (-42%).

LS and C B were constructed using probability density functions based on: the event acollinearity (the complementary of the angle between the two most energetic jets); the (hl + h3) Fox-Wolfram momenta sum; the angle between the lepton and the missing momentum; the invariant mass of

&While the four jets topology characterizes the signal, the two jets configuration is used in the background rejection.

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- Data events SM expectation - Signal

l , , , , l ~ , r , , , , l l i l , l . l l l . l , l l l l l l l l , l . l l , 40-12.5 -I0 -75 -5 -25 0 2 5 5

E 75

In (LsLb)

Data events SM erpectafion - Signal

Figure 1. bbuuqq and (b) ccqqlu topologies. Signal normalizations are arbitrary.

Discriminant variable, ln(Ls/LB), for data, expected SM and signal for (a)

the two jets (when the event is forced into two jets); the Durham resolution variable in the 4 + 3 jets transition13; the total momentum associated to charged tracks in the lepton hemisphere; and the total momentum associated to charged tracks in the opposite hemisphere of the lepton. The discriminant variable, In(& / L B ) , for data, SM expectation and signal events can be seen in figure lb .

In order to recover efficiency, events with no leptons seen in the detector were kept in a fourth sample. This sample analysis is similar to the one made for the bbuuqq topology and, at the preselection level, 234 data events (222.5f4.8 expected form SM) were selected for a signal efficiency of 9.7%.

4. Results and conclusions

The data collected by the DELPHI detector at fi = 200 - 209 GeV show no evidence for the double production of b'-quarks with mb' - 100 GeV/c2. The following preliminary limits were obtained at 95% confidence levelI5:

g e + e - + b l & x (BRbt+bZ)2 < 0.18pb (1)

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These limits can be converted into BR limits assuming a value for the cross section of b'b' production at LEP. Using leading order calculations12, ( T , + , - , ~ , Q = 0.6 pb for fi = 207 GeV. The following limits are then obtained:

BRbl -+bz < 55% (3)

BRbl-+cW < 39% (4) Consequently, B&, '+any th ing else > 6%. However, it should be stressed that QCD and QED higher order corrections can be important and are under study.

Acknowledgements

I would like to thank the financial support of the Fundaqiio para a Ciencia e a Tecnologia in this work. I am grateful to the organizers of the Lake Louise Winter Institute 2003 for the kind reception and to CITA for the financial support.

References 1. ALEPH, DELPHI, L3 and OPAL Coll., D. Abbaneo et al., CERN-EP-2002-

091 (2002). 2. V.A. Novikov, L.B. Okun, A.N. RozanovandM.1. Vysotsky, Phys. Lett. B529,

111 (2002). 3. P.H. Frampton, P.Q. Hung and M. Sher, Phys. Rep. 330, 263 (2000). 4. A. Djouadi, J. Ng. and T. Rizzo in Electroweak symmetry breaking and new

physics at the TeV scale, ed. Barklow, Timothy - World Scientific, Singapore (1997).

5. A. Arhib and W.S. Hou, Phys. Rev. D64, 073016 (2001). 6. ALEPH Coll., D. Decamp et al., Phys. Lett. B236, 511 (1990); DELPHI Coll.,

P. Abreu et al., Nucl. Phys. B367, 511 (1991); L3 Coll., Adriani et al., Phys. Rep. 236, 1 (1993); OPAL Coll., M.Z. Akrawy et al., Phys. Lett. B246, 285

7. DO Coll., S. Abachi et al., Phys. Rev. D52, 4877 (1995). 8. CDF Coll., T. Affolder et al., Phys. Rev. Lett. 84, 835 (2000). 9. DELPHI Coll., P. Aarnio et al., Nucl. Instr. Meth. A303, 233 (1991);

DELPHI coll., P. Abreu et al., Nucl. Instr. Meth. A378, 57 (1996). 10. E. Accomando and Ballestero, Comp. Phys. Comm. 99, 270 (1997). 11. S. Jadach, B.F.L. Ward and Z. Was, Comp. Phys. Comm. 130, 260 (2000). 12. T. Sjostrand et al., Comp. Phys. Comm. 135, 238 (2001). 13. S. Catani et al., Phys. Lett. B269, 432 (1991). 14. G . Fox and S. Wolfram, Phys. Lett. B82, 134 (1979). 15. DELPHI Coll., A.L. Read, DELPHI 97-158 PHYS 737 (1997).

(1990).

CLEO RESULTS ON B 3 D*p AND B += DT

G. P. CHEN Physics Department, Carnegie Mellon University 5000 Forbes Avenue, Pittsburgh, PA 15213, USA

E-mail: [email protected]

Using 9.1 fb-' of T(4S) data collected with the CLEO detector at the Cornell Electron-Positron Storage Ring, measurements are reported for the branching fractions and helicity amplitudes for the decay of B + D*p and branching fractions and isospin amplitudes for the decay of B + Dn. The fraction of longitudinal polarization for Bo + D*+p- is measured to be consistent with theoretical prediction, and indicates that the factorization approximation is quite good. The measurements of B + D?r branching fractions are used to determine the strong phase difference 61 between the I = 112 and I = 312 isospin amplitudes. The measured nonzero value of strong phase difference suggests the presence of final state interactions in the D n system.

1. Introduction

Hadronic decays of heavy mesons are complicated by final-state interactions (FSI) which result from gluon exchange between the final states. However, since the products of B meson decay are quite energetic, it's possible that these complicated QCD interactions are less important. One sensitive test of this factorization ansatz is to compare the polarization in B -+ D*p to that in a similar semileptonic decay '. If the factorization hypothesis is valid, one should see similar polarizations in the corresponding hadronic decay. For instance, the fraction of longitudinal polarization, I'L/l?, in Bo -+ D*+p- should be equal to that in Bo -+ D*+Z-V, evaluated

The decays of B -+ DT have AI = AI, = 1 and thus are characterized by two amplitudes A l p and A3p labeled by the total isospin of the final state. Their decay amplitudes satisfy a triangle relation: d ( B - -+ DOT-) = d(Bo + D+T-) + 2/2d(Bo -+ DOT'). The measurements of the branching fractions for these three processes can then provide information for the relative phase 61 between isospin amplitudes 2 .

Our measurements for B -+ D * p and B + DT are based on 9.1 fb-'

at q2 = VIE: rL/r(Bo -+ ~ * + p - ) = rL/r(Bo -+ D*+Z-Y)~ q2=M; '

193

194

of T(4S) data collected with the CLEO detector at the Cornell Electron- Positron Storage Ring, which is corresponding to 9.7 x lo6 BB events. The detector has good performance and has two phases: CLEO I1 and CLEO 1I.V 4.

2. B + D*p

The decay sequences of B + D*p are B- 3 D*Op- (Bo + D*+p-), D*O -+ Dono (D*+ + Don+), with Do + K-n+,K-n+nO,K-n+n-n+, p- + n-no, and no -+ yy. Charge conjugates are implied here.

The differential decay rate of B + D*p is expressed in terms of three helicity amplitudes Ho, H+ and H- as:

d31' 9 2 -- - - 12110 cos 80. cos 8, + (H+eix + H-e- ix) sin OD* sin 8, 1 , (I) dR3 32n

where: dR3 = dcos8D*dcos8,dX, 80. is the angle of Do in the D* rest frame with respect to the line of flight of the D* in the B rest frame, 8, is the angle of n- in the p rest frame with respect to the line of flight of the p in the B rest frame, and x is the angle between the decay planes of the D* and p.

Tracks with momenta greater than 250 MeV/c are required to come from the interaction point and be well measured. Explicit leptons are excluded, dE/dx consistency for K and n is also required. Soft tracks are only loosely required to be consistent with originating from the interaction point.

Resonances such as no, Do, D*O and D*+, p- are selected according to appropriate mass cuts (Dalitz cut is applied to Do + K-n+no). For B reconstruction, a cut on A E xi Ei - Eb is applied, where Eb is the beam energy. Beam constraint B mass (defined as M = d m ) is used. Off-resonance data are used to eliminate background from the continuum.

An unbinned maximum likelihood fit technique is applied. Both the signal and background probablity distribution functions (PDF) have mass and angular parts. The mass part of the signal PDF is a product of a Gaussian for B mass and a Blatt-Weiskopf form factor modified Breit- Wigner distribution for the p- mass; the mass part of the background PDF is a product of an ARGUS-type background function and a flat p- mass distribution. The angular part of the signal PDF is the B -+ D*p angular distribution, Eq.( l), corrected with the detector acceptance, the angular part of the background PDF is a product of two 2nd-order polynomials of cos 80. and cos 8, and one 1st-order polynomial of cos(x + XO).

195

The acceptance is determined from Monte Carlo. Based on our study, the angle x can be factorized, and the acceptance along x is pretty flat. The acceptance function over (cos OD., cos 0,) is a ratio of reconstructed and generated distributions with an exponential term to model the defor- mation from slow pions. On the other hand, the acceptance depends on the helicity amplitudes but we don't know them prior to the fit, hence, Monte Carlo events are generated with flat distribution and a weighting method is applied. The procedure is iterated until the helicity amplitudes converge.

2.1. Branching Fractions

To extract the number of signal and background events, the reconstructed candidates with 5.20 i M i 5.30 GeV/c2 are fit, and the angular distributions in both the signal and background PDFs are ignored. Assuming equal production of B+B- and BOBo at the T(45'), the resulting measured branching fractions are B(B- + D*Op-) = (0.98 f 0.06 f 0.16 f 0.05)% and B(Bo + D*+p-) = (0.68 f 0.03 f 0.09 f 0.02)%, which compare well with previous CLEO measurements 5 , the recent BABAR measurement 6 ,

and the world average 7. A statistical uncertainty and two systematic uncertainties are quoted in the branching fractions. The first systematic error includes uncertainties in the number of produced BB pairs (2%), the background shape (3%), our Monte Carlo statistics (1 - 2%), and the charged particle tracking and ro detection efficiencies (10 - 18%). The second systematic error comes from uncertainties in the D* and Do decay branching fractions. The contributions from non-resonant D*rro and other non-p- components are small and neglected. The contribution from the helicity amplitude dependence of the efficiency is less than 11% of the corresponding contribution from the Monte Carlo statistics, and hence, is also ignored.

These branching fraction measurements and the BSW prediction for B(B- + D*op-) /B(Bo -+ D*+p-) 8, can be used to extract the ratio of the effective coupling strengths for color-suppressed modes (a2) and color- enhanced modes ( a l ) for the D*p final state. The extraction of a2/al is sensitive to the B+B- and BOBo production fractions; we used f+-/foo = 1.072 f 0.045 f 0.0275 0.024 '. Our data give a2/al = 0.21 f 0.03 f 0.05 f 0.04 f 0.04, where the fourth uncertainty, from f+-/foo, is important here since other experimental systematics partially cancel. This result is in good agreement with the previous CLEO measurement and others '.

196

2.2. Helicity Amplitudes

To extract the helicity amplitudes, B candidates in the B signal region (defined as 5.27 < M < 5.30 GeV/c2) are used. Only the helicity amplitudes are allowed to float, all other parameters are inherited from the previous fit (the number of background events are scaled). Figure 1 shows the one-dimensional angular distributions and the projections from the fit. The helicity amplitudes obtained are listed in Table 1. The errors quoted in the table are the statistical and systematic uncertainties, respectively.

'2171202-007

- . ln - - . 1 0 0 ~ ~ ~ ~ - . - a 0 - a 0 a, D*+ a,

& W 50

50 100

* * 0 0

-1.0 -0.5 0 0.5 1.0 -1.0 -0.5 0 0.5 1.0 -2 0 2 cos $* cos

Figure 1. The cosOo* (left), COSO, (middle) and x (right) distributions for B- + D'Op- (top) and Eo -+ D*+p- (bottom) from the data (dots) and the corresponding fit projections (histograms).

Table 1. The measured helicity amplitudes for B- + g l o p - and Bo -+ D*+p-. The phase of Ho is fixed to zero in each mode. a+ and a- are the phases, in radians, of H+ and H - , respectively: H f = I H f I exp(iah).

Quantity B - -+ D*Op- Bo -+ D*+p-

1.02 f 0.28 f 0.11

0.65 f 0.16 f 0.04

1.42 f 0.27 f 0.04

0.31 f 0.12 f 0.04

The sources of systematic uncertainty are the acceptance parameterization, detector smearing, background level and shape, non-resonant 7r-7ro

contribution, and the polarization dependence on the mass of the p- meson. As can be seen from Table 1, our results indicate possible non-trivial helicity amplitude phases, a+ and a-, which are presumably due to FSI.

The results for the helicity amplitudes correspond to rL/I'(B- +

197

D*Op-) = 0.892 f 0.018f 0.016 and rL/I'(go --+ D*+p-) = 0.885 & 0.016 f 0.012, where the two uncertainties are statistical and systematic, respectively. Within the uncertainties, the fraction of longitudinal polarization for I?' --+ D*+p- is in good agreement with the previous CLEO measurement and with the HQET prediction of 0.895f0.019 '' using factorization and the measurements of the semileptonic form factors. Longitudinal polarization as a function of q2 is plotted in Figure 2 for such a prediction and compared with our new D*+p- result, as well as previous measurements for D*+p'- and D*fD:- 12. The agreement is excellent, indicating that the factorization hypothesis works well at the level of the current uncertainties.

2171202-004

0 2 4 6 8 1 0 q2 (GeV2)

0 Factorization Prediction (1 a) Region I , , , I I , , I , , , I , , , I

0 2 4 6 8 1 0 q2 (GeV2)

Figure 2. and D*+D:-, and compared with factorization prediction.

Measured fractions of longitudinal polarization for Bo t D*+p-, D*+p'-,

3. Isospin Analysis of B + DT

The CLEO measurement l3 for the branching fraction of the color- suppressed decay go + DOTO gives B(B' + DOT') = (2.74:;:;; f 0.55) x which is consistent with the Belle measurement 14. Along with the PDG values of B(B- + DOT-) = (53 f 5) x and B(go + D+n-) = (30 f 4) x it gives cosS1 = 0.89 f 0.08 which is consistent with 1 within the large error.

To reduce the error, CLEO remeasured l5 the branching fractions for B- + DOT- and go --+ D+T-. Quality requirements are imposed on charged tracks and the purity of pions and kaons used to reconstruct D mesons is improved by using dE/dx information if the particle momentum is less than 800 MeV/c. The D's, again, are reconstructed using the three decay modes, the D+s are reconstructed via the mode K-T+T+. The D meson candidates are required to have a mass within 3c of the PDG values. Pre-selection of B candidates requires M > 5.24 GeV/c2 and AE

198

to be between -50 and 50 MeV. Similar cuts as before are applied to eliminate continuum backgrounds. A binned maximum likelihood fit to the M distribution of the surviving B candidates is used to extract the event yields. The branching fractions are measured to be B(B- -+ Don-) = (49.7 f 1.2 f 2.9 f 2.2) x and B(Bo -+ D+n-) = (26.8 f 1.2 f 2.4 f 1.2) x One statistical and two systematic uncertainties are quoted in each of the two branching fraction measurements, the second systematic uncertainty, from f+-/foo, is listed separately.

Using the average of both CLEO and Belle measurements of the color-suppressed branching fraction, and the PDG ratio of B lifetimes, T(B-)/T(BO) = 1.083 f 0.017, we find cos61 = 0.863~~:~~~~~:~",",+_0and obtain a 90% confidence interval of 16.5' < 61 < 38.1". This nonzero value of 61 suggests the presence of final state interaction in the Dn system.

4. Summary

We have made precise measurements for the branching fractions for both B -+ D*p and B -+ DT, as well as the helicity amplitudes for B -+ D*p and the strong phase difference for B + Dn. This increased our understanding of factorization hypothesis and direct CP violation in hadronic B decays.

References 1. J. Korner and G. Goldstein, Phys. Lett. B 89, 105 (1979). 2. J.L. Rosner, Phys. Rev. D 60, 074029 (1999). 3. Y. Kubota et al., Nucl. Instrum. Methods Phys. Res., Sect. A 320, 66 (1992). 4. T.S. Hill, Nucl. Instrum. Methods Phys. Res., Sect. A 418, 32 (1998). 5. M.S. Alam et al., Phys. Rev. D 50, 43 (1994). 6. B. Brau, Int. J. Mod. Phys. A 16, Suppl. 1A 440 (2001). 7. Particle Data Group, Phys. Rev. D 66, 010001 (2002). 8. M. Neubert, V. Rieckert, Q.P. Xu and B. Stech, in Heavy Flavours, edited by

A.J. Buras and H. Lindner (World Scientific, Singapore, 1992). 9. T.E. Browder and K. Honscheid, Prog. Part. Nucl. Phys. 35, 81 (1995). 10. J.D. Richman, in Probing the Standard Model of Particle Interactions, edited

by R. Gupta, A. Morel, E. de Rafael, and F. David (Elsevier, Amsterdam, 1999), p. 640.

11. J.P. Alexander et al., Phys. Rev. D 64, 092001 (2001). 12. S. Ahmed et al., Phys. Rev. D 62, 112003 (2000). 13. T.E. Coan et al., Phys. Rev. Lett. 88, 062001 (2002). 14. K. Abe et. al., Phys. Rev. Lett. 88, 052002 (2002). 15. S. Ahmed et al., Phys. Rev. D 66, 031101 (2002).

SUSY SEARCHES AND MEASUREMENTS WITH THE ATLAS EXPERIMENT AT THE LARGE HADRON

COLLIDER

DAVIDE COSTANZO * Lawrence Berkeley National Laboratory 1 Cyclotron Rd., Berkeley, CA 94720

E-mail: DCostanzoOlbl.gov

The large center of mass energy and luminosity provided by the Large Hadron Collider will offer a unique opportunity to discover new particles in the TeV range. The potential to discover and measure supersymmetric particles with the ATLAS detector is discussed based on SUGRA and gauge mediated supersymmetry breaking models. The ATLAS discovery potential extends up to squark and gluino masses of about 2.5 TeV. Precise measurements of sparticle masses can also be performed, and the fundamental parameters of the theory can be constrained to 10% or better in many cases.

1. Introduction

Supersymmetry (SUSY) is one of the oldest and best motivated of the theories predicting the existence of physics beyond the Standard Model. SUSY models require the existence of at least one SUSY partner for each Stan- dard Model particle, together with a considerably enlarged Higgs sector. With the exception of spin, these SUSY particles ("sparticles") possess the same quantum numbers as their SM counterpart. Such states in nature has never been experimentally observed, and one of the major tasks of the experiments at the Large Hadron Collider(LHC) will be to measure them or to reject SUSY models.

The precise nature of the mechanism with which SUSY is broken to give rise to masses to the sparticles is currently unknown, but candidates include gravity-mediation (e.g. minimal Supergravity or mSUGRA models) as

*talk presented at the lake louise winter institute 2003, on behalf of the atlas collaboration.

199

200

Point 2 Point 3 Point 4 Point 5

well as gauge mediation (GMSB models 2 , and anomaly mediation (AMSB models 3) . A feature of many SUSY models is the absolute conservation of a multiplicative quantum number known as R-parity, which causes SUSY states to be pair produced and forces the Lightest Supersymmetric Particle (LSP) to be stable. Missing transverse energy generated by the escape of two such LSPs from SUSY events provides the classic signature for R-parity conserving SUSY at hadron colliders.

SUSY searches will be one of the most important tasks for the ATLAS experiment in the first few years of LHC operation. In this paper we review the searches in the mSUGRA model, showing that most of the parameter space is accessible with a luminosity corresponding to a few months of data taking at the initial conditions of the LHC collider. After SUSY is discovered, the parameters of the theory can be precisely measured by ATLAS in order to constrain the model.

400 400 10.0 0 200 300 2.0 o + 800 200 10.0 0 + 100 300 2.0 300 +

2. Supersymmetry reach with ATLAS

The experimental sensitivity to supersymmetry is, of course, model dependent. In this paper we will concentrate on the sensitivity to the gravity- mediated model (mSUGRA), the sensitivity to other models is discussed elsewhere 5 .

The mSUGRA model assumes that at the GUT scale all scalars (squark, leptons and Higgs bosons) have a common mass mo, all gauginos and higgsi- nos have a common mass m1/2, and all the trilinear Higgs-sfermion-sfermion couplings have a common value Ao. Thus, the model can be parameterized in terms of these three constants and of the ratio of the Higgs expectation values, tan(@). Instead of exploring all the allowed parameter space, five points have been chosen to cover the main signatures arising in the mSUGRA model. The parameters for the five points are summarized in table 1.

Table 1. periments to assess the discovery potential.

mSUGRA points studied by the LHC ex-

I mo mu2 tan0 Ao c1 I (GeV) (GeV) (GeV)

Point 1 I 400 400 2.0 o +

20 1

Figure 1 (left) shows the region of the (ml/z, mo) parameter space which can be accessed by ATLAS for different luminosity scenarios, 10 fb-I being the total integrated luminosity which will be delivered by the LHC during the first year of operation '.

3. Inclusive SUSY searches with ATLAS Inclusive searches for R-parity conserving SUSY using the generic pT signature will be carried out by ATLAS. In addition to cuts on the gT, cuts can be imposed on the multiplicity and PT of jets and leptons in order to reduce backgrounds from W+jets, Z+jets, tf events and QCD events with a large missing energy due to a jet hitting an uninstrumented region of the detector. An effective mass ( M e f f ) is defined as the scalar sum of jet PT and ST. The expected distribution of M e f f in jet+&+O lepton events 728 is plotted in figure 1 for SUSY and background events in the mSUGRA point 5. It can be seen that the SUSY signal is a few order of magnitude over the background for M e f f > 1 TeV, resulting in a good discovery opportunity.

In addition, the distribution of M e f f correlates with the SUSY mass scale defined as min(M,-,Mc). Hence, from a fit to this distribution, the SUSY mass scale can be measured in a model independent fashion with an ultimate error 5 10%. The normalization of this distribution also provides a measure of the total SUSY production cross-section and together these two pieces of information can be used to contrain the SUSY breaking mechanism.

4. Sparticles mass measurement with ATLAS The measurement of the mass of SUSY particles can be used to constrain the model, however the decay products of each SUSY particle contain an invisible LSP gy, so no masses can be reconstructed directly and the kinematic end points of invariant mass distributions in multi-step SUSY decays, have to be used to determine the mass of the sparticles. In particular we will concentrate on the decay:

IjL + g q -+ @ + r q (1)

for the mSUGRA point 5, as an example on how sparticle masses can be reconstructed.

In order to ensure a clean sample of SUSY events the following event selection has been applied:

202

10

1 10

1 10

I 10

I

lo 0 500 lo00 1500 2wO 2500 3000 3500 4000 M,(GrV)

Figure 1. Left: ATLAS 5 D discovery potential of the inclusive jets + YT channel in the mo - ml/, plane for mSUGRA models with tan@) = 10, ,u > 0 and A0 = 0 assuming O . l f b - l , lfb-' and 1Ofb-' integrated luminosity. Full dark region are excluded by theory, hatched regions by experiment (LEPS and elsewhere). Right: Effective mass distribution for SM background channels and SUSY signal at ATLAS mSUGRA point 5.

0 At least four jets with Pt,l > lOOGeV and Pt,2,3,4 > 50GeV, where the jets are numbered in order of decreasing PT; M e f f > 400GeV;

0 JtT >max(lOOGeV, 0.2Mef f ) ; 0 Two isolated leptons of opposite charge with Pi > lOGeV, 1171 < 2.5.

With these cuts the Standard Model background is negligible.

leptons from the decay: The invariant mass distribution of same-flavor opposite-sign charged

is expected to have a kinematical end point at:

The invariant mass distribution is shown in figure 2 (left) for an integrated luminosity of 100 fb-', with same-flavor lepton pairs weighted positively and opposite-flavor leptons pairs weighted negatively. The

203

e+e- + p+p- - e*p* combination cancels all contributions from two independent decays (assuming e - p universality) and strongly reduces combinatorial background. The fitted end-point is at 108.71 f 0.087 GeV in good agreement with the expected value.

The other kinematic end-points which can be measured involve the presence of hadronic jets and give access to the left-hand side of the decay chain in eq. (1). However, the resolution and energy scale calibration of ATLAS for jets are worse than those for leptons, as jets are much more complicated objects to be reconstructed. It is expected that the hardest jets will be those coming directly from the decay @L + j&. Therefore the smaller of the two masses formed by combining the leptons with one of the two highest Pt jets, should be less than the four-body kinematic end-point. The distribution of the smaller Z+Z-q mass is plotted in figure 2 (right). This distribution is expected to vanish linearly as the end-point is approached. In a similar way the invariant mass of one of the leptons and the jet used in the previous distribution will show an upper-edge.

It can be shown that the maximum invariant mass of the two leptons together with one of the two hardest jets of the event will exhibit a lower edge, which can be measured with ATLAS and used to further constrain the sparticle masses.

Using the knowledge of the edge positions, the mass of the squarks can be measured with a precision of about 3%, while the mass of the invisible LSP can be inferred with a 12% precision. More work is undergoing to better understand the fit to these kinematic distributions. In particular it is important to understand the impact that the detector resolution will have on the measurement of the end-points. This latter point is under investigation using a set of events where the detector has been fully simulated using GEANT3.

5. Conclusions

Studies have been performed of the sensitivity of SUSY particles searches at ATLAS to mSUGRA parameter space and of precise measurements of the sparticles masses. Supersymmetry will be detected with ATLAS, up to a SUSY scale of 2.5 TeV which is, in most of the cases, well beyond what is foreseen by the present models, in addition, if the sparticles have a mass below 1 TeV they can be measured with a precision of 10% or better 6 ,

allowing us to constrain the parameter of the SUSY model observed. This conclusion holds also for models other than mSUGRA, such as

204

Tn 300 -

0

c --I

0 50 100 150

2500

2000

500

0

Figure 2. Left: Distribution of the flavor subtracted Z+Z- invariant mass. Right: Dis- tribution for the smaller of the two l+Z-p masses. A linear fit to the edge region is performed.

amomaly- or gauge-mediated models which have not been covered in this paper.

Acknowledgments

I would like to thank Ian Hinchliffe for useful help and discussion in preparation of this talk and proceedings, all the members of ATLAS collaboration for the work described in this paper. I also thank the organizers of the Lake Louise Winter Institute conference for the wonderful organization in the beautiful setting of Lake Louise.

References 1. L. Alvarez-Gaume et al., Nucl. Phys. B221, 495 (1983). 2. M. Dine et al., Nucl. Phys. B189, 575 (1981); S. Dimipoulos and S. Raby,

Nucl. Phys. B192, 353 (1981). 3. L. Randall and R. Sundrum, Nucl. Phys. B557, 79 (1999); G.F. Giudice et

al., JHEP 12, 027 (1998). 4. ATLAS Collaboration, Technical Proposal, CERN/LHCC/94-43. 5. ATLAS Collaboration, Detector and Physics Performance Technical Design

Report, CERN/LHCC/99-14/5. 6. D.R. Tovey, A T L A S Sc. Note-2002-020. 7. I. Hinchliffe et al., Phys. Rev. D55, 5520 (1997). 8. C.G. Lester et al., JHEP 0009, 004 (2000).

MEASUREMENT OF THE W BOSON MASS AT LEP

J. D’HONDT* Vrije Universiteit Brussel

Inter- University Institute for High Energies (IIHE) Pleinlaan 2,

1050 Brussel, Belgium E-mail: jdhondtOhep.iihe.ac. be

The mass of the W boson has been measured by all LEP experiment by the method of direct reconstruction in the WW decay channels where at least one W boson decays hadronically. This precision measurement Is influenced by many systematic uncertainties which were extensively studied. One example is the possible effect of Colour Reconnection between the decay products from different W bosons in fully hadronic WW final states. These proceedings overview the preliminary results concerning the W mass measurement and the ongoing measurements of the Colour Reconnection effect.

1. Achievements of LEP towards WW events

The LEP accelerator provided between 1996 and 2000 e+e- collisions above the threshold for W+W- production, in the centre-of-mass energy range between threshold fi N 161 GeV and fi N 208 GeV. These events have a branching ratio of about 45% to decay into a fully hadronic final state (qij‘QQ’) and about 45% to decay semi-leptonically (qq’lq). The qq’QQ’ events could be selected with an efficiency of about 90% and a purity of about 70-80% depending on the experiment. For the qij’lYl channel these numbers are similar depending on the lepton flavour. In total about 40000 W+W- events were selected from the full LEP2 data.

2. Applied analysis methods

The clear environment within LEP collisions allows a full kinematic reconstruction of the invariant mass on an event-by-event basis. The W mass

*Work supported by IWT-vlaanderen.

205

206

from both W bosons can be determined directly from the measured kinematics of the observed final state particles usually clustered in jets. A fit algorithm aims to improve the energy resolution of these jets by forcing energy and momentum conservation between the well known initial state and the poorly measured final state.

In the fully hadronic channel the main challenges are to select the correct jet pairing into two W bosons and the treatment of the hard gluon radiation in the perturbative parton shower of the event. The semi-leptonic channel suffers from a decreased W mass resolution due to the neutrino, there the energy resolution is the limiting factor.

Two different methods are applied to extract the W mass from the selected data sample. The most widely used is the technique based on Monte Carlo reweighting, where one reweights observable distributions to different W mass values which can each be fitted to the data distributions. Another method involves a convolution technique of the theoretical predicted Breit-Wigner function with the experimental response function to obtain an event-by-event likelihood. The W width extraction methods are similar to those used for the W mass.

3. Systematic uncertainties

The most significant systematic uncertainties are those which are correlated between the experiments : the knowledge of the LEP beam energy, the fragmentation process and the implementation of the electroweak radiative corrections. In the spirit of common LEP Workshops the influence of the fragmentation process has been thoroughly investigated. Not only the difference in W mass between different fragmentation models, JETSET, ARIADNE and HERWIG, has been looked at, but also possible effect arising from cross-talk phenomena like Colour Reconnection and Bose-Einstein Correlations between decay products of different W bosons.

Table 1 summarizes all systematic uncertainties. Detector systematics include uncertainties in the jet and lepton energy scales and resolution. The 'Other' category refers to uncertainties, all of which are uncorrelated between experiments, arising from simulation statistics, background estima- tion, four-fermion treatment, fitting method and event selection. The current uncertainty assigned due to Bose-Einstein Correlations of 35 MeV/$ is considered as a conservative estimate. Studies of this effect within W+W- events prefer smaller shifts of the W mass.

207

qq'lq 8

19 12 17

4 29 33 44

32

Source qq'QQ' Combined

8 8 18 18 8 11

17 17 90 9 35 3

5 4 101 30 36 30

107 42

29 22

ISR/FSR Hadronisation Detector Systematics LEP Beam Energy Colour Reconnection Bose-Einstein Correlations Other Total Systematic Statistical Total

Statistical in absence of Systematics

4. Measurement of Colour Reconnection

The dominating systematic uncertainty in the fully hadronic channel arises from the possible effect of Colour Reconnection. Several phenomenological models do exist to emulate the effect in W+W- events.

According to the Lund string model it is assumed that Colour Recon- nection happens in the non-perturbative phase-space and acts on low momentum particles and on particles in the angular region between the jets. It is shown that the effect on the W mass could be reduced by neglecting the information content of the event in these regions '.

. , :*-++ DELPHI . .

: i- L3

i . . *. OPAL

. .

. . : . .

I Y LEPO.969M.015

3 1 1.2 1.4

:

L3

0 8 1 1 2 1 4 rat 189 GeV rat189GeV rat189GeV

Figure 1. Preliminary particle flow results using all data, combined to test the limiting case of the SK1 model in which all events are colour reconnected, the ARIADNE model and the HERWIG model. The predicted values of the particle flow ratio, r, are indicated separately for the analysis of each experiment by the dashed lines.

The effect has also been estimated by measuring the average particle

Table 1. Uncertainty decomposition for the combined LEP W mass results

208

flow ratio between the regions between jets from the same W boson and jets from different W bosons. A small amount of Colour Reconnection is preferred of 50 % according to the SK1 model 2 , see Figure 2, and corresponding with a 68 % CL for the model parameter K. of [0.39,2.13]. The maximum effect observed at the l~ level was used to estimate the systematic uncertainty on the W mass. The centre-of-mass energy dependence of the effect was taken into account, see Figure 1. The four experiments have observed a weak sensitivity to the ARIADNE and HERWIG models of Colour Reconnection with the particle flow analysis, as indicated in Fig- ure 2. These fragmentation models without their implementation of Colour Reconnection differ from the measured data value of r by respectively 3.1 and 3.7 standard deviations.

Energy Dependent W Mass Bias

170 180 190 200 210

& [GeV]

Figure 2. connection as used in the LEP combination.

The energy dependent values of the W mass uncertainty due to Colour Re-

An alternative method to measure the Colour Reconnection effect in W+W- events was proposed and performed in Ref. 3. The method infers information about the models which is to a good approximation uncorrelated with that obtained with the particle flow ratio observable. Therefore all LEP experiments are strongly advised to perform a similar analysis, in order that results can be combined. Only when the combined information will become available one will be able to reduce the effect on the W mass.

5. Preliminary results

The results from the individual LEP experiments are in good agreement as can be observed in Figure 3 and yield a combined value of :

209

Winter 2003 - LEP Preliminary Winter 2003 - LEP Preliminary

All P I / [ 1906 20(~0 ha 3 7 Y W ow

L3 11996 Loo01 80 ?6M 077

OPAL [1996-l999] 80 4 m 065

LEP 80 412fo 042

80.0 81.0

MJGeVI

AILI'H 1 I Y Y A iOfJP!

L3 f l y 9 6 Z?f?fI)J

OPAL 11996-19981

LEP 2.15ofo.091

1.5 2 0 2.5

T,[GeYl

Figure 3. Combined W boson mass and width measurements from LEP2 experiments.

mw = 80.412 f 0.029(stat) f O.OSl(syst) GeV/c2

with a probability for being self-consistent of 66 %. In this combination the weight of the fully hadronic channel in only about 9 %, while those events contain in principle the larger amount of information on the W mass. This is due to the large possible effect of Colour Reconnection. The largest part of the systematic uncertainty in the combined W mass value comes from hadronisation uncertainties which are conservatively treated as correlated between the two channels, between experiments and between years. In the absence of systematic uncertainties the precision on the W mass would be 22 MeV/c2. In addition to this result the difference between the W mass estimated with the qq'QQ' and q4'lCl events was estimated as a cross-check:

Amw(q$QQ' - qq'14) = +9 f 44 MeV/c2 .

A significant non-zero value for this measurement could indicate that the Colour Reconnection and/or Bose-Einstein Correlation effects are biasing the value of mw determined in the fully hadronic channel. When estimating the uncertainty on Amw the uncertainties arising from Colour Reconnec- tion and Bose-Einstein Correlations are set to zero. For the W width a value of :

21 0

rw = 2.150 f 0.068(stat) f O.OGO(syst) GeV/c2

was found, with a probability of 71 % to be self-consistent.

W-Boson Mass [GeV] W-Boson Width [GeV]

80.454 -i. 0.059

LEY2 80412 0042

80.426 ? 0.034

NuTeV -A- 8013610084

LEPl/SLD 80.373 If: 0.033

023

80 80.2 804 80.6

m, [GeVl

2.1 15 +_ 0.105

- 2150 t 0091

2.139 f 0.069

2 171 t 0.052

LEPl/SLD 2.091 f 0.003

002

2 2.2 2 4

rw [GeVl

Figure 4. Combined W boson mass and width measurements from different measurements. On the top part of the plot the direct measurements are combined, while in the bottom part they are compared with the indirect measurements.

In Figure 4 the combined LEP results are compared with results from the Tevatron Run I and from indirect measurement of the W boson characteristics. In general a good agreement was found, except with the recent measurement from the NuTeV experiment.

Acknowledgments

The author wishes to express his gratitude to all LEP Collaborations for providing their results and for the helpful discussions.

References

1. J. D’Hondt, Possible reduction of the total uncertainty on the mw measurement at LEP2, Proceedings of the XXXVIIth Rencontres de Moriond 2002.

2. The L E P and SLD Collaborations, A combination of preliminary electroweak Measurements and Constraints on the Standard Model, CERN-EP 2002-091 and hep-ex102 12036.

3. J. D’Hondt and N.J. Kjaer, Measurement of Colour Reconnection model parameters using mW analyses, paper submitted t o the ICHEP Conference 2002 (Amsterdam).

IN-SITU CALIBRATION OF THE CMS ELECTROMAGNETIC CALORIMETER

D. I. FUTYAN EP Division, CERN, CH-1211 Geneva 23, Switzerland.

E-mail: David.FutyanOcern.ch

The in-situ intercalibration of the PbW04 crystals of the CMS electromagnetic calorimeter will be performed using three techniques: An energy-flow method will be used at startup to intercalibrate to a precision of around 2% within about three hours. The energy/momentum measurement of isolated electrons from W -+ ev events will then be used to obtain the design goal precision of 0.5% within about two months. Global intercalibration of different regions of the calorimeter and the determination of the absolute energy scale will be performed using energetic electrons from Z-+ e+e- events.

1. Introduction

The CMS Electromagnetic Calorimeter consists of 75848 lead tungstate crystals. To achieve the target energy resolution, precise in-situ intercalibration of the individual crystals using physics events is required. The importance of this can be seen by considering, for example, the potential discovery and mass measurement of an intermediate mass Higgs boson in the H+ yy channel, which would greatly benefit from an energy resolution with a constant term of less than about 0.5%. The intercalibration error goes directly into this constant term with very little scaling, because most of the energy goes into a single crystal.

2. The CMS Electromagnetic Calorimeter

A detailed description of the CMS ECAL can be found in [l]. Figure 1 shows a transverse section of the ECAL.

Each half-barrel consists of 18 super-modules each containing 20 x 85 PbW04 crystals. The crystals are tilted so that their axes make an angle of 3" with a line from the nominal vertex point, and each covers approximately 0.0174x0.0174 in q$. The crystals are 230 mm in length, which corresponds to 25.8 radiation lengths (Xo) .

21 1

212

Figure 1. Transverse section of the ECAL, as described in GEANT3/CMSIM.

The endcap consists of identically shaped crystals, slightly shorter (220 mm, 24.7 Xo) and a little larger in cross-section than the barrel crystals, grouped in mechanical units of 5 x 5 crystals arranged in a rectangular zy grid, with the crystal axes off-pointing from the nominal vertex by angles between 2” and 5”. A 3x0 silicon strip preshower detector is situated in front of most of the endcap (1771 > 1.653).

3. The Electron/Photon High Level Trigger

The online reconstruction and selection of physics objects will be performed using the CMS High Level Trigger (HLT), described in detail in [2]. This will be done flexibly using a single online CPU farm, made up of approximately 2000 processors, using the same object-oriented environment and code as the offline software. The CPU time targets are already being met.

The Electron/Photon HLT selection is performed in three stages:

“Level-2” : Clusters of crystals are constructed using a bump-finding algorithm. The spray of bremsstrahlung energy radiated in the tracker material is collected in “super-clusters” . At low luminosity, the transverse energy of the super-cluster is required to be greater than 26.0 (14.5) GeV for single (double) triggers. “Level-2.5”: The energy-weighted average impact point of the super-cluster is propagated back to the nominal vertex point and hits in the pixel detector axe sought. If at least two pixel hits are found, the candidate is classified as an electron, otherwise it is classified as a photon. For the photon stream at low luminosity, the transverse energy of the super-cluster is required to be greater than 80 (20) GeV for single (double) triggers.

21 3

Single electron

(3) "Level-3': For electrons, tracks are reconstructed and cuts are applied on the ratio of the super-cluster energy to the track momentum and on the difference in pseudorapidity, q, between the extrapolated track and the super-cluster position. Isolation requirements are made for both electrons and photons.

2 x ~ ~ ~ ~ c r n - ~ s - ' Signal I Bkgnd I Total

W-t ev: lOHz 1 23Hz I 33Hz W+ev: 35Hz I 40Hz I 75Hz Signal I Bkgnd I Total

3.1. Performance

Table 1 shows the electron and photon rates output by the HLT at both low and high luminosity. The single electron background comes from 7rf/xo

overlap, 7ro conversions and genuine electrons from b /c + e. The efficiency for H+ yy for m ~ = 1 1 5 GeV at low luminosity after the complete selection chain is 77% for events with both photons in the fiducial region, and 84% for events for which the photons also pass the offline p~ cuts to be used for Higgs searches.

Double electron Single photon Double photon TOTAL:

Table 1. Electron and photon rates output by the HLT

Z+ ee: 1Hz N O 1Hz Z+ee: 4Hz -0 4Hz 2Hz 2Hz 4Hz 4Hz 3Hz 7Hz

NO 5Hz 5Hz NO 8Hz 8Hz 94Hz

~~ ~

43Hz

4. Int ercalibrat ion Strategy

4.1. Precalibration

The raw intercalibration precision obtained from laboratory measurements of the APD gains and crystal light yields is -4.5%. The precision obtained from the transfer of the test beam precalibration to the assembled detector is predicted to be -2%. However, the present construction schedule implies that less than one quarter of the calorimeter elements can be precalibrated.

4.2. In-Situ Intercalibration Using Electrons From W+ ev

The standard technique which will be used to obtain high-precision local intercalibration of the CMS ECAL is to use the E / p of electrons from W+ eu decays, where E is the energy measured in the calorimeter and p is the measured momentum of the reconstructed track.

Events

21 4

. . . . . . . . . . . , , . . . . . - . . . . , , , , . . . . , . . . . . . . . . . : : : :

: : - ; t . : , . . . . . , . . . . . . . . . . . . . . . . , . . . . . , , , , . . . . . . . . . . . . . . . . . . . . - . .

There are two dominating issues. The first is that the inclusion of electrons with large losses due to bremsstrahlung in the tracker material results in a large tail in the E l p distribution, leading to a tradeoff between electron efficiency and the width of the distribution. Electrons which radiate significantly can be removed by applying very hard cuts on ECAL shower shape variables. Since the amount of bremsstrahlung depends on the amount of material, which varies with 77, the strategy is to intercalibrate crystals within small 77 regions first with loose bremsstrahlung cuts, and then to intercalibrate between the regions with much tighter cuts.

The second issue is that each electron shower involves up to 25 crystals a, so there is a need to deconvolute the 25 individual calibration constants used to reconstruct the energy of each electron. The deconvolution is performed using an iterative algorithm which was used to solve the same problem in the L3 experiment at LEP. The algorithm was tested for electrons simulated in a 10 x 10 crystal matrix. Figure 2 shows the calibration errors as a function of the number of W + ev events per channel. A few tens of events per channel are sufficient to obtain an intercalibration precision better than the target of 0.5%. The time required depends on the cuts applied to remove electrons with large bremsstrahlung losses. Conservative calculations indicate a time scale of around two months at low luminosity.

aA 5 x 5 crystal array is used to reconstruct the energy in the calorimeter.

Figure 2. Calibration errors as a function of the number of W- events per channel,

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4.3. +Symmetry Intercalibration

The standard W-i eu intercalibration requires approximately two months of stable running at 2 x 1033~m-2s-1 luminosity and requires the entire detector to be functioning optimally (e.g. perfect tracker alignment), conditions which may take some time to achieve. &symmetry intercalibration [3] is proposed as a method to rapidly achieve a target intercalibration precision of 2% at startup, by exploiting the uniformity of energy deposition in minimum-bias events to intercalibrate pairs of rings of crystals at fixed I 77 I. Minimum-bias crossings are used to avoid trigger bias, but the use of jet-triggers, which have the advantage of much larger energy deposits, is also being investigated. The number of intercalibration constants can thus be reduced from 75848 (no. of crystals) to 125 (no. of fixed I 77 I ring pairs). Ring-to-ring intercalibration will then be performed using Z+ e+e- events (Section 4.4).

Distributions of the total transverse energy deposited in each crystal from 18 million fully simulated minimum-bias events are formed for 85 (40) pairs of rings in the barrel (endcaps). The summations do not include energy deposits below 150 MeV in the barrel and below 750 MeV in the endcaps in order to exclude noise. The intercalibration precision attainable for each pair of rings is determined from the Gaussian width of the distribution via an empirically determined constant of proportionality.

The technique has been directly tested by performing a complete simulation of the method to a pair of rings with miscalibrations assigned randomly from a Gaussian of width 6%. Figure 3(a) shows the residual miscalibration after a single iteration of the method.

If the symmetry were exact the attainable precision would be proportional to l/a, where N is the number of events. In reality, a limiting precision is reached when the inhomogeneity of tracker material breaks the &symmetry of the energy deposition. This limit can be calculated for each pair of rings by fitting the precision as a function of 1 I n to a function of

the form f ( l / f l ) = 4 7 , + ( m / f l ) where m is a constant and s is the limiting precision. This procedure is illustrated in Figure 3(b).

The intercalibration precision which can be obtained with 18 million minimum-bias events, and the limit on the precision are shown as a function of 77 in Figure 4. The precision with 18 million events is between 1.2% and 3.5% throughout the fiducial region. Allocating lkHz of Level-1 band- width for minimum-bias, 18 million events could be taken in less than three hours. Complete ignorance of the tracker material distribution is assumed.

21 6

I Entries 720 90

80

70

60

50

40

30

20

10

90.1 -0.075 0 0 5 -0025 0 0025 005 0075 0 1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 .1

x10 -- lldN

Figure 3. (a) Distribution of residual miscalibrations, for the 720 crystals in the pair of rings at 171 = 0.23, after a single iteration of &symmetry intercalibration. (b) Vari- ation of the intercalibration precision with l/a, for crystals at 171 = 1.41. The limit corresponds to the y-intercept of the fit.

With knowledge of the distribution after precise independent W+ eu intercalibration, there is the potential for rapid and repeated high-precision intercalibration (< 1% every few hours).

.g3,5 1 2 : . Limit on precision

- Precision with 18 million events .-

0 - - - Q 3 - ._

g t t

- 2 -

0 0.2 0.4 0.6 0.8 1 1.2 1.4 11

1.6 1.8 2 2.2 2.4 2.6 2.8 3 11

Figure 4. bias events and the limit on the intercalibration precision as a function of 1.

Intercalibration precision which can be obtained with 18 million minimum-

21 7

4.4. Intercalibration Using Electrons From Z+ e+e-

High energy electrons from Z+ e+e- events are used

Events

(1) to perform ring-to-ring intercalibration after performing 4-

(2) to perform global intercalibration between different regions of the

(3) to set the absolute energy scale.

symmetry intercalibration of the crystals within the rings,

calorimeter,

The principle of the technique is to reconstruct the Z mass, Mz:

where El and E2 are the energies of the electrons reconstructed in the ECAL and 012 is the 3D angle between them. The same problems described in Section 4.2 are encountered and are solved in a similar manner. The problem of deconvoluting the calibration constants is more acute since the Z mass reconstruction provides information only about the product of the shower energies. Around 100 electrons per ring are sufficient to perform ring-to-ring intercalibration to a precision of 0.5%. This yield can be achieved within a few days.

5. Summary

The in-situ intercalibration of the CMS electromagnetic calorimeter crystals will be performed using three techniques. At startup, +symmetry intercalibration will provide a means of attaining a precision of around 2% within about three hours. The design goal precision of 0.5% will subsequently be achieved using the E/p of electrons from W + eu events in about two months. Global intercalibration of different regions of the calorimeter and the determination of the absolute energy scale will be performed using electrons from Z-+ e+e- events on a time scale of a few days.

References

1. 2.

3.

CERN/LHCC 97-33, CMS TDR 4 , The Electromagnetic Calorimeter Project. CERN/LHCC 2002-26, CMS TDR 6.2, Data Acquisition and High Level n i g - ger. D. Futyan and C. Seez, Intercalibration of ECAL Crystals in Phi Using Sym- metry of Energy Deposition. C M S Note-2002/031. To be published in J. Phys. A: Nucl. Part. Phys.

SPIN PHYSICS AND ULTRA-PERIPHERAL COLLISIONS AT STAR

C. A. GAGLIARDI Cyclotron Institute, Texas ABM University

College Station, T X 77843 USA E-mail: cggroup@comp. tamu. edu

STAR COLLABORATION http://www.star. bnl.gov/STAR/srnd/wllab/sci-apr03.pdf

The STAR Collaboration is investigating the spin structure of the nucleon in polarized proton collisions and diffractive vector meson production in ultra-peripheral heavy-ion collisions. The STAR spin physics program will measure the gluon polarization in the proton, perform a flavor decomposition of the quark and antiquark polarizations, and investigate the transverse spin structure. Results from the first RHIC polarized proton run and plans for the future are described. STAR is also investigating ultra-peripheral heavy-ion collisions, in which the nucleons in the colliding nuclei participate coherently in interactions via long-range fields. STAR has measured large cross sections for coherent po production, in agreement with t h e oretical predictions that include factorization of diffractive processes and nuclear excitation. This opens a new laboratory to investigate diffractive interactions.

1. Introduction

The STAR Collaboration at RHIC has three major physics efforts underway. The goals of the STAR spin physics effort are to measure the contribution that gluons make to the spin of the proton, determine the polarization of the valence and sea quarks within the proton, and characterize the proton's transverse spin structure. The STAR ultra-peripheral heavy-ion collision program is opening a new laboratory to investigate diffractive interactions. It will provide a unique window to study the gluon density in heavy nuclei, quantum interference, and high-field &ED, while complement- ing existing efforts in photo- and electro-production. The STAR Collabo- ration is also searching for a new form of matter, the quark-gluon plasma, which is predicted to be created in ultra-relativistic heavy-ion collisions, as described elsewhere in these proceedings [ 13.

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2. Spin Physics

In the naive quark model, the spin of the proton arises from the contributions of its three constitutent quarks. However, polarized deep-inelastic scattering (DIS) experiments have shown that the spins of the quarks and antiquarks in the proton only contribute ~ 1 / 4 of the total proton spin. The rest must arise from polarization of the gluons or from orbital motion. At present, the contribution from the gluons to the proton spin (AG) is poorly determined because existing DIS data only constrain AG through the scale dependence of the polarized structure functions.

The primary goal of the STAR spin physics program is to measure the polarization of the gluons within the proton as a function of the momentum fraction x carried by the gluon, over the range 0.01 < x < 0.2, and to determine the total contribution AG that gluons make to the proton spin with a precision of f0.5. This will be achieved by investigating the two-spin longitudinal analyzing power ALL for the process p p + y+Jet+X, with p; > 10 GeV/c. At the partonic level, -90% of the cross section for this process arises from the quark-gluon Compton scattering reaction qg + qy. The momentum fractions x1 and 5 2 of the incident partons may be determined from measurements of the final-state kinematics. When x1 >> 22, the probability is high that x1 = xq and x2 = xg. The kinematics can also be chosen so that the analyzing power for quark-gluon Compton scattering is large and the effective quark polarization is known from previous polarized DIS measurements. Thus, a measurement of ALL for p p + y+Jet+X can be used to infer AG/G(x).

STAR will also perform a flavor decomposition of the polarization of the quarks and antiquarks in the proton, through measurements of the single-spin longitudinal analyzing powers AL for W* production in p p collisions. Current efforts are underway to utilize semi-inclusive polarized DIS to determine the separate contributions that u and d quarks and ti and d antiquarks make to the proton spin, but they are limited by uncertainties in the fragmentation functions. The STAR measurement will not be sensitive to these ambiguities. STAR is also planning to investigate the transverse spin structure of the proton and the sensitivity of fragmentation to the spin of the parent parton.

The STAR spin program began with the first polarized p p collisions at RHIC during Winter, 2001-02. This was the first time that polarized beams had been studied in a hadron collider. The collision energy, f i = 200 GeV, represented a ten-fold increase compared to the highest energy

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p oy (a)

-4-4 STAR PRELIMINARY

0 0 1 1 1 3 I 2 5 I IS .am1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

' I , , , , , I , , , , , , / . .

0 0.5 1 1.1 I 2.5 1 .a.Wl """""

E :.I E BNI

Figure 1. Preliminary transverse spin asymmetries for inclusive charged particle production in 3.3 < 171 < 5 , as measured with the STAR Beam-Beam Counters. Panel (a) shows the results for the left-right (solid circles) and updown (open squares) asymmetries measured when the vertically polarized beam was directed toward the BBC. Panel (b) shows the asymmetries measured when the vertically polarized beam was directed away from the BBC.

polarized pp collisions investigated previously. Unfortunately, due to the failure of one of the major power supplies for the AGS, the polarization of the two proton beams was < 20%. This made it impractical to perform ALL measurements, so STAR focused on transverse spin measurements.

A new set of beam-beam counters (BBC) that subtend the pseudorapidity ranges 3.3 < Ir]l < 5 were added to STAR prior to the pp run. They were used to produce a minimum-bias collision trigger and to monitor the luminosities of the circulating beams. Each of the two BBCs was divided into four quadrants. Thus, left-right and up-down spin asymmetries could be measured simultaneously. Figure 1 shows the results. A significant left- right asymmetry was observed, comparable in magnitude to the asymmetry measured by the p-carbon Coulomb-nuclear interference polarimeter that is the current standard in use at RHIC. The proton beams were polarized in the vertical direction, so no up-down asymmetries were expected, and none were seen. The BBC count rate is very high, so this asymmetry may be large enough to be used in the future for local polarimetry at STAR.

The STAR time-projection chamber (TPC) was used to measure the transverse single-spin asymmetry of the leading charged particle a t midrapidity. Perturbative QCD predicts that this asymmetry should go to zero for sufficiently large p ~ . It is important to verify this prediction, since the same theoretical framework is used to calculate the analyzing power for quark-gluon Compton scattering. The angular distributions of leading charged particles were measured with respect to the proton spin direction in events that contained at least 4 charged particles within the TPC. No

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pr + p + 2 + x = 0.5 1 STAR FPD Preliminary Data Assuming A,(CNI)=0.013 p,=l.l-2.5 GeVIc &do0 GeV

1

-0.1 1 I Syot. Uncer. = f 0.05

4+1

Figure 2. Preliminary transverse spin asymmetries for forward T O production in p + p -+ K O + X collisions at (11) = 3.8. From top to bottom, the curves show predictions from models that attribute the asymmetries measured by FNAL E704 to the Collins effect [3], to the Sivers effect 141, and to twist-3 quark-gluon correlations [5].

x,=E/(lOO GeV)

significant asymmetries were found for leading charged particles in the range 0.2 < p~ < 5 GeV/c.

Large transverse analyzing powers were measured by Fermilab E704 for forward pion production in p p collisions at f i = 20 GeV [2]. Several models that have been proposed to explain the large analyzing powers predict that they should persist to RHIC energies [3, 4, 51. Prior to the p p run, STAR installed four separate electromagnetic calorimeters to detect high-energy .IT' produced in the range 3 < q < 4. Three calorimeters consisted of lead-glass Cerenkov detectors. The fourth was a lead-scintillator sampling calorimeter, with additional scintillators to measure the shower transverse profiles at the shower maxima. This calorimeter could reconstruct the no invariant mass with a resolution of < 25 MeV. Figure 2 shows the results. A significant transverse spin asymmetry was seen for E, > 45 GeV. The magnitude is consistent with model calculations that were tuned to match the asymmetries observed by E704.

During the next p p run at RHIC, the STAR goals include confirming the BBC asymmetry measurement, repeating the forward no asymmetry measurement with much higher precision to discriminate between the existing models, and to get a first look at the gluon polarization through measurements of ALL for inclusive jet production. These measurements will lay the groundwork for future measurements of quark-gluon Compton scattering.

3. Ultra-Peripheral Collisions

In ultra-peripheral heavy-ion collisions, the two nuclei geometrically 'miss' each other, and no hadronic nucleon-nucleon collisions occur. However, the

nuclei can still interact at impact parameters b >> ~ R A through photon exchange and photon-photon or photon-Pomeron collisions. The exchanged bosons can couple coherently to the nuclei, which leads to large total cross sections and small final state transverse momenta. Recently, the STAR Collaboration reported the first observation of coherent po production in ultra-peripheral heavy-ion collisions at a center-of-mass energy = 130 GeV/nucleon pair [6 ] . Two different reactions were observed - coherent exclusive production, Au+Au --f Au+Au+po, and coherent po production together with nuclear excitation, Au+Au -+ Au* +Au(*)+po. In exclusive po production, a virtual photon is emitted by one nucleus, fluctuates into a virtual po meson, then scatters elastically from the other nucleus. The elastic scattering process may occur via Pomeron exchange. The gold nuclei are not disrupted, and the final state consists solely of the two nuclei and the vector meson decay products. This leads to a characteristic signature in the STAR TPC: an opposite-sign pair of tracks with very small pair ptypically < 100 MeV/c, in an otherwise empty detector. Such collisions are identified by triggering on events with single hits in the two opposite horizontal quadrants of the STAR central trigger barrel, and no hits in the other two quadrants. Coherent production together with nuclear excitation occurs when the Au nuclei excite each other through the exchange of additional virtual photons. This leads to a similar event signature in the TPC, but in coincidence with neutrons from the breakup of the Au nuclei observed in one or both of the STAR zero-degree calorimeters. Reference [6] shows that the measured cross sections for both of these processes agree with theoretical predictions [7] that treat coherent po production and nuclear excitation as independent, factorizable processes.

More recently, STAR has extended these results to Au+Au collisions at Js?vnr = 200 GeV. Figure 3 shows preliminary results for exclusive coherent po production. The statistics are improved substantially, compared to the previous measurement at 130 GeV, which will permit a detailed investigation of the reaction mechanism. For example, it is impossible to determine which Au nucleus is the source of the virtual photon and which scatters it into an on-shell po. Thus, the two contributions must be added coherently. This leads to a quantum interference effect [8], similar to the interference between two slits separated by a typical distance (b) M 40 fm. The po p~ spectrum is being analyzed to isolate this quantum interference.

STAR is also studying other products of ultra-peripheral collisions. Co- herent e+e- final states have already been seen. These are produced in photon-photon scattering. They will permit unique investigations of strong-

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8 x+x- pJ z+lc+,n-m

-Monte Carlo

0.5 0.6 0.7 0.8 0.9 1 M(m) Gt

1

Figure 3. The left panel shows the preliminary p~ spectrum for n+n- pairs produced in ultra-peripheral Au+Au collisions at fi = 200 GeV, without excitation of either nucleus. The histogram is a sum of the p~ distribution predicted for coherent exclusive po production and the experimentally measured background from like-sign pairs. The right panel shows the invariant mass distribution of the pion pairs with p~ < 150 MeV/c, together with a fit to the po mass peak.

field QED, since Za M 0.6 for the Au nuclei. At the other extreme, the Pomeron is rich in gluons. Thus, the cross section for J / $ production in photon-Pomeron collisions will provide a measurement of the gluon density in the Au nuclei [9], which plays a central role in ultra-relativisitic heavy- ion collisions. Finally, STAR can also observe ultra-peripheral collisions in other systems. For example, Pomeron-Pomeron interactions in p p collisions are likely to produce final states containing glueballs.

In summary, ultra-peripheral heavy-ion collisions at STAR provide a new laboratory to investigate a broad range of diffractive interactions.

References 1. J.L. Klay, contribution to these proceedings. 2. D.L. Adams et al., Phys. Lett. B261, 201 (1991); B264, 462 (1991). 3. M. Anselmino et al., Phys. Rev. D60, 054027 (1999). 4. M. Anselmino and F. Murgia, Phys. Lett. B442, 470 (1998). 5. J.W. Qiu and G. Sterman, Phys. Rev. D59, 014004 (1999). 6. C. Adler et al. (STAR Collaboration), Phys. Rev. Lett. 89, 272302 (2002). 7. A.J. Baltz, S.R. Klein, and J. Nystrand, Phys. Rev. Lett. 89, 012301 (2002). 8. S.R. Klein and J. Nystrand, Phys. Rev. Lett. 84, 2330 (2000). 9. L. Frankfurt, M. Strikman and M. Zhalov, Phys. Lett. B540, 220 (2002).

LATEST RESULTS ON TIME-DEPENDENT C P VIOLATION FROM BELLE

T. J. GERSHON, REPRESENTING THE BELLE COLLABORATION IPNS, KEK,

Tsukuba-shi, Ibarabi-ken,

305-0801, Japan Email: gershonQbmail.kek.jp

1-1 Oho,

The latest results on time-dependent CP violation from the Belle experiment are reviewed. Using 78 ft-' of data collected at the T(4S) resonance at the KEK-B asymmetric e+e- collider, C P asymmetries in b + cFs and b -+ wiid transitions are studied.

1. Introduction

B meson decays to CP eigenstates are the ideal environment to study CP violation.' By using different final states, which are sensitive to different weak phases, B factory experiments aim to probe the CP violating part of the Standard Model; in particular to test the unitarity of the Cabibbo- Kobayashi-Maskawa (CKM) quark mixing matrix.'

In order to understand the phenomenology of such decays, first define Xcp = 54. Here q and p are related to mixing in the Bo - Bo system (1q/pl z 1 in the Standard Model), and A (A) is the amplitude for Bo (Bo) decay to the CP eigenstate fcp of interest. At a B factory, B mesons are produced in coherent B - B pairs from "(4s) decays, and it can be shown that the time-dependent decay distribution is given by

,-lAtll?-,o Psp(At) = [1+ q {SCP sin(AmAt) + ACP cos(AmAt)}], (1) 47~0

where

224

225

and q = +1 (-1) indicates that the other B was tagged as a Bo ( D o ) at time At = 0.

In the theoretically clean case that the decay amplitude is dominated by one weak phase, 1A/Al = 1, and so ACP = 0 whilst Scp = -&p sin &,, where (cp is the CP of fcp, and (pw is the weak phase difference between Bo --+ fcp and Bo H Bo --+ fcp. If more than one weak phase contributes significantly, interpretation of Scp becomes non-trivial, however non-zero ACP, corresponding to direct CP violation, becomes possible.

2. Procedure to Measure Time-Dependent C P Violation

In order to measure time-dependent CP violation, five criteria need to be satisfied.

Collect a large sample of B - B decays Identify and select events containing the desired final state fcp Tag the flavour of the other B Measure the decay time difference At Fit the sample to obtain Scp & ACP.

Owing to the outstanding performance" of the KEK-B a~celerator,~ the first criterion has been achieved in style. The data sample accumulated by summer 2002, and used in the analyses described here, corresponds to 78 ft-' containing 85 x lo6 BB pairs.

The second, third and fourth criteria depend on the performance of the Belle d e t e ~ t o r . ~ The reconstruction of specific final states will be discussed later, as will the CP fitting procedure. Flavour tagging is performed by removing the charged tracks used in the reconstruction of fcp, and using inclusive B meson decay properties to determine whether the remainder of the event originated from a Bo or a The flavour tagging algorithm returns two pieces of information; q which is the expected flavour of the tagging B (see Eq. l), and T which is a measure of the likelihood that q is correct. Using flavour-specific final states, the wrong tag fraction (w) is determined by measuring the mixing amplitude, which is equal to 1 - 2w, for each of 6 categories of T . The effective tagging efficiency, defined as Cf==,y(l - 2wl), is 28.8 f 0.6%.

Since KEK-B is an asymmetric collider, the produced Bs are moving in the laboratory frame. Thus, the decay time difference At can be related to

*At the time of writing, the peak luminosity has exceeded 9.5 nb-ls-', whilst the total integrated luminosity exceeds 130 fb-'.

226

the vertex separation: AZ = zcp - ztag M (,br)-rcAt, where (@r)r = 0.425 at KEK-B. The vertices are obtained using prompt tracks in fcp (for ZCP),

and good tracks in the remainder of the event (for ztag). The obtained At resolution is N 1.4 ps, and is dominated by the resolution of the tagging side vertex.6

3. Results

3.1. b 4 cEs h n s i t i o n s

Final states which are accessed via b + CCS transitions, are dominated by a single weak phase. These therefore provide a theoretically clean measure of the mixing phase, which is equal to -241b in the Standard Model. For this reason, ACEs is fixed to zero in the CP fit. A single fit is performed combining 2958 candidates for several cEs final states.* The cleanest mode is J/$Ks, with J / $ + 1+1- & Ks + ?T+?T-, for which there are 1116 candidate events. Other modes include J/+KL (1230 candidates) which has the opposite CP. The fit result is

sin(241) = 0.719 f 0.074(stat) f 0.035(syst),

and is shown superimposed on the raw asymmetries‘ in Fig. 1.

Figure 1. (b) CP odd modes only (mainly J / $ K s ) ; (c) C P even modes only (J/+,KL).

Raw asymmetries as a function of At for (a) all b + ccs modes combined;

’4i,42 & 4 3 are the angles of the Unitarity triangle; 41 +42+43 = A. In the Wolfenstein parametrization’ of the CKM matrix, 41 = ?r - arg(&) & 43 = arg(V* zlb ). ‘The raw asymmetry is the difference between the number of events with q l = -1 and q( = +1 divided by the sum.

227

3.2. b += uGd Tmnsitions

The decay B + 7r+7r- can be mediated by either a tree or a penguin diagram. Since the tree amplitude contains V&, in the absence of penguins one would obtain S,, = sin(242). The presence of penguin amplitudes complicates the theoretical situation. Experimentally, the situation is difficult due to the small branching fraction (B(B + 7r+7r-) = (4.8f0.5) x 10W6 9 ) ,

and potentially large backgrounds from the kinematically similar Bo + K-n+ decay, as well as continuum (e+e- + qtj, q = u, d , s, c) processes. Kaon/pion separation is achieved by combining subdetector responses in a likelihood variable. A pion identification requirement is made which has an efficiency of N 91%, with a kaon misidentification rate of N lo%, for tracks in the momentum range of interest. By reversing this requirement, a K7r dominated sample is obtained. To reject continuum background, events which appear likely to come from those processes, based on a likelihood ratio (LR) constructed by combining event shape information and the reconstructed B flight direction are rejected.

After these event selections, a total of 760 candidate events remain.1° Event-by-event signal and background probabilities are obtained by fitting the A E distribution, as shown in Fig. 2. The CP violation parameters

AE (GeV)

Figure 2. A E distribution for d a - candidate events in the high LR region. The distribution is fitted to components corresponding to R R signal (central Gaussian), K R feeddown (shifted Gaussian), three body charmless B decays (shape at low AE) and continuum processes (linear). There are 275 candidates in the AE signal region of which the fit indicates that lOS+i; originate from B + d a - .

dAE is the difference between the reconstructed B energy and the beam energy.

Can thern obtained by maximizing the likehood,

228

where f,,, fK, & f q B are obtained from the AE fit, P,, is given by Eq. 1 whilst KT is treated as a flavour specific final state,e h i g is the At resolution function, and the shape of Pqg @ RqB is determined from a continuum dominated sideband region.

Prior to performing the CP fit, a number of cross-checks are performed. The Kn sample is fitted for the mixing parameter Am, both KT and TT samples are fitted for the lifetime, TBO, and a number of control samples are fitted to test null asymmetry hypotheses. In all cases, results consistent with their expected values are obtained, and possible discrepancies are accounted for in the systematic error.

Additional tests on the linearity of the fit are performed using Monte Carlo pseudo-experiments (toy MC). Events are generated according to the PDF used in the fit (Eq. 2). The toy MC is also used to determine (S,, , A,,) confidence regions using the Feldman-Cousins approach," and furthermore the statistical error of S,, (A,,) is taken from the R.M.S. of the S,, (A,,) distribution. By measuring the statistical error in this way, it is consistent with the confidence regions, it does not depend strongly on the central value of the measurement, and it is free of possible fluctuations.

The result of the fit is

A,, = +0.77 f 0.27(stat) f 0.08(syst), S,, = -1.23 f 0.41(stat)?~:~8,(syst),

and is illustrated in Fig. 3. It can immediately be noted that the central

E . , I , , , , I I . . I . I : . I -5 0 5

At (PS)

Figure 3. B +- a+n- fit result: (a) background subtrxted At distributions for ax candidates in the high LR region; (b) background subtracted asymmetry for the same events; (c) (S,,, A,,) confidence regions.

ePossible C P asymmetries in Ka are accomodated in the systematic error.

229

value lies outside the physical constraint S:, + A:, 5 1. Using toy MC the probability for a fluctuation this large or larger is found to be 16.6% when the true values of (S,,,A,,) are at the physical boundary, but only 0.07% when the true values are (0,O). Therefore, this result constitutes evidence for CP violation in B + T+T- at 99.93% confidence level. The two-dimensional confidence regions are shown in Fig. 3.

Expressions for S,, & A,, can be written in terms of the angles $1,

$ 2 , 4 3 , the ratio of amplitudes JP/TJ and the strong phase difference 6.l2 By taking the measured value of &, a theoretically preferred range for IP/TI and using $1 + 4 2 + $3 = T , the (S,,, A,,) confidence regions can be translated into ( $ 2 , S) confidence regions. In this way, the bound 78" < 49 < 152" is obtained at the 95.5% confidence level.

4. Conclusions

The procedure for time-dependent CP violation measurements is well- established. The measurement of sin(2#1) is reaching the precision level, whilst evidence for CP violation in B + T+T- has been seen.

Acknowledgements

The author thanks the organizers for a truly enjoyable conference. The author is supported by the Japan Society for the Promotion of Science.

References 1. For a general introduction, see CP Violation, 1.1. Bigi & A.I. Sanda, Cam-

bridge University Press, 2000. 2. M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). 3. E. Kikutani ed., KEK Preprint 2001-157 (2001), to appear in Nucl. Instr.

and Meth. A. 4. A. Abashian et al., Nucl. Instr. and Meth. A 479, 117 (2002). 5. H. Kakuno et al., in preparation. 6. H. Tajima et al., hep-ex/0301026, submitted to Nucl. Instr. and Meth. A. 7. L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983). 8. K. Abe et al., Phys. Rev. D 66, 071102(R) (2002). 9. Heavy Flavour Averaging Group, March 2003,

http://hepl.phys.ntu.edu.tu/h.pchang/rare-hfag.html. 10. K. Abe et al., hep-ex/0301032, submitted to Phys. Rev. D. 11. G. J. Feldman and R. D. Cousins, Phys. Rev. D 57, 3873 (1998). 12. M. Gronau and J.L. Rosner, Phys. Rev. D 65, 093012 (2002).

GLOBAL OBSERVABLES AND IDENTIFIED HADRONS IN THE PHENIX EXPERIMENT AT RHIC

HANS-AKE GUSTAFSSON Division of Experimental High Energy Physics,

Department of Physics, Lund University,

Box 118, SE-2.21 00 Lund,

Sweden, For the PHENIX Collaboration,

E-mail: hans-ake.gustajssonQhep.1u.se

The PHENIX experiment is one of the two large experiments at RHIC. It addresses most of the signals suggested from the Quark-Gluon Plasma. This paper focuses on the measurements of global observables and identified hadron spectra and particle ratios from the two first runs with Au+Au collisions at 130A GeV and 200A GeV. The energy density reached in the most central collisions is about 5 GeV/fm3. The spectral shape of the transverse momentum spectra as well as the < p~ > dependence on centrality indicate a strong collective expansion of the system in central collisions. The observed number of protons and p is about the same indicating that we are approaching a net baryon free region at mid rapidity. A larger number of protons than pions above about 2 GeV/c is observed.

1. Introduction

The aim of high-energy heavy-ion physics is to study strongly interacting matter under extreme conditions of high energy density and high temperature. The theory of strongly interacting matter, Quantum Chromody- namics (QCD), describes colored particles (quarks and gluons) as being confined into hadrons. However, in systems of temperatures above 150-200 MeV and energy densities above 1-2 GeV/fm3, deconfinement of quarks is expected, i.e. quarks are no longer bound into hadrons but can move “quasi-freely” over volumes where supercritical conditions are prevailing. In high-energy heavy-ion collisions the volumes are of the size of the colliding nuclei. At very high collision energies we expect to observe the transition from hadronic matter to a plasma of deconfined quarks and gluons, the so-called Quark-Gluon Plasma (QGP). This new state of matter is sup-

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posed to have been present till about 10-5s after the Big Bang. Thereafter, matter condensed into hadronic matter. After more than a decade of experiments at CERN SPS the general understanding is that compression effects have been observed and that they are strong enough to reach energy densities in the interesting regime for the phase transition to occur. Most experiments at CERN have shown anomalies that seem to be consistent with the formation of the QGP. The PHENIX experiment at RHIC addresses all those observables that showed anomalies in the CERN experiments. Since large energy densities are produced at RHIC energies, the QGP should be produced more abundantly compared to SPS energies. PHENIX together with the other RHIC experiments are very well suited to give better evidence of QGP formation.

2. RHIC and PHENIX

The Relativistic Heavy Ion Collider (RHIC) [l] at Brookhaven National Laboratory is the first dedicated high-energy heavy-ion collider in the world. It consists of two independent rings of superconducting magnets with a cir- cumference of about 4 km. The collider is accelerating and storing beams of ions ranging from H (proton) to Au at maximum energy of 250 GeV for protons and lOOA GeV for Au nuclei. Polarized protons for spin physics studies are also available. The PHENIX experiment [2] is a two arm central spectrometer with an axial field magnet and two muon endcap spectrometers. The experiment covers I 77 I< 0.35 for electrons, photons and hadrons and 1.2 < I 77 )< 2.5 for muons.

3. Global observables

3.1. Centrality selection

An important parameter in high-energy heavy-ion collisions is the number of nucleons that interacted inelastically, i.e. the number of participants. The PHENIX experiment is determining this quantity by using Zero Degree Calorimeters (ZDC) in combination with Beam-Beam Counters (BBC). The ZDC measures the energy carried by the spectator neutrons while the BBC measures the number of charged particles in the region 3.1 <I 77 I< 3.9. The relation between the ZDC and BBC signals could be used to calculate the event classes corresponding to a certain percent of the cross-section [3].

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3.2. Charged particle multiplicity and Transverse Energy distributions

The production of charged particles in high-energy heavy-ion collisions arises from many different physics processes. Together with contributions from soft processes seen at lower energies also contributions from hard processes, rescattering and shadowing play important roles [4]. The extracted values of (dN,h/dq),=o and (dET/dq),=o per participant pair as a function of the number of participating nucleons are shown in figure 1 for the two energies 130A GeV and 200A GeV. From these distributions the achieved energy density as a function of centrality can be determined by using the Bjorken description [5] based on the longitudinal expansion of the system. For the most central collisions we obtain an energy density of about 5 GeV/fm3 that is well above the critical value for a phase transition to the QGP of about 1 GeV/fm3 predicted from lattice QCD calculations. The obtained energy density at RHIC is about a factor 1.5 times higher that what was found at the SPS energy. The yield grows faster than the number of participants indicating a contribution from hard processes. The distributions can be confronted with different model calculations. The high energy QCD gluon saturation model KNL [6] and the two component mini jet model with nuclear shadowing [7] fit the data fairly well while others like the HIJING-model [8] and EKRT saturation model [9] fail to fully describe the data.

4. Identified hadrons

4.1. Transverse Momentum Spectra

The produced hadrons carry important information about the collision dynamics along with the evolution of the system from the early stage of the collisions to the final state interactions. The PHENIX experiment has a very good capability for particle identification for both charged hadrons and neutral pions over a broad transverse momentum range.

Figure 2 shows the transverse momentum spectra of protons and p. The spectra show a smooth behaviour over many orders of magnitude and they can for all centralities be characterized by a Boltzman distribution in mT. A striking feature of these distributions is that there is almost as many p as protons indicating that we are approaching a net baryon free region at central rapidity. The same smooth behaviour of the transverse momentum spectra is also seen for the other particle species.

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Figure 1. dET/dq (top panel) and dN,h/dq (bottom panel) per participant pair versus the number of participants N, measured at == 130 GeV (left panel) and -= 200 GeV (right panel)

Figure 2. Transverse momentum spectra for protons (left panel) and p (right panel) for different centrality classes ranging from the most central at the top to the most peripheral at the bottom

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4.2. Mean Transverse Momentum

In order to quantify the observed mass dependence of the slopes of the transverse momentum spectra, the mean transverse momenta < p~ > were extracted for the different centralities and for different particle species. The results as a function of the number of participating nucleons are shown in figure 3. In both the 130 GeV and 200 GeV results, < p~ > increases from the most peripheral to the most central and tends to saturate at large Npart. The mean transverse momentum also increases with particle mass which suggests the existence of a collective hydrodynamical expansion of the system.

PHENIX Prcltmioer

Figure 3. Mean transverse momentum of identified charged hadrons as a function of the number of participants N p a r t . The left panel shows the positive particles and the right panel shows the corresponding negative particles. Open symbols are the 130 GeV data and the closed are the 200 GeV data.

5. Particle Ratios

Particle ratios provide information on the chemical properties of the collision system. Ratios like T-/T+, K- /K+, p/p and others have been measured as a function of centrality by PHENIX. Independently of particles species, centrality or energy, the particle ratios are almost flat as a function of p~ with the exception for the p/p ratio for peripheral collisions where a decrease at high p~ is observed.

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The particle composition at high p~ is interesting in order to understand the baryon production, system evolution and the interplay between soft and hard processes as well as jet quenching in hard processes. Figure 4 shows the p/7r ratio as a function of transverse momentum for central and peripheral collisions. The data has a clear centrality dependence and the ratio for central collisions reach unity at a p~ of 2-3 GeV/c, while the ratio for peripheral collisions saturates at a value of 0.3-0.4. The observed behaviour in central collisions may be attributed to a combination of two effects namely a larger flow effect for protons as compared to pions and a pion suppression effect at high p ~ .

DT IGeVlcl

Figure 4. momentum.

p / r ratios for central and peripheral collisions as a function of transverse

References

1. www.bnl.gov/rhic. 2. www.bnl.gov/rhic/PHENIX.htm. 3. K. Adox et al., Phys. Rev. Lett. 86, 3500 (2001). 4. X.N. Wang and M. Gyulassy, Phys. Rev. D44, 3501 (2001). 5. J.D. Bjorken, Phys. Rev. D27, 140 (1983). 6. D. Kharzeev and M. Nardi, Phys. Lett. B503, 121 (2001) and D. Kharzeev and E. Levin Phys. Lett. B523, 79 (2001). 7. S. Li and X.N. Wang, Phys. Lett. B527, 85 (2002). 8. X.N. Wang and M. Gyulassy, Phys. Rev. Lett. 86, 3498 (2001). 9. K.J. Eskola et al., Nucl. Phys. B570, 379 (2001) and Phys. Lett. B497, 39 (2001).

LEP LIMITS ON HIGGS BOSON MASSES IN THE SM, IN THE MSSM AND IN GENERAL 2HD MODELS

SIGVE HAUG Department of Physics, University of Oslo

P.O. Box 1048 Blindern, 0316 Oslo, Norway E-mail: sigve. haug @fys. uio. no

Before shutting down in 2000 the four LEP experiments ALEPH, DELPHI, L3 and OPAL collected a total of 2461 pb-l of data from electron positron collisions at centre of mass energies between 189 GeV and 209 GeV. Combining this data the LEP Higgs Working Group has deduced lower limits for Higgs boson masses at the 95% confidence level. For the Standard Model Higgs boson the limit is at 114.4 GeV/c2. Limits for the light CP-even and the CP-odd neutral Higgs bosons of the Minimal Supersymmetric Standard Model are also reviewed together with the mass limit on charged Higgs bosons obtained from searches in general two Higgs doublet models at LEP.

1. Introduction

The Standard Model (SM) contains one complex Higgs doublet which ac- commodates electroweak symmetry breaking and fermion masses. The doublet leads to one physical Higgs boson Ho. Extensions of the SM with two complex Higgs doublets (2HD) have five physical Higgs bosons ; a charged pair H*, one neutral CP-odd scalar Ao and two neutral CP-even scalars, ho and Ho. In the Minimal Supersymmetric Standard Model (MSSM) a 2HD is required.

At the Large Electron Positron Collider (LEP) the four experiments ALEPH, DELPHI, L3 and OPAL collected 2461 pb-l of data from electron positron collisions a t centre of mass energies between 189 GeV and 209 GeV. On this basis the LEP Higgs Working Group has deduced lower limits on the Higgs boson masses using the modified frequentist method. In this method a signal plus background hypothesis is considered as excluded at a 95% confidence level when the statistic CL,, defined as the ratio of the p-value of the signal plus background hypothesis to the p-value of the background only hypothesis, is smaller than or equal to 5%.

The search results for neutral Higgs bosons within the SM and the

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MSSM are reviewed here. Also the result from the search for charged Higgs bosons within a general 2HD model is considered. The numbers presented are the latest. Final results are expected from the LEP Higgs Working Group by the end of 2003. Further searches for Higgs bosons within other extensions of the SM are reported elsewhere.

2. Limit on the SM Higgs boson mass

The contribution to the SM Higgs production at LEP was dominated by the Higgs Strahlung process e+e- + HoZo. In the relevant search channels the WW fusion e+e- + HOeue became significant at the kinematical limit due to the Zo mass. The ZZ fusion remained subdominant. The searches were structured in channels based on the relative fractions of the various decay modes of the Zo boson. Due to the Higgs boson's prefered decays into b-quark pairs, b-tagging has been essential in the analyses.

The two upper plots in Figure 1 are instructive plots of the probability density functions (pdf) of the constructed observable -2Zn(Q) where Q is the likelihood ratio of the two alternate hypotheses. The dashed line is the pdf for the signal plus background hypothesis and the solid for the background only hypothesis. The vertical solid line indicates the observed value. To the left a Higgs mass hypothesis m H o = 110 GeV/c2 is assumed, to the right m H o = 116 GeV/c2. The separation between the hypotheses decreases with increasing mass according to the falling cross section. The shaded area on the right side of the observed line is now the p-value for the signal plus background hypothesis. The left lower plot shows the CL, for Higgs mass hypotheses from 100 GeV/c2 up to 120 GeV/c2. In the region where the CL, is below the horizontal 5% line, the hypothesis is considered excluded. The expected CL, leads to a limit at 115.3 GeV/c2. The observed CL, yields a limit of 114.4 GeV/c2.

The lower right plot shows the comparability of the data with background only hypotheses, the 1 - CLb, in the Higgs mass range from 100 GeV/c2 to 120 GeV/c2. The observed solid line lies within the two sigma band in the whole range. The largest deviations appear in the vicinities around 100 GeV/c2 and 116 GeV/c2. The dashed-dotted line indicates the 1 - CLb for the signal plus background hypotheses.

3. Limits on the neutral MSSM Higgs boson masses

In the MSSM search a constrained model with a CP conserving Higgs sector and seven parameters, MSUSY, M2, p, A, tanp, mA and mg, is used.

[email protected] 2

3

e

z0.04

9 20.03

0.02

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0 -60 -40 -20 0 20 40 60

lo 100 102 104 106 108 I10 112 114 116 118 120 mdGeV/cz)

-9.14 $0.12 $ 0.1 4 0.08 0.06 0.04 0.02

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100 102 104 106 108 110 112 114 116 118 120 m,,(GeV/cz)

Figure 1. The upper plots show the probability density functions of the observable -21n(Q) at two different test masses. The lower plots show the CL, and the 1 - CLb for Higgs mass hypotheses from 100 GeV to 120 GeV. The bands in the CL, plot correspond to one and two standard deviations.

Three benchmark scenarios are examined. The Max mho scenario yields a maximum mass for the lightest neutral Higgs boson and leads to a conservative mass limit. The No Mixing scenario corresponds to the Max mho,

but without mixing in the stop sector, enabling the study of the mixing influence. The Large p scenario ( p = 1 TeV) is designed to illustrate regions in the parameter space where ho does not decay into pairs of b-quarks. In addition to the SM processes the MSSM contains the associated pair production e+e- + Aoho for the lightest Higgs boson ho.

In Figure 2 scans in the tanP versus mhO/AO plane are shown for the Max mho and the No Mixing scenarios. To the left one can see that the lightest CP-even Higgs boson mass is excluded up to 91.0 GeV/c2 for Max mho and 91.5 GeV/c2 for No Mixing. The CP-odd Higgs boson is excluded up to 91.9 GeV/c2 and 92.2 GeV/c2 respectively. The right plots show that tanP is excluded from 0.5 till 2.4 in the Max mho scenario and from 7.0 till 10.5 in the No Mixing scenario.

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Figure 2. Exclusion scans in the tanP versus mho plane and in the tanP versus mAo plane for the Max mho and the No Mizing scenarios. The dotted lines indicate the expected exclusion contours. The exclusion level is 95%.

The Large p scenario is excluded entirely and thus not shown.

4. Limit on the charged 2HD model Higgs boson mass

In a general two Higgs doublet extension of the SM, the charged Higgs bosons are produced via Z or y exchange in the process e+e- -+ H+H-. The most important decay channels are (cS)(Cs), (T+Y,)(T-O,) and

In Figure 3 the upper plots show the 1 - CLb and the difference between data and expected background for the L3 experiment only. The case

( C S ) ( T + V , ) -k ( C g ) ( T - F , ) .5

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L3 preliminaly

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1' 0

I LEP 189-209

..... Exptedbackpund Br(H+lvj.O

...,,,,,. Expectedsignal i

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inH (GeV/?j

Figure 3. The two upper plots are for L3 alone. The left shows the 1 - CLb scan in the non leptonic decay channel. The bands correspond to one and two standard deviations. The mass histogram contains the difference between data and background. The lower plots show combined results from all four experiments. To the left the CL, scan is plotted, to the right the exclusion scan in the BT(H+ -+ 7vr) versus mH;t plane. The exclusion level is 95%.

where B r ( H f -+ r+vT) = 0, is shown. In the vicinity of 68 GeV/c2 the observed 1 - CLb is more than three standard deviations away from the expected background only hypotheses. The histogram to the right shows the excess responsible for this deviation. However, the other experiments do not confirm this interesting observation. Combined for all four experi-

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m€io mho mAO tan p mho m.40 tan p m”+

ments the results are shown in the lower left 1 - CLb scan. The lower right exclusion scan shows for which m H * the signal plus background hypotheses are excluded as a function of the BT(H+ -+ -r+vr). A branching ratio independent lower exclusion limit is obtained at m H f = 78.6 GeV/c2. The exclusion level is 95%.

Expected limit / GeVc-2 Observed limit / GeVcP2 Model

115.3 114.4 SM 94.6 91.0 95.0 91.9

(0.5,2.6) (0.5,2.4) 95.0 91.5

95.3 92.2 No mixing (0.8,16.0) (0.7,10.5)

MSSM Max mho

MSSM

78.6 2HD

5. Summary

The LEP Higgs Working Group has calculated lower mass limits on Higgs bosons based on the combined data from the four LEP experiments. The limits for the SM Higgs boson, the neutral MSSM Higgs bosons and the charged Higgs bosons within a general two Higgs doublet extension of the SM, are summarised in Table 1. The results are preliminary and final numbers are expected to appear by the end of 2003. LEP limits on Higgs bosons in other models and scenarios are reported elsewhere.

Table 1. 2HD Higgs bosons.

Expected (median) and observed 95% LEP limits on SM, MSSM and

References

1. A. L. Read, Modified Fkequentist Analysis of Search Results, in F. James, L. Lyons and Y. Perrin (eds.), Workshop on Confidence Limits, CERN Yellow Report 2000-05, available through weblib.cern.ch.

2. K. Hagiwara et aL, Phys. Rev. D66, 010001 (2002). 3. LEP Higgs Working Group, Search f o r the Standard Model Higgs Boson at

LEP, LHWG Note 2002-01. 4. LEP Higgs Working Group, Searches f o r the Neutral Higgs Bosons of the

MSSM, LHWG Note 2001-04. 5. A. Djouadi, J. Kalinowsky and P. M. Zerwas, Z. Phys. C57, (1993) 569. 6. LEP Higgs Working Group, Search fo r Charged Higgs B o s o m , LHWG Note

2001-05.

THE AMS-02 EXPERIMENT *

R. HENNING FOR THE AMS COLLABORATION. Massachusetts Institute of Technology

77 Massachusetts Ave. Cambridge, MA 02139, USA E-Mail: rhenningamit. edu

The Alpha Magnetic Spectrometer (AMS-02) is a high-energy particle physics experiment that will be mounted on the International Space Station for three years. It will collect 10 billion cosmic rays in an attempt to resolve important cosmological questions, such as possible existence of large antimatter domains in the universe and the nature of dark matter. This talk will review the physics goals and design of the AMS-02 experiment.

1. Introduction

The Alpha Magnetic Spectrometer (AMS-02) is a high-energy particle physics experiment that will be mounted on the International Space Station Alpha (ISS) in 2005 for 3 years. An engineering version of AMS-02, AMS- 01, was flown on board the space shuttle Discovery in June, 1998. The physics results from this flight are discussed in P. Zuccon's presentation from this conference. The AMS-01 flight also served as an important and successful test of particle physics detector technology in space for AMS- 02. This talk will review the physics motivation and design of the AMS-02 experiment.

2. Physics Motivation for AMS-02

AMS-02 is a TeV particle detector in space. By measuring cosmic rays in near earth orbit, AMS-02 will attempt to unlock some of the most significant puzzles in cosmology and particle physics. The two main physics goals of AMS-02 are:

'see also article by p. zuccon on ams-01 in these proceedings

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Figure 1. AMS-02 in space shuttle payload bay, prior to installation on the ISS.

2.1. Search for Cosmic Antimatter:

AMS-02 will attempt to determine if cosmologically significant amounts of antimatter exist in the universe. A direct method to detect this antimatter is to search for antimatter nuclei with 2 < -1 in cosmic rays. The detection of a single cosmic ray antihelium nucleus would provide compelling evidence for the existence of large amounts of antimatter in the universe, while the detection of a single anticarbon nucleus would be irrefutable proof of new physics, since there are no known astrophysical sources of such heavy antinuclei l . Antiprotons 6) and positrons (e+) have been observed in cosmic rays, but the observed fluxes to date are consistent with production via spallation of cosmic ray protons on interstellar gas.

2.2. Search for Dark Matter

Certain dark matter candidates can be detected by their signatures in cosmic rays. One promising cold dark matter candidate is the neutralino (xo), the lightest stable particle in R-parity conserving minimally supersymmet-

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ric theories. AMS-02 could detect xo dark matter indirectly by searching for anomalies that xoxo annihilation would generate in cosmic ray spectra '. There are several cosmic ray species that are promising candidates for observation of these anomalies. One is cosmic-ray antiprotons; an excess of antiprotons below - 1 GeV would indicate a possible xo dark matter annihilation signal. However, this signal is difficult to interpret due to the astrophysical spallation background and solar modulation 3. A more promising signal is an excess antideuterium ( D ) at low energies, where the spallation astrophysical background is highly suppressed. AMS-02 may be able to detect a few D in some models 4 .

The most promising signal xoxo annihilation may produce is anomalies in the e+ spectra. The primary features AMS-02 would look for are deviations from the power law e+ spectra expected from secondary spallation sources at energies above several GeV 5 .

2.3. Other Physics

AMS-02 will also be able to perform many other studies and searches. These include, but are not limited to :

Strangelets in cosmic rays6. 0 Primordial black hole evaporation7. 0 Microquasar searchess. 0 Cosmic ray propagation and lifetime studies. 0 The dynamics of cosmic rays near earth g.

No experiment to date has performed cosmic ray measurements in this energy range in near-earth orbit with the sophistication and precision of AMS-02, which makes the prospect of discovering unpredicted phenomena a major motivation as well.

3. The AMS-02 Detector

3.1. Design Considerations

AMS-02 will collect N 1O1O cosmic ray events in 3 years and has to be able to identify single cosmic rays, i.e. anticarbon nuclei, hence good discrimination and resolution are crucial elements incorporated into its design. AMS-02 will also face challenges in a space environment that terrestrial particle detectors do not. Some of these are: temperature fluctuations of N 100°C, removal of waste heat, ionizing radiation in space, vibrations (6.8Grms) and

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AMS 02 ( Exploded View)

Ring Radiator

u Photomultiplie

Radiator

Reflector Phoiomulhpliers

TRD: Transition Radiation Detector

ToF: (sl ,s2) Time of Flight Detector

T R Silicon Tracker

AC: Anticoincidence Counter

MG: Magnet

ToF (s3,s4) Time of Flight Detector

RICH: Ring image Cherekov Counter

EMC: Electromagnetic Calorimeter

Lead I Fiber Pancake &fS %$et;c Spectrometer (1"Side)

R.Becker 07/11/01 I n t e g r a t i o n

Figure 2. An exploded view of AMS-02 showing the various subdetectors.

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accelerations (up to 17G has to be foreseen) during launch, very tight weight (14 8091b.) and power (2kW) constraints, constant exposure to vacuum, orbital debris and micrometeorites, and safe and reliable operation without services for three years.

3.2. Subdetectors

Figure 1 shows a schematic of the AMS-02 experiment in the space shuttle cargo bay. Figure 2 shows a more detailed view with the different subdetectors, separated for clarity. AMS-02 has six subdetectors: a transition radiation detector (TRD), a time of flight detector (TOF), a silicon tracker and magnet, a ring imaging Cherenkov counter (RICH), and an electromagnetic calorimeter (EMC, aka. ECAL). I will discuss each subdetector individually, starting from the top of the detector.

The TRD allows the separation of e+ and protons beyond 2 GeV, where the TOF cannot resolve e+ from the much more abundant protons. The ability to detect structure in the positron spectra, as mentioned earlier, is important for the indirect xo dark matter search.

Transition radiation (TR) is emitted when an ultra-relativistic particle traverses the interface between media with different dielectric constants. The useful feature of TR is that the energy in the emitted photons is a monotonically increasing function of the relativistic gamma factor of the particle. This means that a e+ at 10 GeV will emit considerably more TR than a proton at the same energy, allowing e+ /p+ discrimination. The TRD consists of about 5000 multilayer kapton proportional tubes of 6mm diameter filled with a Xe:C02 (4:l ratio) gas mixture at 1.2 Bar to detect the TR X-ray photons. The space between tubes is filled with polypropylene fiber radiator material that generates the TR.

Immediately outside the bore of the magnet is the AMS-02 TOF detector. Its functions are to determine particle velocity via time of flight, perform charge measurements via the energy deposit, and to separate upward and downward-going particles. It consists of two upper and two lower planes of scintillator paddles. Each scintillator paddle is read by two PMTs at each end. The TOF has a time resolution of about 120ps.

The magnet is a state-of-the-art cryogenic superconducting magnet. It consists of two dipole coils to generate the bending field and 12 flux return coils to bring the fringe magnetic field and dipole moment to levels accept- able to NASA. The generated magnetic field is OAT, which allows particle rigidity measurements up to 1 TV.

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Inside the magnet is the silicon strip detector. It determines particle rigidity by accurately measuring the path of the particle inside the magnetic field of the magnet. The estimated rigidity resolution is dR/R = 2% for 1 GeV protons. It consists of 8 planes of silicon sensors with a total surface area of about 6.5 m2. The silicon strips on the sensors have a pitch of 27.5pm in the bending plane and 104pm in the non-bending plane.

Directly below the magnet is the Ring Imaging Cherenkov Counter (RICH). By reconstructing the Cherenkov cone generated by the cosmic ray particle as it traverses an aerogel radiator, the RICH allows very accurate velocity measurements. This is important for isotopic separations, which will allow cosmic ray propagation studies.

At the bottom of the detector is the Electromagnetic Calorimeter (EMC). The main function of the EMC is to separate e* from p* by studying the shower profile. The EMC is a flat, square slab of lead with embed- ded scintillator fibers. The light from the scintillator fibers are captured by PMT mounted at the edges of the EMC. The geometry of the fibers is such that it allows a three-dimensional reconstruction of the shower profile. The EMC has

All the subdetectors, electronics, and heat radiators are mounted on a Unique Support Structure (USS 11) consisting of aluminium alloy beams.

p* rejection at 95% e* efficiency.

4. Conclusion

The AMS-02 experiment will perform measurements of cosmic rays in near earth orbit to unprecedented accuracy. The measurements from AMS-02 could have significant implications for cosmology and particle physics. It will also perform important measurements relating to the origins and propagation of cosmic rays.

References 1. G. Steigman, ARA&A, 14, 339. 2. Gerard Jungman, Marc Kamionkowski, Kim Griest, Phys. Rept., 267, 195,

(1996). 3. L. Bergstrom et al, astro-phf9902012 4. F. Donato et al, Phys. Rev. D62, 043003 (2000). 5. E. Baltz et al, Phys. Rev. D65, 063511 (2002). 6. Jes Madsen, astro-phf9809032. 7. A. Barrau et al, astro-ph/0112486. A. Barrau et al, A&A, 398, 403, (2003). 8. S. Heinz and R. A. Sunyaev, astro-phf0204183 9. M. Aguilar et al, Phys. Repts., 366, (2002), 331.

RARE B DECAYS IN BABAR

A.HICHEUR On Behalf of the BaBar collaboration

LAPP IN2P3-CNRS 9 Chemin de Bellevue - BP 110

74941 Annecy-le-Vieux CEDEX - FRANCE E-mail: hicheurQlapp.inZp3.fr

Measurements and searches for rare B decays have been performed with the BaBar detector at the PEP-I1 e+e- asymmetric B Factory, operating at the T(4S) resonance. We report some recent branching fraction measurements on hadronic and radiative B decays, occuring from b -+ s l d and b + u transitions. Most of the results presented here are based on a data sample corresponding to a luminosity of 81.9 fb-’.

1. Motivations

Most of the decays of the B meson occur from a b + c tree transition. This produces final states such as B -+ Dn, B + Dp,. . . All the decays that don’t belong to this category are referred to as rare decays. These are generated by the b + u and the b -+ s l d loop (“penguin” 1,2) transitions. Given the huge data sample available at the B factories, precise measurements of rare B decays could be used to probe new physics. This is particularly true for the penguin diagrams where virtual Higgs bosons or SUSY particles could be involved in the loop. On the other hand rare CP eigen states bring additional information to test the CKM unitarity triangle. Direct CP (or charge) asymmetry defined as:

is non-zero only if there are at least two contributing diagrams to a given process, with both different weak and strong phases. It is therefore sensitive to extra contributions arising from new physics for processes driven by a single contribution in the Standard Model.

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2. Radiative and electroweak penguins

2.1. b + sy

The b + sy transition leads to the decay B + X,y where X , is a strange hadronic system recoiling against an energetic photon. Two approaches have been adopted: a fully inclusive analysis where only the photon is reconstructed (method a) and a semi-exclusive analysis (method b) in which a photon, a kaon and up to three pions are combined to form a B candidate. In both methods, we look for a photon whose energy in the T(4S) center of mass frame (E;) is above 2.1 GeV and below 2.7 GeV. Figure 1 shows the resulting E; spectrum from method a and the branching ratio a,s a function of the X , system invariant mass from method b, respectively.

1.8 2 2 2 2.4 2.6 2.8 3 3.2 3.4

Ei (GeV)

Figure 1. B + X,r analyses: inclusive photon energy spectrum (data in solid points, background expectation in open triangles) and branching ratio vs. rn(X,). The curves superimposed on the rn(X,) spectrum represent fits relying on heavy quark effective theory parameters.

A fit to the m(X,) spectrum enables to extract heavy quark effective theory parameters 516.

The total branching ratio is:

B(B + X,y) = (3.86 f 0.36(stat.) f 0.37(syst.)+~:~~(modeZ)) x low4

for the inclusive analysis and

B(B + X,y) = (4.3 f 0.5(stat.) f 0.8(syst.) f 1.3(modeZ)) x

for the semi-exclusive analysis.

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2.2. B + K(*)l+l-

The search for the electroweak penguin transition b + s 1+1- have been done through the reconstruction of the modes B + K(*)Z+l- ’. A charged or neutral K or K* is combined to a e+e- or p+p- pair to form a B candidate. Background from the charmonium modes B -+ J /$K(*) , $(2S)K(*) is vetoed by applying a cut on the lepton pair invariant mass. Figure 2 shows the distribution of beam energy constrained B mass, MES = JEtearn - pf32, and energy difference, AE = Eaearn - Eg, for the K1+1- and K*l+l- modes.

oL----------J 5.2 5.22 5.24 5.26 5.28

mEs (GeVk’) -0.2 -0.1 0 0.1 0.2

A E (GeV)

Figure 2. modes.

MES and A E projections for the combined K 1+1- (a,b) and K’ 1+1- (c,d)

The corresponding rates are:

B(B + K Z+Z-) = (0.78+0,;2,;:(st~t.)f!::~(syst.)) x B(B + K* Z+Z-) = (1.68?!:z!(stut.) f 0.28(syst.)) x or

< 3 x l o r6 62 90% C.L

These results are in the range expected in the Standard Model 819910.

25 1

3. Hadronic rare decays

Rare hadronic decaysa can be separated into two categories: those who are dominated by the penguin b -+ s l d g* transition and those who are dominated by the suppressed b -+ u tree transition.

3.1. Gluonic penguins

The decay B -+ q’K is dominated by the b -+ sg* transition while B -+ +K(*) is a pure penguin. The large rate observed for B -+ q’K has stimulated a huge amount of theoretical studies l2?l3. The neutral mode Bo -+ q’K; is a CP eigen mode and can be used for the extraction of sin(2P). The 71‘ has been reconstructed in both q7r+7r- and poy channels 14. Figure 3 shows the MES and AE distributions for Bf -+ q’Kf and Bo -+ Q’K: channels.

5 2 5.22 5.24 5.26 5.28 2 rnES (GeVIc’) AE (GeV)

Figure 3. M E S and AE projections for B* + q’K* (a,b) and Bo + q’Ki (c,d). Points with errors represent data, solid curves the full fit functions, and dashed curves the background functions; the shaded histogram represents the &,K subset.

The measured rates are:

B(B* -+ $Kf) = (76.9 f 3.5(stut.) f 4.4(syst.)) x B(Bo -+ q’Ko) = (55.4 f 5.2(stut.) f 4.0(syst.)) x loF6

and the measured charge asymetry for B* -+ q’K*,

dCF($K*) = 0.037 f 0.045(stut.) f O.Oll(syst.),

aIn this note, we only present results on two body modes. Recent measurements of three body charmless decays are detailed in reference l1

252

is consistent with zero. B + q5K* has been studied in both the charged and neutral modes l5 with K** being reconstructed in the channels KErf and K f r o and K*O being reconstructed in the channels K*rF and KEro. Figure 4 shows the MES distribution for B* + +K** and Bo + q5K*O.

16

-* 12

>,

Z 8 I

: a2

I

0 5.lW 5.225 5.250 5.175 5.Na 5.2W 5.125 5.250 5.275 5.m

m, (G~v/c*) m, (G~v/c*)

Figure 4. M E S projections for B -+ dK* . Open histograms represent the full data, solid curves the full fit functions, and dashed curves the background functions; the hatched histograms represent the @K**(-+ K*7ro) and dK*O(-+ Kz7ro) subsets.

The branching ratios and charged asymetries are:

B(B* + 4K**) = (12.lt:::(stat.) f 1.5(syst.)) x

B(Bo -+ q5K*O) = (ll.l+::P(stat.) f l.l(syst.)) x ACp($K**) = 0.16 f O.l7(stat.) f 0.04(syst.)

ACp(q5K*O) = 0.04 f 0.012(stat.) f 0.02(syst.)

3.2. Suppressed tree transition

The decay Bo + r+r-, dominated by the tree b + u transition, is used for the extraction of sin(2a). For this purpose, one needs to unfold the penguin b + dg* contribution. This could be done with an isospin analysis involving the measurements of the modes Bo + roro and Bf + r*ro 16.

Figure 5 shows the MES and AE distributions for B* + r*ro. A Bf -+ r*ro signal is observed with a 7.7 u significance and a charge

asymmetry consistent with zero while only a 90% confidence level upper limit on Bo + noro is set:

B(B* + r*ro) = (5.5+A:;(stat.) f O.G(syst.)) x

B(Bo + roro) < 3.6 x dCp(r*rO) = -O.O3+~:~~(stat.) f 0.02(syst.)

253

3 %.2 -0.1 0 0.1 m,, (GeV/c2) AE (GeV)

Figure 5 . data, solid curves the full fit functions, and dashed curves the background functions.

M E S (a) and A E (b) projections for B* + sfso. Histograms represent

References

1. 2. 3.

4.

5. 6. 7.

8. 9.

J.Ellis et al., Nucl. Phys. B 131, 285-307 (1977). K.Linge1 et al., Ann. Rev. Nucl. Part. Sci. 48, 253 (1998) - hep-ex/9804015. The BaBar collaboration, B.Aubert et al., hep-ex/0207076, submitted to the 31st International Conference on High Energy Physics, July 2002 (ICHEP 2002), Amsterdam, The Netherlands. The BaBar collaboration, B.Aubert et al., hep-ex/0207074, submitted to ICHEP 2002, Amsterdam, The Netherlands. A.Kagan and M.Neubert, Eur. Phys. J. C7, 5 (1999) Z.Ligeti et al., Phys. Rev. D 60, 034019 (1999). The BaBar collaboration, B.Aubert et al., hep-ex/0207082, submitted to ICHEP 2002, Amsterdam, The Netherlands. A.AB et al., Phys. Rev. D 61, 074024 (2000). A.Faessler et al., Eur. Phys. J . C4, 18 (2002).

10. M.Zhong et al., hep-ph/0206013, to’appear in the proceedings of ESO - CERN - ESA Symposium on Astronomy, Cosmology and Fundamental Physics, Garching, Germany, 4-7 March 2002.

11. The BaBar collaboration, B.Aubert et al., hep-ex/0304006, submitted to Phys. Rev. Lett.

12. C-W. Chiang and J.L. Rosner, Phys. Rev. D 65, 074035 (2002), and references therein.

13. M. Beneke and M. Neubert, Nucl. Phys. B 651, 225 (2003). 14. The BaBar collaboration, B.Aubert et al., hep-ex/0303046, submitted to

15. The BaBar collaboration, B.Aubert et al., hep-ex/0303020. 16. The BaBar collaboration, B.Aubert et al., hep-ex/0303028, submitted to

Phys. Rev. Lett.

Phys. Rev. Lett.

RECENT RESULTS IN B-PHYSICS AND PROSPECTS FOR HIGGS SEARCHES AT DO

M. HOHLFELD for the DO Collaboration Universitat Mainz, Institut fur Physilc, 55099 Mainz, Germany

The upgraded DO detector at the Tevatron proton-antiproton collider provides an excellent environment to study a broad spectrum of interesting physics. This includes a large B-physics program, that is complementary to the B factories. Furthermore, the Tevatron is the accelerator, where a search for the Higgs boson can be performed. Both the first B-physics results and prospects in B- as well as Higgs physics are summarized in the present paper.

1. Introduction

The Tevatron collider, which operates at a center-of-mass energy of & = 1.96 TeV, offers a good possibility to explore &quark physics. B hadrons are produced at a large rate at the Tevatron, where the pp + bb cross section is predicted to be x 150 pb for Run 11. Contrary to the e+e- B factories, that operate at the T(4s) resonance, where the e+e- +. BB cross section is in the order of 1 nb, all species of B hadrons, including Bd, B,, B* mesons and Ab baryons, are produced at the Tevatron. On the other hand, the backgrounds at a hadron collider are significantly larger compared to the relatively clean environment of e+e- machines.

Furthermore, the Tevatron is the only place to search for the Higgs boson until the LHC comes online. For the Higgs boson search a good understanding of &jets is necessary since in the low mass region ( M H < 135 GeV) the Higgs bosons decays dominantly into bb pairs. Despite the fact, that the low mass region is the most favoured one, the Higgs decay into WWpairs offers the possibility to search for heavier Higgs bosons up to MH x 200 GeV.

2. The DO Detector in Run I1

In 2001, a new running period, called Run 11, has started at the Tevatron. Up to now, data corresponding to an integrated luminosity of JLdt x 50 pb-l, have been accumulated.

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255

To accommodate to the Tevatron environment in Run 11, the DO detector has undergone a major upgrade. The new tracking system consists of a silicon microstrip vertex detector that are located inside a 2 Tesla solenoidal magnet. The scintillating fiber tracker covers the region in pseudorapidity up to q = 1.65 and the forward disks of the silicon fiber tracker allow track reconstruction up to q = 2.5 demonstrating the excellent forward coverage of the tracking system. The impact parameter resolution reaches M 10 pm for high p~ tracks and is close to the expectations, even without final optimization.

The DO muon sytem consists of three layers of proportional drift tubes with a 2 Tesla toroidal magnet between the inner two layers, that allows a momentum measurement in the muon system itself. The muon system has been upgradetd to extend the q coverage and to improve the spatial resolution. Furthermore the trigger thresholds can be lowered.

have been added in front of the DO calorimeter to improve electromagnetic shower identification, both in central and forward region.

The upgrade of the trigger system includes a central track trigger at Level 1 and an impact parameter trigger at Level 2. These triggers have not been used for the results presented in this paper, but wiIl improve the B physics capability in the future. They allow to reduce p~ thresholds for single lepton and dilepton triggers, which will result in a significant increase in the yield of Bo + J/9Kf candidates.

and a scintillating fiber tracker

Preshower detectors

3. The DO B Physics Program

The broad B physics program of the DO collaboration includes lifetime measurements of Bf and A,,, studies related to CP violation, Bf mixing, cross section measurements and rare decays.

The first J / 9 + p+p- candidates, that DO has measured in Run 11, are presented in Fig. 1 (left). Using these events to search for B mesons, DO has observed its first exclusively reconstructed B hadrons in the decay mode B* + J /9Kh . The mass peak, corresponding to an integrated luminosity of Ldt = 5 pb-l, is shown in Fig. 1 (right).

3.1. Measurement of the Average B Lifetime

The same 5 pb-l sample can be used to derive the average B hadron lifetime. The proper decay length of the J / 9 + p+p- signal is shown in Fig. 2. The contributions can be divided into three main parts. The first

256

E

_ _ 4 ' ' hli ' 24 ' 2I6 ' ili ' ;

Figure 1. Run I1 data.

Dimuon invariant mass distribution (left) and B* resonance (right) in DO

one, that has a long-lived component, are the J/iP7s from B decays. This contribution can be described by an exponential decay convoluted with a Gaussian, that takes into account the B lifetime resolution. Prompt J/iP's from the primary vertex are represented by a double Gaussian centered at zero. The third contribution, fakes from sequential B decays and cornbina- torics, can be determined from events of the sidebands of the J/iP peak. It is parameterized by a Gaussian and positive and negative exponential tails. The fit of all three contributions describes the data well and yields 416 f 30 J / Q candidates from B decays. The average B hadron lifetime is found to be cr = 492 f 37 pm, which is in good agreement with the world average value of 469 pm. The errors are statistical only.

i 30 signal events

----- .. .__

Figure 2. Proper decay lentgh for J / Q candidates corresponding to 5 pb-l of D 0 data.

257

3.2. Prospects for a Measurement of the &, Lifetime

A measurement of the Ab lifetime is interesting because previous measurements in semileptonic decay channels found a ratio of T(hb)/7-(Bo) = 0.797 f 0.053, which is in disagreement with theoretical predictions based on a naive spectator model. Using dilepton triggers, it will be possible to reconstruct sufficient Ab baryons in the fully hadronic J / Q A o mode, which has the advantage, that the hi, momentum can be measured with high precision. Monte Carlo calculations show that a lifetime resolution of 0.11 ps can be achieved.

3.3. Prospects for measuring CP Violation

In the context of the Standard Model, CP violation is introduced by a single complex phase in the CKM matrix. This phase can be measured using the time dependent asymmetry in Bo + J/QK: and Bo + J / S K : decays. This asymmetry is given by

r(B0 + J/QK:) - r (B0 + J/QK:) A C P ( t ) = r(Bo + J/QK,O) + r (B0 -+ J/QK,O) = sin(2p) sin(Amdt) ( 1 )

where Am, = rn(Bieavy) - m(B&,J is the Bo - Bo oscillation frequency and ,4 = aty(-vcdv,*,/&dvb) is one angle of the unitarity triangle.

With 2 fb-', DO expects to reconstruct 40 000 events in the J / Q + p f p - mode. The final predicted resolution on sin(2p) is 0.03. This precision can be achieved because of the good muon acceptance, low trigger thresholds, tracking in the far forward region and good flavour tagging.

3.4. B: mixing

A measurement of the mixing between the neutral Bo mesons (B: and B:) is interesting, because the measurement of the ratio of oscillation fre- quencies Amd/Am, allows to constrain the CKM matrix element ratio &dvb/VcdV,+b, representing one side of the unitarity triangle. Oscillations have already been observed in the B: system, but not for B: mesons. At the moment, the Tevatron is the only place to look for B; mixing, since B; mesons cannot be produced at the e+e-B factories. The B: mixing can be observed at DO in semileptonic decays, which, unfortunately, have a limited lifetime resolution due to a neutrino in the final state. Contrary the fully hadronic modes yield an excellent lifetime measurement, however it is very hard to trigger. The DO reach for x, = A m s / r , is x, M 30.

258

4. Higgs Physics at DQ,

The search for the Higgs boson is one of the major D 8 physics goals. Depending on the Higgs mass, the cross section is in the order of 0.1-2 pb. In the low mass region, where the Higgs boson decays mainly into bb pairs, the associated production together with a W or Z boson has to be used to get an additional lepton from the vector boson decay. This is necessary because of trigger issues and to suppress the very large dijet background. However, the cross section is decreased by an order of magnitude compared to the dominant gluon fusion process.

In the high mass region, the Higgs decays into WW pairs, with subsequent decay of the W bosons into electrons or muons, offer a clean signature with two leptons accompanied by missing transverse energy. Thus the gluon fusion process can be used to look for the Higgs boson.

4.1. Associated Production W / Z H with H + bb

Because of the two bjets in the final state, the btagging capability is very crucial to detect the Higgs boson in this channel. The efficiency and fake rate for the btagging is determined by the impact parameter resolution. Monte Carlo simulations show, that a btagging efficiency of 60% can be achieved with a mistag rate of 15% for c-quarks and a few percent for light quarks.

Furthermore, a good understanding of the dijet mass distribution and an excellent mass resolution is necessary to see the small bump of Higgs decays on top of the large background. The dijet mass spectrum for W+jets events with W + lu decays is shown in Fig. 3 (left). The data are represented by the points with error bars, the Monte Carlo prediction for W+jet production is normalized to the data and superimposed. The shaded band reflects the experimental uncertainty.

4.2. H + WW + lulu

In this decay channel the spin correlations between the two charged leptons can be used to suppress most of the backgrounds. Because of the decay of the spin-0 Higgs boson into two spin-1 vector bosons, the opening angle A@ between the charged leptons tends to be small in contrast to most backgrounds, where the leptons are either back to back or the A@ distribution is flat. The A@ distribution in the dielectron final state for signal and various backgrounds after final selection is shown in Fig. 3 (right). The

259

data (points) are consistent with expectations from known standard model physics processes.

D 0 Run II Preliminary

- Data - MC

10 t

DO Run I I Preliminary * Data -W+]ets -Multi-jet -W+ - 2 3 I ee -~ -Z&:

0 100 200 MU (GeW A @ee

Figure 3. electron plus missing transverse energy final states (right) in DO Run I1 data.

Dijet mass distribution in W+jet events (left) and Aaee distribution in two

5. Conclusion

The DO detector at the Tevatron offers the possibility to successfully study B physics in Run I1 and to make competitive contributions in various areas of B physics such as sin(2P) measurements and studies of B: mixing. In the next few years D 0 can verify if there is a low mass Higgs boson. Before that first results sensitive to alternative Higgs models with enhanced cross section can be expected.

References 1. M. Roc0 for the DQ) Collaboration, FERMILAB-CONF-98/356-E. 2. D. Adams et al., Nucl.Phys.Proc.Supp1. 44, 332 (1995). 3. P. Baringer et al., Nucl.Instrum.Meth. A469, 295 (2001). 4. S. Aronson et al., Nucl.Instmm.Meth. A269, 492 (1988).

THE HARP HADRON PRODUCTION EXPERIMENT AND ITS SIGNIFICANCE FOR NEUTRINO FACTORY DESIGN

L. C . HOWLETT ON BEHALF OF THE HARP COLLABORATION Department of Physics and Astronomy,

Hounsfield Road, Shefield S6 3RH, England


A neutrino factory would provide a high flux beam of electron and muon neutrinos with well understood energy and flavour composition for detailed studies of neutrino oscillations. Such a beam requires a large number of muons and hence pions, which would be provided by a proton driver and pion production target. The optimal design of such a pion production target and the necessary pion capture system need accurate knowledge of hadron production at energies of several GeV. HARP, a large acceptance particle spectrometer of conventional design, aims to measure hadron production cross sections on thin and thick nuclear targets in the range of beam momentum 2-15 GeV/c in order to provide the desired data.

1. Introduction

There is now compelling evidence that neutrinos have mass. Neutrino oscillations have currently been measured using four independent neutrino sources: atmospheric neutrinos, solar neutrinos, reactor neutrinos and conventional neutrino beams'. Despite this wide range of neutrino sources which are utilized by current experiments, a neutrino factory will be required in order to fully parameterize the neutrino mixing matrix and determine the pattern of neutrino masses.

2. The Neutrino Factory

2.1. Overview

A conceptual design for a neutrino factory is shown in Figure 12. A proton beam is directed at a target, producing pions. These pions are captured using a magnetic capture system and then decay producing muons. The muons undergo a phase rotation, where the bunches which are initially short with a large spread in momentum are passed through rf cavities which slow

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down the faster muons and accelerate the slower ones, resulting in a bunch which has a small spread in momentum but is extremely long. The muons are transversely cooled using an ionization cooling system and accelerated. Finally the muons are fed into a storage ring where they decay producing intense beams of neutrinos.

, - Proton driver I~

Target Mini-cooling 3.5 m of LH , 10 m drift

Induction linac No.1 100 m

Drift 20 m Induction linac No.2

80 m Bunching 56m Cooling 108 m

Linac 2.5 GeV

v beam

Storage ring 20 GeV

Drift 30 m Induction linac No.3

80 m

Recirculating Linac 2.5 - 20 GeV

Figure 1. Diagram showing typical schematic of a neutrino factory.

As previously mentioned a neutrino factory will allow us to probe regions of parameter space which are inaccessible to conventional beams. This is for three distinct reasons. Firstly a neutrino factory provides Y, and L, in addition to the v p and Tp which can be provided by conventional beams. Secondly the neutrino factory will have lower statistical errors due to its much higher event rates (there will be an estimated 1021 muon decays per year). Lastly the neutrino factory will have lower systematics since the beam will have extremely well known energy spectrum and flavour composition.

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2.2. Required hadron production data

Proton drivers currently under consideration for use in a neutrino factory have beam momenta between 2 and 50 GeV/c. In order to achieve the required event rates a beam power of several MW is needed. While this is in itself not difficult to achieve it causes a huge power density in the target. Several designs are being considered for the neutrino factory target including liquid mercury jets and rotating metal band targets. In order to optimize the design of the target and pion capture systems it is necessary to have Monte Carlos which will reliably predict the pion production fluxes for target materials and geometries under consideration. FLUKA and MARS are the codes currently used for this purpose, however these two codes show significant discrepancies in regions of interest3.

These discrepancies can be traced to a lack of suitable hadron production data. Unfortunately existing hadron production data was taken mostly in the 60’s and 70’s with either bubble chambers or fixed or movable arm spectrometers. Bubble chamber data suffers from low statistics and a limited range of target materials, while spectrometer data has limited angular coverage and measures a limited range of secondary momenta.

The data that would be of interest for neutrino factory design would be protons with momenta between 2 and 24 GeV/c in 1 GeV/c steps on high Z targets. The range of secondary pion momentum of interest is 100-700 MeV/c for longitudinal momentum and less than 250 MeV/c in transverse momentum. The secondary proton yield is also of interest in order to study induced radiation.

3. The HARP Experiment

The purpose of the HARP experiment is to fill the existing gap in hadron production data4. The experiment was proposed in 1999 with the aim of carrying out a program of measurements of secondaries produced by beams in the momentum range from 2-15 GeV/c, on a range of thin and thick nuclear targets, over the full solid angle. In order to get the experiment up and running on a relatively short time scale efforts were made to re-use equipment from existing experiments. In 2000 HARP underwent a technical run with the experimental infrastructure in place, beam line installed and ready, dipole and solenoid magnets installed and running and some subsystems installed. By 2001 all subsystems were installed and operational. HARP had gone from proposal to data taking in just two years.

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3.1. Experimental setup

HARP is a charged particle magnetic spectrometer of conventional design (see Figure 2). The beam hits a target in the centre of the Time Projection Chamber (TPC) which sits inside a solenoid magnet and gives momentum measurement and particle identification by dE/dx at large angles. This particle identification at large angles is complemented by Resistive Plate Chambers (RPCs) which form a layer around the TPC and provide particle identification by time of flight allowing electron/pion separation in momentum regions where this is not possible in the TPC. Momentum measurement in the forward direction is provided by drift chambers recuperated from the NOMAD experiment on either side of dipole magnet. Particle identification in the forward direction is provided by a threshold Cherenkov detector and a Time of Flight (TOF) Wall. Further downstream additional particle identification is provided by an electron and muon identifier.

TPC + RPCs in

old Cherenkov

‘beam

Figure 2. Diagram showing the setup of the HARP experiment.

3.2. Suitability of results for neutrino factory requirements

The HARP experiment has excellent phase space coverage. Proton/pion separation is possible in the TPC at momenta below 1.2 GeV/c. Using the TOF, proton/pion separation is possible below 3.5 GeV/c (in the region of geometrical acceptance) and the Cherenkov can separate protons and pions above 3 GeV/c. This combination of detectors provides comprehensive

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50

73

82

1

1

7 8

coverage over almost the entire phase space and completely covers the region of interest for a neutrino factory. There are also regions of overlap useful for cross calibration of detectors.

The range of target materials used by HARP is shown in Table 1. A range of thin (0.05 A) solid targets was used to study primary interactions and a range of thick (1.0 A) targets was used to study re-interactions within the target. HARP has also taken data with replica targets from two conventional beam experiments, K2K and MiniBooNE in order to provide accurate predictions of their neutrino flux. Finally HARP took data with a range of cryogenic targets which will be used as input for calculations of atmospheric neutrino flux.

1.13

0.48

0.85

Table 1. Targets used by the HARP experiment.

Material

Be

Be

C

A1 A1

c u

Sn Ta

P b

H2

D2

Nz 0 2

13 1.98

29 l3 I 0.30

1.0 X / cm

40.70

39.44

15.00

11.14

17.05

Comment

MiniBooNE target replica

K2K target replica

6 cm

6 cm

6 cm

6 cm

HARP has now completed all data taking. During its two data taking runs in 2001 and 2002 it took over 330 million triggers. Efforts are now turning to completion and refinement of reconstruction software and data analysis. First results are anticipated in the near future.

4. Summary

An accurate knowledge of hadron production is essential for the optimal design of targetry and pion capture systems for a neutrino factory. Cur- rent knowledge of hadron production is insufficient for this purpose. The

HARP experiment will provide measurements covering much of the range of incident beam energies of interest, for a range of solid targets. Particle identification of secondaries can be achieved over the relevant phase space. The results will allow the optimization of Monte Carlos and hence will be crucial for the optimal design of neutrino factories.

References 1. A. de Santo, Int.J.Mod.Phys. A16, 4085 (2001). 2. D. Ayres et al., arXiv:physics/9911009 (1999). 3. J. Collot, H.G. Kirk, N.V. Mokhov, Nucl. Instrum. Meth. A451, 327 (2000). 4. M.G. Catanesi et al., CERN-SPSC/99-35 SPSC/P315 (1999).

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A MONTE CARL0 TEST OF THE OPTIMAL JET DEFINITION

D. YU. GRIGORIEV1*27*, E. JANKOWSK13>t, F. V. TKACHOV21g Mathematical Physics, Natl. Univ. of Ireland Maynooth,

Maynooth, Co. Kildare, Ireland 21nstitute for Nuclear Research of R A S ,

Moscow 1 1 7312, Russia Department of Physics, University of Alberta,

Edmonton, AB, T6G 2J1, Canada a E-mail: [email protected]

t E-mail: ejankowsOphys.ua1berta. ca E-mail: ftkachouOms2.inr.ac.r~

We summarize the Optimal Jet Definition and present the result of a benchmark Monte Carlo test based on the W-boson mass extraction from fully hadronic decays of pairs of W’s.

1. Introduction

Jets of hadrons which appear in the final states of scattering experiments in high energy physics correspond, to the first approximation, to quarks and gluons produced in the collisions. Quarks and gluons, interacting strongly, are not observed as free particles. Only some combination of them, hadrons, can avoid the strong interaction at large distances and only those combinations appear in experiments. If the energy of the colliding particles is high enough, the quarks and gluons produced in the collision manifest themselves as jets of hadrons which move roughly in the same direction as the quarks and gluons originating them.

Let us consider an example high energy event. An electron and positron collide at the CM energy equal to 180 GeV. The electron and positron annihilate and a pair of W-bosons is produced. Each of the W’s decays into two quarks. When the quarks move away from each other, potential energy of the strong interaction between them grows quickly and new pairs of quarks and antiquarks are created out of this energy. The many quarks and antiquarks combine into colorless hadrons which form 4 or more jets.

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267

We are interested, for instance, in extracting the W-boson mass from a collection of events similar to the one described above. It would be much easier if we were able to observe directly the quarks coming from decaying W’s. But we observe jets of hadrons instead and when we make the analysis we have to deal with the jets. And this may not be always easy. Jets may be wide and/or overlap. It is hard to say even how many jets we have and how to share the particles between them.

Another aspect is that when we have a procedure to recognize and reconstruct jets it may give different answers for the same physical process depending whether it is applied at the level of quarks and gluons in theoretical calculations or at the level of hadrons from Monte Carlo simulations or at the level of calorimeter cells in experiments.

The Optimal Jet Definition avoids most of the problems of the conventional schemes. The derivation of OJD from the properties of the strong interaction and specifics of measurements involving multi-hadronic final states is contained in [2], [’I. A short introduction to the subject is [‘I. An efficient FORTRAN 77 implementation of OJD, called the Optimal Jet Finder (OJF), is described in [5 ] and the source code is available from [‘I. Below we summarize OJD and present the result of a benchmark Monte Carlo test based on the W-boson mass extraction from fully hadronic decays of pairs of w’s.

2. Jet algorithms

The analysis of events with many hadrons is often performed with the use of so called jet algorithms. A jet algorithm is a procedure to associate the particles into jets. It decides which particle belongs to which jet. Often it determines also how many jets there are. (When we say particles it may mean as well calorimeter cells or towers when the analysis is applied to experimental data or partons in theoretical calculations.)

After the content of each jet is known, some rule is chosen to compute the properties of the jet from the properties of the particles that belong to that jet. A simple and logical prescription, but not necessarily the only possible (see [‘I for discussion), is that the 4-momentum of the jet, qjet, is the sum of 4-momenta pa of all particles that belong to that jet: qjet =

There have been many jet definitions developed by various collaborations over the years. Examples are the class of cone algorithms (various variants) and the family of successive recombination algorithms such as ICT

C t h e jet P a -

268

(Durham), Jade, Geneva. Cone algorithms define a jet as all particles within a cone of fixed radius.

The axis of the cone is found, for instance, from the requirement that it coincides with the direction of the net 3-momentum of all particles within the cone.

Successive recombination algorithms, in the simplest variant, work as follows. The “distance” dab between any two particles is computed according to some definition, for example, Eb = EaEb (1 - cos cab) for JADE and (Fab = min (E:, E t ) (1 - coseab) for k ~ , where Ea is the energy of the a-th particle and eab is the angle between the a-th and the b t h particles. Then the pair with the smallest difference is merged into one pseudo-particle with the 4-momentum given (for example) by pab = pa + pb. In that way the number of (pseudo-) particles is reduced by one. The procedure is repeated until the required number of pseudo-particles is left (if we know in advance how many jets we want) or until dab > gcut for all a, b, where ycut is some chosen parameter. The remaining pseudo-particles are the final jets. The described scheme corresponds to so called binary algorithms as they merge only two particles at a time (2 -+ 1). Other variants may correspond to 3 + 2 or more generally to m -+ n.

With many available jet definitions, an obvious question is how to decide which algorithm should be used. It should be clear that the jets are defined (through the jet algorithm used) for the purpose of data analysis. In the example used it is the W-boson mass extraction. In this case we can measure how good the jet definition is based on how small the uncertainty in the extracted mass is. On this idea we based our benchmark test of the Optimal Jet Definition.

3. Optimal Jet Definition

The OJD works as follows. It starts with a list of particles (hadrons, calorimeter cells, partons) and ends with a list of jets. To find the final jet configuration we define Q R , some function of a jet configuration. The momenta of the input particles enter f l ~ as parameters. The final, optimal jet configuration is found as the configuration that minimizes Q R .

The essential feature of this jet definition is that it takes into account the global structure of the energy flow of the event. Above mentioned binary algorithms take at a time only two closest particles into account, to decide whether to merge them or not.

A jet configuration is described by the so-called recombination matrix

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zaj , where a=1,2, ..., Npart indexes the input particles with 4-momenta pa and j=1,2, ..., Njets indexes the jets. zaj is interpreted as the fraction of the a-th particle that goes into formation of the j-th jet. The conventional schemes correspond to restricting zaj to either one or zero depending on whether or not the a-th particle belongs to the j-th jet. Here we require only that 0 5 zaj 5 1 and Cj zaj 5 1. The 4-momentum of the j-th jet is given by: q j = Ca zajpa. The 4-direction of the j-th jet is defined as i j j = (1, $), where $ = g, / 1% I is the unit direction vector obtained from q j = (Ej, Q). The explicit form of RR is: RR = & cj q j @ j + Ca (1 - cj z a j ) . E,. The first term in the above equation “measures” the width of the jets and the second is the fraction of the energy of the event that does not take part in any jet formation. The positive parameter R has the similar meaning to the radius parameter in cone algorithms in the sense that a smaller value of R results in narrower jets and more energy left outside jets. A large (2 2) value of R forces the energy left outside jets to zero.

If the number of jets that the event should be reconstructed to is already known one finds zaj that minimizes RR given in the above equation. This value of zaj describes the final desired configuration of jets. The minimization problem is non-trivial because of the large dimension of the domain in which to search the global minimum, Npart x Njets = 0 (100-1000) of continuous variables zaj. However, it is possible to solve it due to the known analytical structure of RR and the regular structure of the domain of zaj .

An efficient implementation, called the Optimal Jet Finder (OJF), is described in detail in [5 ] and the FORTRAN 77 code is available from [‘I. The program starts with some initial value of zaj , which in the simplest case can be entirely random, and descends iteratively into the local minimum of RR. In order to find the global minimum, random initial values of zaj are generated a couple of times (ntries) and the deepest minimum is chosen out of the local minima obtained at each try.

If the number of jets should be determined in the process of jet finding, one repeats the above described reconstruction for the number of jets equal to 1,2,3, ... and takes the smallest number of jets for which the minimum of RR is sufficiently small, i.e. RR < ucut, where ucut is a positive parameter chosen by the user. wcut has a similar meaning to the ycut parameter in the successive recombination algorithms.

The shapes of jets are determined dynamically in OJD (as opposed to the fixed shapes of cones in the cone algorithms). Jet overlaps are handled automatically without necessity of any arbitrary prescriptions. OJD

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is independent of whether input particles are split into collinear groups (collinear safety). OJD is also infrared safe, i.e. any soft particle radiation results in soft (small) only change in the structure of jets. (So, it avoids the serious problems of cone algorithms based on seeds.) OJD, as opposed to successive recombination algorithms, takes into account the global structure of the energy flow in the event (rather than merging a single pair of particles at a time).

4. Details of the test

We performed a simple, benchmark Monte Carlo test of the Optimal Jet Definition. The analysis was modelled after a similar one performed by the OPAL collaboration from LEP I1 data [7].

We simulated the process e+e- + W+W- + hadrons at CM energy of 180 GeV using PYTHIA 6.2 [*I. We reconstructed each event to 4-jets using OJF and two binary jet algorithms: kT and Jade for comparison. For OJF, we chose R=2 and employed the most primitive variant of OJF- based algorithm with a fixed ntries=10 for all events. The jets can be combined into two pairs (supposedly resulting from decays of the W’s) in three different ways. We chose the combination with the smallest difference in invariant masses between the two pairs and calculated the average m of the two masses. We generated the probability distribution x ~ ( m ) with the W-boson mass M as a parameter. The smallest error of parameter estima- tion corresponding to the number Nexp of experimental events (as given by

Rao-Frechet-Cramer theorem) is 6Mexp [Nexp dm ( d l n x ~ (m) / d M ) 2 -;. We can use this number directly to evaluate the jet algorithms.

5. Results

The statistical error 6Mexp of the W-boson mass corresponding to a 1000 experimental events is displayed in the table below:

ALGORITHM 6MeXp f 3 MeV OJD/OJF

JADE 118

(The error of 3 MeV in our results is dominated by the uncertainties in the numerical differentiation with respect to M.) Within the obtained precision Durham and OJF are equivalent with respect to the accuracy, JADE appears to be worse.

27 1

An important aspect is the speed of the algorithms. The average pro- cessing time per event depends on the number of particles or detector cells in the input Npart. We observed the following empirical relations (time in seconds): 1.2 x lo-’ x x N p r t x n+,ries for OJF. Npart varied from 50 to 170 in our sample, with the mean value of 83. However, the behavior was verified for Npart up to 1700 by splitting each particle into 10 collinear fragments (similarly to how a particle may hit several detector cells).

We observe that OJF is slower for small number of particles or detector cells whereas for a large number of particles it appears to be relatively much faster. In the process we studied it starts to be more efficient for

It may be a strong advantage. For instance [l], in the CDF or DO data analysis, where binary ICT algorithm is commonly used, it is not possible to analyze data directly from the calorimeter cells or even towers because it would take forever. The preclustering procedure (defined separately from the jet algorithm) is necessary to reduce input data to approximately 200 preclusters. With OJF, it is possible to test how the preclustering step affects the results or even skip it altogether.

for ICT and 1.0 x

Npart x 9 O G .

6. Summary

We performed a Monte Carlo test of the Optimal Jet Definition. We found that in the process we studied it gives the same accuracy as the best algorithm applied previously to the similar analysis. OJD offers new options yet to be explored, e.g. the weighting of events (according to the value of R) to enhance the precision. We found that the already available implementation of OJD is very time efficient for analyses at the level of calorimeter cells.

References 1. Run I1 Jet Physics, e-Print hep-ex/0005012~2. 2. F. V. Tkachov, Int. J. Mod. Phys. A17, 2783 (2002). 3. F. V. Tkachov, Int. J. Mod. Phys. A12, 5411 (1997). 4. D. Yu. Grigoriev, E. Jankowski, F. V. Tkachov, e-print: hep-ph/0301185. 5. E. Jankowski, D. Yu. Grigoriev and F. V. Tkachov, e-print: hep-ph/0301226. 6. http://www.inr.ac.ru/”ftkachov/projects/jets/. 7. Technical report CERN-EP-2000-099. 8. T. Sjostrand et al., Comp. Phys. Comm. 135, 238 (2001).

SINGLE PHOTOELECTRON DETECTION IN LHCB PIXEL HPDS

S. JOLLY Department of Physics,

Imperial College, London, SW72AZ, UK

E-mail: stephen.jolly0ic. ac.uk

To achieve the particle identification (PID) performance required by LHCb, the photodetectors in its Ring Imaging Cerenkov (RICH) detectors must be capable of identifying single-photon signals accurately. Such a requirement sets strict performance constraints on the components of candidate photodetectors. The constraints on the electrical performance of the detector chip of one such photodetector, the Pixel Hybrid Photon Detector (HPD), and some strategies for keeping to them are considered.

1. Introduction

LHCb is a single-arm forward spectrometer detector for the LHC, designed to take advantage of the high bunch-crossing rate and CoM energies of that collider to probe the physics of b-hadrons in greater depth and detail than is possible with the current generation of experiments. To provide good particle identification (PID) performance it features two RICH detectors, which perform accurate measurements of particle velocity over a wide range of energies. Each RICH contains one or more radiator media, in which cones of Cerenkov light are induced by traversing particles. Spherical and flat mirrors then focus and guide the light onto plane arrays of photodetectors. The final choice of photodetector has not yet been made; one candidate is the Pixel Hybrid Photon Detector (HPD)l.

Figure 1 shows the design of the HPD. Incoming photons pass through the glass entrance window and release an electron from the photocathode on its inner surface with a quantum efficiency of 27% at 270nm. The photoelectrons are accelerated to 2OkeV and cross-focussed by electric fields before striking the anode assembly at the rear of the tube, releasing -5000 electrons within it2. The anode assembly is comprised of a silicon pixel

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Figure 1. A schematic diagram of the Pixel HPD.

detector and the LHCBPIXl binary readout chip, bump-bonded together. Both chips contain an array of 256x32 pixels; the detector chip pixels are simple reverse-biased p-n junctions, but those of the readout chip are rather more complicated, as can be seen in Fig. 2.

pirrl a-l

i

Figure 2. Block diagram of a single pixel of the LHCBPIXl binary readout chip.

Each pixel has analogue and digital parts. In the analogue part, the incoming signal from the detector pixel is amplified, shaped and passed through a discriminator, the binary output of which is fed into the digital part of the chip, where it is clocked, buffered and read out (if triggered).

An important parameter to determine is the threshold voltage of the discriminator. This is set by a Digital to Analogue Converter (DAC) referred to as "Pre-VTH" to a value higher than the background noise but lower than the pulse height of an incoming photoelectron. An issue with pixel detectors is that of "charge sharing", in which a single photoelectron distributes its energy between two (or occasionally more) adjacent pixels. To ensure efficient single photoelectron detection despite this, it has been

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determined that the threshold should be less than -2000e- and the electronic noise less than -250e- for all pixels. These values translate to -20mV and -2.5mV respectively at the discriminator. Owing to the limited accuracy of the manufacturing process, each pixel responds slightly differently to the Pre-VTH signal. The result is a distribution of measured thresholds.

To ensure that the width of the threshold distribution does not prevent some pixels on the chip from meeting the standards set out above, the threshold of each pixel can be adjusted with its own three-bit DAC known as “THOl2”, which applies a correction to the threshold between OmV and a value determined by the value of a second chip-wide DAC, “dis-biasth”. It is these THO12 bits that are used to minimise the threshold distribution width.

2. Performing the Minimisation

The first minimisation step is to find the optimum value for dis-biasth. A value too large will decrease the resolution of the THO12 DACs: increasing the width of the minimised distribution by preventing the use of their full range. A value too small will mean that the threshold of some bits cannot be shifted far enough, again increasing the width. Since the thresholds follow a Gaussian distribution (Fig. 4), we expect the minimised distribution to be described by:

G(x‘ - 3.5a)

G(x’ + 3 . 5 ~ )

x’ < -;a

x‘ > f a xi=-, G ( ( n + f ) a + x’) -;a < x’ < $a (1)

where G(x) is the Gaussian probability distribution of mean p and width a (in mV) and a is the change in threshold in mV due to incrementing a THO12 DAC (ie 8a is the full range of TH012). Integrating this numerically over a range of values for a shows (Fig. 3) that, as expected, the curve displays a broad trough. The integration predicts a minimum at 8a M 5a. The results of an actual dis-biasth scan are also shown: while the two curves are similar qualitatively, they differ in their predictions of the optimal value of dis-biasth and of the achievable minimisation; this is interpreted as being due to the considerable non-linearity of the THO12 DACs.

Having chosen a value for dis-biasth, the second step in the optimisation is to select an algorithm to find values for the THO12 DACs. To simplify this

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Minimised threshold distribution width as a function of dis-biasth

1.2 1 I

0.4 (D

* * . *

0 5 10 15 20

Value of dls-blasth I sigma of unmlnlmlsed dlstribution

Figure 3. dis-biasth.

Simulated and measured threshold distribution widths as a function of

process, we introduce two concepts: the “effective width” of the distribution and the “target threshold”. The effective width w 8a is the full range of each THO12 DAC as described above. The target value is the threshold to which we try and adjust each pixel using its THO12 DAC. Since the effect of these DACs is to reduce the threshold, this is the lower end of the distribution, at p - w/2.

The simplest possible minimisation algorithm is then, for each pixel, to divide the difference between its unminimised threshold and the target threshold by a: rounded to the nearest integer. This gives the new value for that pixel’s THO12 DAC. The results of this algorithm are shown in Fig. 4: the unminimised distribution has a fitted deviation of 1.02mV; the algorithm reduces this to 0.43mV, a factor of -2.5 improvement.

The main assumption of the above algorithm is that the THO12 DACs are linear. Figure 5 shows the distribution of threshold changes due to incrementing a THO12 DAC. All seven possible increments from all 8,192 DACs are plotted. If the DACs were perfectly linear, the width of the distribution would be zero; as it is, they are (as postulated above) significantly non-linear: some increments even result in a threshold shift of the opposite sign. The mean incremental change in a DAC is 0.80f0.36mV.

Since the average difference between adjacent THO12 settings is already almost twice the standard deviation of the minimised threshold distribution, further reduction seems unlikely. However, to see if reconsidering the linearity assumption results in a further improvement in the minimisation, a second, “optimal” algorithm was tested. Eight measurements of the thresholds were performed, with a different chip-wide setting for THO12 each time.

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1600 n

14001 U

Figure 4. LHCBPIXI “chip 9”.

Simply-minimised (left) and unminimised (right) threshold distributions for

Figure 5 . Threshold changes due to THO12 incrementation in “chip 9”.

Then, for each pixel, the measured threshold closest to the target value was chosen and its corresponding value of THO12 chosen as the optimal value. The results of a scan taken following this procedure is shown in Fig. 6. The width of the distribution is “0.41mV - a negligible improvement over the simpler algorithm.

The minimisation techniques described above were tested on a second

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600

400

200

0 10 1 20 25 30

Threshold I mV

Figure 6. The optimally-minimised threshold distribution of “chip 9”.

chip, with similar results.

3. Conclusion

Pixel HPDs remain a promising candidate photodetector for the RICH detectors of LHCb. The pixel chips already meet LHCb threshold and signal to noise ratio requirements. Should it become necessary, however, the chip’s built-in features for minimising the width of the threshold distribution can be used to reduce it by a factor of -2.5. The two algorithms tested gave similar results; the simpler, faster algorithm that assumes linear THO12 DACs is thus favoured.

Acknowledgements

The assistance and support of C. Newby, D. Websdale and K. Wyllie is gratefully acknowledged.

References 1. M. Girone, “The hybrid photon detectors for the LHCb-RICH counters”, 7th

International conference on advanced technology and particle physics, Como, Italy, 15-19 Oct 2001.

2. T. Gys, “A support note for the use of pixel hybrid photon detectors in the RICH counters of LHCb” , CERN/LHCb-2000-064, 12 Apr 2001.

NONEQUILIBRIUM PHASE TRANSITIONS IN THE EARLY UNIVERSE

SANG PYO KIM Department of Physics, Kunsan National University,

Kunsan 573-701, Korea E-mail: sangkimakunsan. ac.kr

We review the current issues of nonequilibrium phase transitions, in particular, in the early Universe. Phase transitions cannot maintain thermal equilibrium and become nonequilibrium when the thermal relaxation time scale is bigger than the dynamical time scale. Such nonequilibrium phase transitions would have happened in certain evolution stages of the early Universe because the rapid expansion quenched matter fields. We discuss the physical implications of nonequilibrium phase transitions in the early Universe. In particular, it is shown that higher order quantum corrections decrease the density of topological defects.

1. Introduction

A system undergoes a phase transition when its symmetry is broken explicitly.172 Phase transitions are either equilibrium or nonequilibrium (out of equilibrium) depending on the ratio of the thermal relaxation time to the dynamical time. When the thermal relaxation time is shorter or longer than the dynamical time, it is equilibrium or nonequilibrium. In particular, in a quenched system, it undergoes nonequilibrium phase transition when the quench rate is faster than the relaxation rate. Matter fields are believed to have undergone such nonequilibrium phase transitions in the early Universe as the Universe expanded and temperature dropped rapidly. It is likely that such nonequilibrium phase transitions of matter fields can be realized and observed in RHIC and LHC experiments in the near future.

The finite-temperature field theory has been the most popular approach to equilibrium phase transition^.^ The effective potential of quantum fluctuations around a classical background provides a convenient tool to describe the phase transitions. However, quantum fluctuations of long wavelength modes suffer from instability during the phase transition, become unstable, and grow exponentially. This is the origin of the imaginary part of the

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effective action for phase transitions, which gives the decay rate of the false v a ~ u u m . ~ Thus the finite-temperature effective action does not properly take into account the dynamical processes of phase transitions.

On the other hand, nonequilibrium phase transitions have been fre- quently treated in the closed-time path integral defined in a complex time plane by Schwinger and Ke ldy~h .~ Other methods are the Hartree-Fock or mean field method: 1/N expansion method, variational Gaussian effective potential, Schwinger-Dyson equation method, and etc. In this talk, we shall use the recently developed Liouville-von Neumann (LvN) m e t h ~ d . ~ ? ~The LvN method is a canonical method based on the quantum LvN equation, which turns out another quantum picture independently of the Schrodinger and Heisenberg pictures and unifies quantum theory with quantum statistical theory.

2. Phase Transitions

To understand the symmetry breaking or restoration mechanism, we shall consider a scalar field model with the potential

When m2 is negative, the symmetry of the system is broken. However, quantum fluctuations around the true vacuum may restore the symmetry when the temperature is high enough so that the thermal energy can overcome the potential energy difference between the true and false vacua. To find the thermal contribution (correction) to the classical potential, we divide the field, $ = $c + q5f, where #c is the classical background field and q5f denotes quantum fluctuations around 4,. Then the effective potential is given by

where p is the density operator and mR and X R are renormalized coupling constants. For the broken symmetry m2 + -m2, one has the potential

The system thus restores the broken symmetry when T > T,. In other words, the symmetry can be spontaneously broken when the temperature drops below the critical temperature T,.

In the early stage of evolution after the Big Bang the Universe would have undergone a sequence of phase transitions as the temperature dropped

280

due to the expansion. A possible sequence of phase transitions based on particle physics is the GUT phase transition at T, M - 1OI6 GeV, the EW (electroweak) phase transition at T, M 10' GeV, and Color define- ment/Chiral phase transition at T, M lo2 MeV. Depending on the particle physics model, the system produces different type of topological defects.' The full symmetry of the system is broken to a subgroup after a phase transition. The structure of the vacuum manifold rn, the homotopy group, determines the type of topological defects: domain walls for ~ ~ ( r n ) # 1, strings for ~ ~ ( r n ) # 1, and monopoles for ~'(rn) # 1.

3. Kibble-Zurek Mechanism

Kibble used the principle of causality and the Ginzburg temperature to find the correlation length. The Ginzburg temperature is the one where the thermal energy is comparable to the free energy of a correlated region, kbT, M t 3 ( T ~ ) A F ( T ~ ) , so that the field can overcome the potential barrier to jump to other configurations. In this case topological defects lose stability. This temperature restricts the size of correlation length for stable defects. Topological defects are located along the boundaries of correlated regions. Thus there is one monopole per volume t3 and the density of monopoles is given by ./t3 and one string per area t2 and the density by

On the other hand, the Zurek mechanism incorporates the dynamics of equilibrium processes. In the adiabatic cooling (quenching) the equilibrium correlation length increases as 5 = ~ o ) c ) - ~ , and the equilibrium relaxation time as T = T O I C I - ~ , where c = (T, - T)/T,. Here p and Y are model- dependent parameters. Also 6 is related with the quench rate as € = t /TQ.

As temperature approaches the critical value (T + T, or t + 0), the equilibrium relaxation time becomes sufficiently longer and the process critically slows down. However, the correlation length increases indefinitely but the propagation of small fluctuations is finite; so T cx </v -+ 00. Therefore, there is a time t* when the correlation length freezes: Jt*J = ~ ( t * ) . From the above equations the correlation length is given by <(t*) M ~ 6 " ~

dt2.

4. Nonequilibrium Phase Transitions

There are many cases to which equilibrium phase transitions cannot but nonequilibrium phase transitions can be applied. Matter fields in a rapidly expanding universe are such an example, where the Tolman temperature drops as T( t ) = To x ao/a(t ) , where a is the scale factor of the universe.

28 1

Another example is the rapid quenching processes such as in the rapid cooling of quark-gluon plasma in the Heavy Ion Collision and the liquid helium He3 and He4, where domain walls and vortices (strings) may be formed.

As a field-theoretical model for nonequilibrium phase transitions, we consider the scalar field p ~ t e n t i a l ~ ~ ~ ~ ~ ~ ~ J ~

where the parameter m2 changes signs from m2(-m) = m: to m2(+m) = -m;. When TQ is the time scale for the quench, one can classify the adiabatic quench process, Am2/TQ << 1, and the rapid quench process, Am2/TQ >> 1. For instance, an analytical model m2(t) = -m2 tanh(t/rQ) may be considered, in which m2 + +m2 for t + -m and m2 + -m2 for t -+ +m. In the limiting case TQ + 0, one has an instantaneous quench, m2 = +m2 for t < 0 and m2 = -m2 for t > 0. The field model can be easily generalized to an expanding universe

The Minkowski spacetime is the special case of u = 1. As before, dividing 4 = +c + $f, we obtain the equations of motion for the classical field

and for quantum fluctuations

To handle the model (4), we shall use the recently developed LvN method, which is based on the quantum LvN equation 7 ~ 8 , 9

d d t i-oL + [OL,H] = 0.

The LvN method requires an auxiliary field equation, which for initial symmetric states such as the Gaussian vacuum or thermal state (4f) = 0 and the zero moment 4c = 0, is

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Roughly speaking, the modes with k < mf become unstable after the phase transition and grow but those with k > mj are still stable and oscillate. Soon after the phase transition, the effect of 44 term is small and can be neglected. Then the unstable long wavelength modes have the solution

7 (10) a k e(m; -k*)’”t pk e-(m; -k2)’/’t + fi(m2f - k2)l12 fi(m2f - k2)l12 (Pk =

where lakI2 - = 1, whereas the stable short wavelength modes oscillate. For the minimal uncertainty state ((Yk = l), the correlation function is approximately given by

5. Domain Growth and Topological Defect Density

To find the non-Gaussian effect^,^ we need to include both the Gaussian part HG and the non-Gaussian part Hp into the Hamiltonian H = HG + XHp, where

1 1 1 3x HG = -r2 + --(V4)2 + -(m2 + 2 2 2 1 3 Hp = -44 - -($2)42. 4! 4 (12)

The wave function beyond the Gaussian approximation can be found as

n= 1

where XJ2$) and ‘@$I are the wave functions of HG. The equal-time correlation function from the Gaussian wave function Q:),

yields the correlation length

It shows the Cahn-Allen scaling behavior of classical theory. More importantly, the correlation length beyond the Gaussian approximation is

En@) = m t G ( t ) , (16)

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which is a consequence of multiple scattering among different unstable modes.g The physical implication of the non-Gaussian effects is that the correlation length increases by (2n+ 1)1/2, where n is the order of quantum contributions which depends the time for crossing the spinodal line, that is, the period for the field rolling from the false vacuum into the true one.

6. Conclusion

As a field model for nonequilibrium phase transitions, we have considered a scalar whose parameters, in particular, the mass term changes signs during the phase transitions and whose quench rate is faster than the thermal relaxation rate. This model is a quantum model for the classical Landau- Ginzburg theory. It is likely that quantum decoherence of long wavelength modes by short wavelength modes may lead to the classical theory of order parameter. It is found that the topological defect density can be reduced by factors (2n + 1)3/2, which is a consequence of the non-Gaussian effects and where n depends on the duration of the instability.

Acknowledgments

The author would like to thank F. C. Khanna and C. H. Lee for parts of collaboration and useful discussions. This work was supported by Korea Research Foundation under Grant No. KRF-2002-041-C00053.

References 1. T. W. B. Kibble, J . Phys. A9, 1387 (1976); W. H. Zurek, Nature 317, 505

(1985). 2. A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological De-

fects (Cambridge Univ. Press, Cambridge, 1994). 3. L. Dolan and R. Jackiw, Phys. Rev. D9, 3320 (1972). 4. E. J. Weinberg and A. Wu, Phys. Rev. D36, 2474 (1987). 5. J. Schwinger, J. Math. Phys. 2, 407 (1961); L. V. Keldysh, Sow. Phys. JETP

20, 1018 (1965). 6. D. Boyanovsky, D.-S. Lee, and A. Singh, Phys. Rev. D48, 800 (1993); M.

Bowick and A. Momen, Phys. Rev. D58, 085014 (1998). 7. K. H. Cho, J.-Y. Ji, S . P. Kim, C. H. Lee and J . Y. Ryu, Phys. Rev. D56,

(1997). 8. S. P. Kim and C. H. Lee, Phys. Rev. D62 (2000); Phys. Rev. D65 (2002); S .

P. Kim, S. Sengupta and F. C. Khanna, Phys. Rev. D64 (2001). 9. S. P. Kim and F. C. Khanna, "Non-Gaussian Effects on Domain Growth ,

hep-ph/0011115 (unpublished). 10. R. Rivers, Int. J . Theor. Phys. 39, 1623 (2000).

RECENT RESULTS IN ELECTROWEAK AND TOP PHYSICS AT D 8

MARKUS KLUTE FOR THE DO COLLABORATION Universitat Bonn, Physikalisches Institut, 0-53012 Bonn

We present recent measurements of Electroweak and Top Physics properties in proton-antiproton interactions, performed by the DO experiment at the Fermilab Tevatron collider.

1. Introduction

Studies of the W and Z bosons and the top quark provide testing grounds for many important properties of the Standard Model (SM). In the SM the mass of the top quark and the W boson constrain the Higgs boson mass. Precision measurements help to guide searches for the SM Higgs boson. The measurement of the W width provides a stringent test of the SM and constrains certain scenarios beyond the SM.

The large mass of the top quark sets it apart from all other fermions. With a lifetime of 10-24s, the top quark decays before hadronization. This gives an unique opportunity tQ study the properties of a bare quark. Significant deviations from the SM predictions in mass, width and decay characteristics could lead to new physics.

2.

RunI of the Tevatron (1992-1995) delivered about 125 pb-I of data. This dataset was used by CDF and DO to discover the top quark in 1995l. In 2001 a new running period has started with significant improvements, both of the collider and the detectors. DO uses currently 50 pb-l integrated luminosity of RunII data for physics analysis.

The RunII D 0 detector consists of a vertex detector, precision tracking chambers, a finely segmented hermetic liquid argon calorimeter, a muon spectrometer and fast data acquisition system with three levels of online trigger. It was built on the strength of the RunI detector with an excellent

The Tevatron and the DO detector

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lepton identification. The major improvement is the tracking system, with a silicon micro vertex detector and a scintillating fiber detector.

3. Recent results in Electroweak Physics

3.1. Introduction

The very large number of W and Z boson events DO will collect will yield precision measurements of the W mass and width, which are fundamental parameters of the SM. The Vector boson dataset will provide other important advances in the field of electroweak physics and will be the starting point of most new physics searches. It can be used to calibrate the detector and normalise the dataset to reduce systematic uncertainties in unrelated measurements.

3.2. Studies of W and Z bosons

An initial dataset of 50 pb-' integrated luminosity accumulated during the summer and fall 2002 was used to collect W and Z events with electrons and muons in the final state. Measurements of the production cross sections and W width as well as searches for exited Z bosons are being finalised. Figure 1 shows the invariant di-muon mass (left) and the transverse mass of muon+&- events (right).

+ + t+ + 1 + ++

0

M , , (GeV/cZ) M (GeV/c2)

Invariant di-muon mass (left) and the transverse mass (right). Figure 1.

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3.3. Measurement of W += eu and Z -+ ee production

The inclusive cross section times branching fraction into electrons for Z and W bosons and their ratio in proton-antiproton collisions at fi = 1.96 TeV with integrated luminosity of 7.5 pb-l accumulated during Winter-Spring 2002 was measured. The results are:

DZ . B(Z 3 ee) = 266 f 20(stat) f 20(syst) f 27(Zurni) pb

(TW . B(W 4 ev) = 2670 f 60(stat) f 330(syst) f 270(2urni) pb ( 1 )

From these measurements we derive their ratio 10.0 f 0.8(stat) f 1.3(syst) and we deduce the W width:

rw = 2.26 f 0.18(stat) f 0.29(syst) f 0.04(theory) GeV (2)

A summary of cross section measurements at various centre of mass energies (points with error bars) and their theoretical prediction ( c u ~ v e s ) ~ ? ~ are shown in Figure 2.

DO and CDF Run2 Preliminary t t I

L

t t 1

Center of Mass Energy (TeV)

Figure 2. energies (points with error bars) and their theoretical prediction (curves).

2 + 1+1- and W + Zv cross section measurements at various centre of mass

4. Recent results in Top Physics

4.1. Introduction

At the Tevatron most top quarks are pair-produced via the strong interaction. In the SM, the top quark decays almost exclusively to a W boson and

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a b quark. Therefore, the final state of a tt decay is characterised by the decay modes of the two W bosons. The event topology can be used to separate signal and background. The identification of b quark jets in semileptonic decays or the lifetime of the b quark are powerful tools to further suppress background. All decay channels have been used in various studies of top quark properties, including the tt production cross section of 5.7 f 1.6 pb

and the top quark mass of 172.1 f 7.1 GeV by the DO Collaboration 5 ,

see Figure 3.

-" , .

- Laenenetal.

Berger el al.

Catani el al.

Kidanakis

_ _ _ _ _ 15 ., \\ '.., . . .. ' . . . . .. . . .. . . . . . . . . . .

140 150 160 170 180 190 Top Quark Mass (GeV/c')

0

Figure 3. DO measured t5 production cross section as a function of the top quark mass (shaded band) and at the D 0 measured top quark mass (point with error bars). Also shown are theoretical predictions.

4.2. Studies toward a first tz production cross section

The first 50pb-1 luminosity in Run11 was used for first studies toward measurements of the t? cross section and the mass of the top quark.

The characteristic topology of the lepton+jets signature is one isolated high transverse momentum electron or muon, large ~ T T and four or more high transverse momentum jets. The two main backgrounds are the W multijet production and QCD multijet events. The analyses are done in two steps. The first step consists in defining a data sample enriched in W+jet and top events, which is used for the normalisation of backgrounds. Figure 4 shows the distribution of W(+ pv)+jets events. The W multijet production is believed to follow a logarithmic law (Berends scaling6). In

measurement

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the second step, kinematic cuts or the identification of b quarks are used to further reduce the background. An enhancement at W+4jets indicates the contribution from tf + l vbbj j contribution. The first Run11 tf production cross section measurement is being finalised.

I , , , , , , , , , , J 2 3 4 '

' N,,s

Figure 4. jets.

Inclusive number of W(+ pu)+jets events as a function of the number of

4.3. New Top Mass Measurement

A new preliminary measurement of the mass of the top quark from t? data in lepton+jets channels has been carried out to reduce the statistical and systematical uncertainty and to introduce a new method for future measurements. The data was accumulated by the DO experiment in Run1 of the Tevatron.

The new method uses the full kinematic information of the t? candidates. The differential cross section of tz and W+jets production convoluted with the detector response is used to assign an event signal and background probability as a function of the mass of the top quark. The probability distribution for all candidates determines the top quark mass and its statistical error, see Figure 5 .

Another aspect of this method is that it provides the possibility of determining the mass of W decaying hadronically, and therefore offers the possibility of recalibrating the jet energy scale (JES) on the same events. Studies are ongoing to utilise the JES information to reduce the systematic uncertainty in the measurement of the top mass.

The preliminary result of the new measurement is:

Mt = 179.9 f 3.6(stat.) f G.O(syst.)GeV

510

538

536 .. 70 80 90 70 75 80 85 90

w mOP. (CC”) w m051 Ice”)

289

(3)

Figure 5. a) Negative of the log of the likelihood as a function of the top quark mass for 22 tf candidates. b) Probability distribution determined from the likelihood. The hatched area corresponds to the 68% probability interval. c) Negative of the log of the likelihood as a function of the W mass. d) Probability distribution determined from the likelihood.

References 1. CDF Collaboration, Phys. Rev. Lett. 74, 2626 (1995). DO Collaboration,

Phys. Rev. Lett. 74, 2632 (1995). 2. R. Hamberg, W. L. van Neerven and T. Matsuura, Nucl. Phys. B359, 343

3. W. L. van Neerven and E. B. Zijlstra, Nucl. Phys. B383, 11 (1992). 4. D 0 Collaboration, tx production cross section in pjj collisions at fi = 1.8TeV,

et al., Phys. Rev. D67, 012004 (2003). 5. DO Collaboration, Direct Measurement of the Top Quark Mass by the DO Col-

laboration, Phys. Rev. D58, 052001 (1998). 6. F.A. Berends, H. Kuijf and B. Tausk, Nucl. Phys. B357, (1991) 32-64.

(1991).

SEARCHES FOR HIGGS BOSONS BEYOND SM AND (STANDARD) MSSM AT LEP

M. KUPPER Particle Physics Department, Weizmann Institute of Science,

Rehovot 761 00, Israel E-mail: [email protected]

Searches by the four LEP collaborations for Higgs bosons beyond the Standard Model have been reviewed. The analyses focus on the e+e- collision data collected at center-of-mass energies between 189 and 209GeV. In addition to the presently available LEP combinations of results beyond the (MS)SM, searches for Higgs bosons in the CP violating MSSM scenario, searches for doubly charged Higgs bosons, as well as decay mode independent searches are presented here. No evidence for a Higgs particle beyond SM and MSSM has been found yet, and bounds on Higgs boson masses and model specific parameters have been derived.

1. Introduction

The result, that no evidence for Higgs bosons within the Standard Model (SM) or the Minimal Supersymmetric Standard Model (MSSM) has been found at LEP, might be a consequence of a yet too restricted interpretation. If models beyond the SM or the scanned parameter regions of the MSSM are valid, different and probably weaker signatures of Higgs bosons can be observed in LEP data. Therefore it is sensible to extend the Higgs boson searches to other production mechanisms and decay modes, such as general hadronic, photonic, or invisible decays. More exotic scenarios, involving the existence of anomalous couplings, CP violation in the MSSM Higgs sector, or left-right symmetric models with doubly charged Higgs bosons, have been considered. In the most general search for a new neutral scalar boson so far, no assumptions on the decay mode were made at all, and not only mass peaks, but also continuous mass distributions have been investigated.

The searches presented here are mainly based on 2461pb-1 of LEP2 data collected during the last three years of operation, at center-of-mass energies between 189 and 209 GeV. Where necessary, earlier data at lower energies have been added, in particular LEPl data at & = 91.2 GeV.

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29 1

2 . Searches

2.1. Reinterpretation of the SM Higgs Boson Search

Instead of computing the confidence level of the Standard Model Higgs Bo- son to be contained in the data, one can vary its production coss-section g H Z Z and calculate the confidence level of Q H Z Z , assuming the particle does exist. The so derived 95% CL exclusion limit on the ratio cz = allows for a model independent interpretation, only restricted to the decay modes taken into account. Figure l(a) shows the exclusion curve for t2 assuming SM decays. Similar plots for H + b6 and H + T+T- are in progress. This result is based on the final combination of all four experiments' analyses, considering LEPl and LEP2 data1.

% ( g i : : > 2

1 8 * .I .a - 8 ri? 10 -l v) Q\

-2

lo 20 40 60 80 100 120 mH(GeV/c5

a)

D

Figure 1. (a) Observed and (median) expected exclusion curve (at 95% CL) for the cross-section of a Higgs boson with SM decays, in units of the SM cross-section. The dark (green) and light (yellow) shaded areas mark the la and 2a deviation, respectively, from the expectation. (b) Combined LEP exclusion limits for the branching ratio of a photonically decaying Higgs boson. The branching ratio predicted by the Standard Fermiophobic Model lies within the excluded area for masses up to 109.7 GeV

2.2. Other LEP Combined Results

In some two-Higgs doublet models, the neutral Higgs bosons couple prefer- ably to down-type quarks. Then, h + ce or h +gluons via a top loop can become the dominant decays. Thus, the model dependence of the searches can be reduced by not exploiting the flavor information of the observed jets.

For other specific parameter choices, the couplings to fermions can be suppressed, enhancing photonic decays. This may also happen through

292

anomalous couplings or additional particles, e.g. light SUSY partners, entering loops. The Standard Fermiophobic Model assumes SM branching ratios, but all fermionic couplings of the Higgs boson are set to zero.

If supersymmetry exists, the light neutral Higgs boson might decay into the lightest supersymmetric particle (LSP), if kinematically accessible. As the LSP can not be seen in the detectors, the Higgs boson is called invisible. Other models, like the Majoron model, provide invisible decays too.

The LEP collaborations have combined their flavor-blind analyses2 as well as their searches3 for H + yy and invisible Higgs bosons4. No excess above the SM background has been found. Assuming SM cross- section and full hadronic branching ratio, the observed 95% CL limit is mH > 112.9 GeV, where 113 GeV was expected. This is 1.5 GeV below the combined mass limit for the Standard Model Higgs boson due to the missing b-jet identification. The Standard Fermiophobic Model has been excluded up to mh = 109.7GeV (expected: 109.4GeV), as shown in Fig. l(b). The combined 95% CL limit for an invisibly decaying Higgs boson with SM production cross-section is m h > 114.3GeV, slightly above the median expected limit of 113.6 GeV.

2.3. Anomalous Couplings

The Standard Model can be extended via a linear representation of the SU(2) xU(1) symmetry breaking mechanism. While the lowest order corresponds to the Standard Model, higher orders enable new interactions between Higgs and gauge bosons, such as Hyy or HZy, and modify the CQU-

plings H Z Z and H W + W - . The higher order terms can be parametrized by 5 anomalous couplings: d, d B , Agf, AL,, and 6 ~ . The latter one, 6z, governs a global scaling factor of all Higgs couplings, and can therefore be restricted by a reinterpretation of the Standard Model analyses, like the one shown in Sec. 2.1.

The L3 collaboration5 has searched for anomalous couplings in associated production e+e- -+ H y and Z*/y* fusion e+e- + He+e-, considering Higgs boson decays to yy, Zy, and WW(*).

The diagram in Fig. 2(a) shows the 95% CL limits for d in the dependence upon the Higgs boson mass. The other anomalous couplings were set to zero. Like in the three other exclusion plots, which are not shown here, the lower limit on the Higgs boson mass is around llOGeV, and the bounds on the anomalous couplings become wider at mH > 160, when H + W+W- becomes dominant and thus complicates the analysis.

293

1

0.8

0.6

0.4

0.2

u o -0.2

-0.4

-0.6

E u

10

-0.8

-1 0 20 40 60 80 100 120 140

Figure 2. (a) Exclusion limits for the anomalous coupling d from an L3 data analysis. The plots for d g , A K ~ , and Agf, which are not shown here, look similar, with 95% CL limits I d s [ , ~AK,I > 0.75 and lAgfl > 0.4 at r n ~ = 150 GeV. (b) Preliminary result for the Hi boson from OPAL searches within the CP violating benchmark scenario. The dark shaded area (blue) of the parameter space is excluded at 95% confidence level. The dotted line shows the median expected limit. The medium dark shaded area (red) is excluded by 2 width constraints.

2.4. Higgs bosons in the CP violating MSSM

In the CP violating MSSM, where parameter phases in the Higgs sector can have values different from zero, the neutral mass eigenstates ( H I , H2, H3)

do not have defined CP quantum numbers and can therefore no longer be identified with the set ( h , H , A ) . All three neutral Higgs bosons could be produced at LEP, with a negligible cross-section for H3, though. For some parameter settings, H I decouples completely from the 2 and remains accessible through H2 + H1H1 decays only. OPAL is currently developing new analyses to detect e+e- + H l H 1 2 , e+e- -+ H22, and other typical signatures of the CP violating MSSM.

The CP violating benchmark scenario has been defined in order to maxi- mize dissimilarities with the CP conserving model. In particular, the SUSY mass scale has been lowered to 1/2TeV, and the argument of the trilinear Higgs-squark coupling has been set to 90". OPAL' has scanned the parameter space of tan@ = 0 . . .40 and rn; = 0 . . . l TeV. Note, that the usual MSSM scan parameter mA has no physical meaning in this scenario.

In a preliminary study, which does not yet include all of the new analysis upgrades, OPAL has set a lower bound on tan @ at 2.9. At present, no tan ,b independent mass limits for the Higgs bosons can be set (Fig. 2(b)).

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2.5. Doubly Charged Higgs Bosons

Doubly charged Higgs bosons appear in MSSM extensions like left-right symmetric and Higgs triplet models. At LEP, they would be produced pairwise and decay into samesign pairs of charged leptons, gauge and Higgs bosons.

The interpretation of the results in terms of left-right symmetric models depends mainly on the Yukawa coupling h,,, which remains as a free parameter. For h,, > 10-7s, the decay into tau pairs takes place close to the interaction point; for h,, < s, it may happen inside the detector or beyond. In order to cover the entire range of sensible lifetimes, DELPHI has searched for the T+T+T-T- signature as well as for final states with two heavy stable particles7.

The lowest DELPHI mass limit has been given for the right-handed Hhf in the h,, = 4.10-* s scenario. All other left-right symmetric models lead to higher mass limits. Thus, the overall lower bound on mH*f is 97.3 GeV, where 97.6 GeV was expected.

2.6. Decay Mode-Independent Search

OPAL has performed a topological search for an unknown neutral scalar in associated production with the Z boson by studying the recoil mass spectrum in Z + e+e- and Z + p+p- events'. For technical reasons, dedicated searches for the signatures S Z + nyvv and S Z -+ e+e-vv had to be included to maintain mode independence. The analysis is sensitive to all combinations of hadronic, leptonic, or invisible decay particles of the hypothetical boson, which is called S here, as well as to non-decaying S.

Exclusion limits were not only given for the cross-section of a boson S with a mass-peak at ms, but also for continuous mass distributions, as they appear in Uniform Higgs and Stealthy Higgs models. Figure 3(a) shows the upper limit on the S Z production cross-section, normalized to the SM cross-section of an equally heavy Higgs boson, for masses ranging from lop6 GeV to 100GeV. A new boson with SM Higgs production properties is excluded up to 81 GeV.

In a simple example of a Uniform Higgs model, one assumes a continuous coupling K = l/(mB - mA) for m~ < m < mB and zero elsewhere. A mass combination ( m ~ , mB) is excluded, if the 95% CL limit of K(m)dm is less than one. The excluded area in the ( m ~ , m ~ ) plane is displayed in Fig. 3(b).

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1

10 1

10 lo4 10 20 30 40 50 60 70 80 90 100

ms@(GeVl

i

100 90

so Exwed mduded d m

70

60 50 40 - E-plr. m,25 DIV, m p P DIV

30 20

10

‘0 50 100 150 200 250 300 350

Figure 3. (a) Result of the decay modeindependent OPAL search for a new boson S in SZ production. The observed and expected exclusion curves refer to the ratio ( T S Z / ( T $ : ( ~ H = ms). (b) Excluded combinations of ( m a , m ~ ) in a Uniform Higgs model with constant coupling between mA and m ~ , as explained in the text. The dark (red) line limits the region of observed 95% CL exclusion, the shaded area marks the median expectation.

3. Conclusions

No evidence for a Higgs boson beyond the Standard Model and its minimal supersymmetric extension has been seen at LEP. Lower mass bounds for Higgs bosons decaying into hadrons, photons, and invisible particles have been established between 100 and 115GeV by combining results from all four LEP experiments. Similar mass limits are valid in the presence of anomalous couplings, as found by L3. In the benchmark CP violating MSSM, OPAL has shown tan /3 > 2.9, and work on tan ,&independent mass limits is in progress. According to DELPHI, doubly charged Higgs bosons in left-right symmetric models are heavier than 97 GeV. An unknown neutral scalar with the production cross-section of a SM Higgs boson is excluded by OPAL at masses smaller than 81 GeV, regardless of its decays.

Acknowledgements

The author’s participation at the Lake Louise Winter Institute was made possible with support from the Canadian Institute for Theoretical Astro- physics (CITA).

References 1. LEP Collaborations and LHWG, “Search for the Standard Model Higgs Boson

at LEP”, Jan. 25, to be submitted to Phys. Lett. B.

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2. LEP Collaborations, LHWG Note 2001-07. 3. LEP Collaborations, LHWG Note 2002-02. 4. LEP Collaborations, e.g. ALEPH 2001-36 CONF 2001-056. 5. L3 Collaboration, L3 Note 2774. 6. OPAL Collaboration, OPAL Physics Note PN505. 7. DELPHI Collaboration, CERN-EP/2002-077, accepted by Phys. Lett. B. 8. OPAL Collaboration, CERN-EP/2002-032, submitted to Eur. Phys. J. C.

POLARIZATION DEPENDENCE OF BASIC INTERACTIONS IN STRONG MAGNETIC FIELDS

D. A. LEAHY Dept. of Physics and Astronomy

Univeristy of Calgary Calgary, Alberta, C A N A D A


The application of quantum electrodynamics in strong magnetic fields only fairly recently has been a subject of interest. The motivation for these studies was the discovery in the 1970’s of neutron stars with very high magnetic fields, of order 10l2 Gauss. In the 1990’s good evidence for neutron stars with fields up to 1015 Gauss has been found. With such high fields, a number of rates for basic processes have required recalculation since previous calculations were carried out with the assumption that the magnetic field was limited to << B,, = 4.414 x 1013 Gauss. The strong magnetic field provides a highly anisotropic background, so the polarization dependence of the rates is strong. Polarization here refers to both the electron and positron spin polarization and also to the photon polarization vector.

1. Introduction

Since 1968 with the discovery of radio pulsars, magnetic fields of - 1 O I 2 Gauss were known to exist. X-ray pulsars were discovered in 1971 and also had surface magnetic fields of - 10l2 Gauss. For both types of pulsars the magnetic fields were estimated from their rates of spin-down or spin-up due to magnetic dipole radiation torques. Cyclotron absorption features observed in x-ray pulsars’ spectra in the 1980’s and early 1990’s yielded more accurate values of surface magnetic fields, ranging from 10l2 to l O I 3 Gauss. Also during the 1980’s and early 1990’s’ millisecond radio pulsars and low mass x-ray binaries had magnetic fields estimated to be in the range lo8 Gauss to 1O1O Gauss. In the later 199O’s, anamalous x-ray pulsars and a few soft gamma-ray repeaters were discovered (eg. Vasisht and Gotthelf l ,

Kouveliotou et al. z), with evidence for extremely strong magnetic fields

Quantum electrodynamic processes such as magnetic pair production and synchrotron radiation in strong magnetic fields play an important role

- 1015 Gauss), and given the name magnetars.

297

298

in radio pulsar models (e.g. Daugherty and Harding 3) . One-photon pair production is likely to be the dominant source of e+-e- pairs in fields exceeding 10l2 Gauss (Harding '). For X-ray pulsars, the emission region is much more optically thick and the radiation transfer is anisotropic in the strong magnetic field, so a detailed understanding of the microscopic processes is needed (e.g. Meszaros 5 ) .

With the discovery of magnetars, quantum electrodynamic calculations which are valid for very high fields have become of great interest. Most previous calculations were carried out assuming B << B,, = = 4.414 x lot3 Gauss so they could use photon normal modes which apply only in the weak field limit ( B << B,,). They also used Johnson-Lippmann electron wavefunctions which are valid only in weak fields (Graziani 7).

More complete discussions of quantum electrodynamic processes in strong magnetic fields can be found in the review paper of Canuto and Ven- ture 8 , the PhD thesis of Frangodimitraki-Georgiadou or in Meszaros '. The first reference introduces the basic problem of quantum electrodynamics in strong magnetic fields. The second reference above includes a good discussion of the various electron spinors that have been used in the past and which ones are approximate, and valid only under certain conditions, and includes a discussion of what is valid for magnetic fields large enough to violate B << B,,.. The third reference is a monograph which includes a general discussion of physics in strong magnetic fields followed by more detailed discussions on magnetized plasma response to electromagnetic waves, vacuum polarization, electron scattering, bremsstrahlung, synchrotron radiation, pair production and annihilation, radiation transfer and applications to radio and x-ray pulsars.

This brief paper presents some results of the dependence of rates of some basic interactions on polarization of the photons and of the polarization of the electrons and positrons. A brief introduction to quantum electrodynamics in strong magnetic fields is given in Leahy lo and Leahy l1

The calculations summarized below utilize the electron wavefunctions of Sokolov and Ternov 12, and are valid for strong fields.

2. Example Electron-Photon Interactions in an External Magnetic Field

Processes that occur in a strong magnetic field include processes that are forbidden in the absence of a magnetic field and processes that are strongly modified by the presence of the magnetic field. Examples of the first kind

299

are electron-positron annihilation into one photon, and the inverse process of one photon pair creation. Both would be forbidden by momentum conservation in the absence of a magnetic field but with a magnetic field are allowed: momentum perpendicular to the field is not conserved, as is apparent even in the cyclotron motion of a single electron.

2e+08 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1

~ unpolarized radiation E(1) ~ ( 2 ) (times 100) E(+)

E(-)

. . . . . . . . . . .

y....: ....._..

Oe+00 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

o (MeV)

Figure 1. The attenuation coefficient for pair production, R, as a function of photon energy, w. The five curves are for: unpolarized radiation; the two linear polarization modes; and the two circular polarization modes. The electron has spin-down, the positron has spin-up, the radiation is propagating at 0 = 7r/2 with respect to the magnetic field and B = BcT.

Daugherty and Harding carried out calculations of several aspects of one-photon pair creation and contain a list of references of previous calculations. The calculations are valid only for B << Bcp. Frangodimitraki- Georgiadou reanalyzed pair production using wave functions valid for large B. Semionova and Leahy l3 generalized this work to include electron

300

1 e+08

8e+07

6e+07 h

,5

‘E 0 v h

3 4e+07

2e+07

Oe+00 1

- r=-I, r’=+l r=-1 , r’=-I and r=+l , r’=+l r=+l, r’=-I

. . ~ ~ ...... ~

2

\

2.5 3

Figure 2. The attenuation coefficient for pair production, R, as a function of photon energy, w. The three curves are for: electron spin-down/ positron spin-up; electron spin- down/ positron spin-down or electron spin-up/ positron spin-up; and electron spin-up/ positron spin-down. The radiation is unpolarized and is propagating at 0 = s/2 with respect to the magnetic field and B = BcF.

and photon polarizations. The pair creation rate depends the photon polarization (Fig. l) and on the final state electron and positron spin (Fig. 2). The rate exhibits many resonances- each one occurs due to new final allowed states as photon energy increases.

Two photon pair annihilation can occur at low magnetic field strengths, but for B approaching B,, the one photon pair annihilation process becomes dominant. Early calculations were valid only for B << B,, and also did not treat electron spin. Semionova and Leahy l4 present work correcting these problems. The pair annihilation rate is strongly spin dependent on the photon polarization (Fig. 3) and on electron and positron spin. The electron spin-down, positron spin-up rate is the largest and the electron

30 1

0 2 4 6 6 l o Bi

Figure 3. The annihilation cross-section normalized to the free-space 2-photon nonrel- ativistic cross-section, uo, for e- with N = 0 and r = -1 (spin down), and e+ with N' = 0 and T' = +1 (spin up). For all cases p , = 0. ulo is for photon polarization .dl) and p: = 0 and is equal to the total unpolarized cross-section since the dz) cross-section is zero, upo(= ulo/2) is for i ( f ) and p i N 0 (and is equal to that for the d - 1 case). ulzmc is for dl) and p', = 2mc and is equal to the total unpolarized cross-section since the dz) cross-section is zero, upzmc(= ulzmc/2) is for i(+) and p: = 2mc, (and is equal to that for the d - 1 case).

spin-up, positron spin-down rate the smallest of the four cases. The one- photon annihilation rate rapidly increases with B for B < B,,, reaches a maximum near B,, and declines slowly for larger B.

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3. Summary

A great deal of previous work has considered the case of moderately strong magnetic fields B << Bcr. Current research efforts are extending calculations for many electromagnetic processes of interest to the regime of magnetic fields B >_ B,,, e.g. Semionova and Leahy l5 discuss two-photon emission. This work has been motivated by the discovery that such strong field objects actually probably exist in nature. There is a separate field of study regarding how one applies the fundamental quantum electrodynamic interactions, in terms of cross-sections and transition rates, to understand the behaviour of matter and radiation in the magnetospheres of radio and of x-ray pulsars. That involves several areas of physics, including radiation transfer, and is discussed in review monographs such as Meszaros '.

Acknowledgments

Partial support for this work was provided by the Natural Sciences and Engineering Research Council of Canada.

References 1. G. Vasisht and E. Gotthelf, ApJ486 L129 (1997). 2. C. Kouveliotou, et al., ApJ 510 L115 (1999). 3. J. Daugherty and A. Harding, ApJ 273 761 (1983). 4. A. Harding, in Proceedings of the International Conference on "Coherent Ra-

diation Processes in Strong Fields " (the Catholic University, 1990). 5. P. Meszaros, High Energy Radiation from Magnetized Neutron Stars (Univer-

sity of Chicago Press 1992). 6. M. Johnson and B. Lippmann, PRD 76 828 (1949). 7. C. Graziani, ApJ412 351 (1993). 8. V. Canuto and J. Ventura, Fund. Cosmic Phys. 2 203 (1977). 9. M. Frangodimitraki-Georgiadou, Ph.D. Thesis, University of Tubingen (1991). 10. D. Leahy, in Fundamental Interactions, Proceedings of the 16th Lake Louise

Winter Institute, eds. Astbury, Campbell, Khanna, Vincter (World Scientific 2002) 277.

11. D. Leahy, in Fundamental Interactions, Proceedings of the 17th Lake Louise Winter Institute, eds. Astbury, Campbell, Khanna, Vincter (World Scientific 2003) in press.

12. A. Sokolov and I. Ternov, Synchrotron Radiation (Berlin: Akademie 1968). 13. L. Semionova and D. Leahy, A B A 373 272 (2001). 14. L. Semionova and D. Leahy, A 6 A Supp. 144 307 (2000). 15. L. Semionova and D. Leahy, PRD 60 073011 (1999).

SELECTED CHARM PHYSICS RESULTS FROM BABAR*

w. s. LOCKMAN+ REPRESENTING THE BABAR COLLABORATION

Santa Cmz Institute for Particle Physics 11 56 High Street,

Santa Craz, CA 95064, USA E-mail: lockmanOslac.stanford.edu

We perform a search for mixing and C P violation in Do decays from a 57 ft-' dataset acquired by the Babar experiment near the Upsilon(4S). We measure the time-dependence of wrong-sign decays Do t K+T- and also the lifetime ratios 7(D0 + K-?r+)/7(D0 -+ K-K+) and T(DO + K-?r+)/7(D0 -+ T-T+). For the decays Do -+ K$K*T- and Do t K$K+K- , we present preliminary measurements of their branching fractions relative to that of Do + K:T+T-, together with an analysis of their Dalitz plot distributions.

1. Introduction

Mixing is characterized by two dimensionless parameters x G Am/r and y = AF/(2F), where Am = ml - m2 and A r = - r2 are the mass and width differences of the two neutral meson mass eigenstates D1 and D2, and is their average width. For DODO-mixing, the Standard Model (SM) predicts1y2 values for x and y which are undetectable by current experiments. Hence, the observation of DODO mixing would indicate new physics. Observation of CP violation (CPV) in DoDo mixing would be an unambiguous sign of new phy~ics . l*~

Mixing and CPV may be observable in the wrong-sign (WS) decay Do + K+T- (charge conjugation is implied). The Do may decay to K+T- directly through a doubly-Cabibbo suppressed (DCS) decay amplitude, or by mixing to a Do, followed by a Cabibbo-favored (CF) decay of the Do.

*This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-INPPJ (France), BMBF and DFG (Germany), INFN (Italy), FOM (the Netherlands), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). tThis work is supported by DOE grant DE-FG03-92ER40689

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To distinguish these two possibilities, we measure the proper time dependence of the WS decay rate together with that of the CF right-sign (RS) decay, Do + K-7r+. Preliminary BABAR results of this measurement are presented in Section 3. a In Section 4, we present preliminary BABM measurements of the lifetime ratios T(DO + K-7r+)/7-(D0 + K+K-) - l and 7(D0 + K-X+)/T(D' + 7 r + ~ - ) - 1. In the limit of CP conservation, these quantities are equal to y. For the decays Do -+ K:K%T and Do K:K+K-, we present preliminary BABAR measurements of their branching fractions relative to that of Do + K:n+7r- , together with an analysis of their Dalitz plot distributions in Section 5.

2. Event selection overview

The data for all three analyses were acquired with the BAl3AR d e t e ~ t o r . ~ The decay D*+ 7r$ Do is used to suppress backgrounds and to distinguish Do from Do. The Do decay products are identified using dE/da: from the tracking detector together with light output from a Cherenkov detector. To remove Do mesons from B decays and to reduce combinatorial backgrounds, each Do is required to have a center of mass momentum greater than 2.6,2.4 and 2.2 GeV/c for the analyses presented in Sections 3 , 4 and 5, respectively. Other criteria are imposed to select high quality tracks and to further reduce background^.^*^>^ Each event sample may be characterized by the invariant mass DO of each candidate Do, the difference 6m between the invariant masses of the D* and Do candidates, and for the mixing analyses, the proper time t and its error nt. Sidebands in mgo and 6m are used to determine the level of background.

3. Do mixing: wrong sign decays

From a 57 ft-' BABAR dataset, each neutral D candidate is assigned to one of four categories based on its origin as Do or Do and its decay as RS or WS. In each of the Do and Do datasets, the mixing parameters are determined by unbinned, extended maximum likelihood fits to the RS and WS samples simultaneously. The RS sample fixes the Do lifetime and signal resolution parameters. The mixing parameters themselves are determined from the WS sample; its t distribution is shown in Figure l(a). In total, there are approximately 120,000 (430) RS (WS) signal events.

measure d and y', where xf = x cos 6~~ + y sin b ~ ~ , yf = -x sin 6~~ + y cos G K = , and 6~~ is an unknown strong phase between the CF and DCS amplitudes.

305

We present results for three different fit cases: first, a fit allowing for both CPV and mixing, where the WS Do and Do samples are fitted separately; secondly, a fit allowing for mixing but no CPV, where the WS samples are fitted together, and finally, a fit where we assume no mixing, but allow for direct CPV. Here, we compute the CP asymmetry AD = (RA - R,)/(RA + RE), where + (-) refers to the Do (no) sample.

0 06

0.04

0.02

0

-0.02

-0.04

-0.06

-0.08

-0.1 - 2 - 1 0 1 2 3 4 5

xt2 I 1 om3

Figure 1. (a): Proper time distribution of WS events for data (points) in the signal region (main figure) and in a sideband (inset). The open (shaded) histograms are the fit results for signal (background). (b): 95% CL limit contours determined for the Do (dashed) and no (dotted) data sets separately, for the case allowing CPV and mixing. The solid contour is for the case assuming CP conservation. For this case, the solid point represents the best fit and the open point is the best fit with the constraint 2'' > 0.

The 95% confidence level (CL) limits are shown in Figure l(b). Toy Monte Car10 (MC) experiments generated from the probability density function (PDF) of the fit are used to evaluate the CL limits. System- atic uncertainties arising from uncertainties in the PDF parameterization, detector alignment and charge asymmetries, and the event selection criteria are included in the limit calculation. Projecting the contours onto the coordinate axes yields the limits for the mixing parameters for the different cases shown in Table 1.

4. Do mixing: lifetime ratios

In the limit of CP conservation where the mass eigenstates D1 and DZ are also CP even and odd eigenstates, respectively, the following lifetime ratios can be used to estimate y:

T(DO -+ K-T+) T(DO -+ K-T+) - 1. (1)

T(D0 -+ 7r-.+) - 1, Y7r7r = T(D0 -+ K-K+) YKK =

306

B h m preliminary y measurement (%) Y K K 1.6 f 1.2"::; Yrr 1.0 f 1.7fi::

combined 1.4 f 1.0+8:~

Table 1. Preliminary BABm WS analysis results including systematic errors. A central value is reported for both the full fit allowing xi' < 0 and from a fit

Experiment Y (%I BELLE^ -0.5 f 1.0:::; CLEOg -1.2 f 2.5 f 1.4 E7911°

FOCUS1' 0.83 f 2.89 f 1.3 3.42 f 1.39 -+ 0.74

with zf2 fixed at zero. The 95% CL limits are for the c-ase where d2 is free.

Fitted Central Value Fit case Parameter d 2 free 2'' fixed at 0 95% CL

R: [%I 0.32 0.35 0.18 < RA < 0.62 RE [%] 0.26 0.27 0.12 < R, < 0.56

CPVand xi+' -0.0008 0 x'+' < 0.0035 mixing xj-' -0.0002 0 d+' < 0.0036

Y'+ 0.017 0.007 -0.075 < y'+ < 0.034 Y'- 0.012 0.009 -0.057 < 3'- < 0.036 RD [%] 0.30 0.31 0.22 < RD < 0.46

Y i 0.013 0.008 -0.037 < 9' < 0.024 No CPV 2'' -0.0003 0 Xt2 < 0.0021

No RD [%I 0.357 f 0.022 (stat) f 0.027 (syst) mixing AD[%] 9.5 f 6.1 (stat) f 8.3 (syst)

Table 2. samples used in the lifetime ratio analysis.

The sizes and purities of the Do

Channel Events signal purity Do t K - d 158,000 99.5% Do t K-K+ 16,500 97.1% Do + 7r-n+ 8,350 92.4%

Many systematic uncertainties present in the individual lifetime measurements cancel in the ratio of lifetimes. From a 57 fb-' BABAR dataset we show the signal yields and purities in Table 2; the lifetime ratios from an unbinned maximum likelihood fit in Table 3 and the sources of systematic error in Table 4. The combined results from the WS decay and lifetime ratio analyses indicate no mixing and no C P V , consistent with SM predictions.

5. Three-Body Do decays

From a 22 fb-I BABm dataset, we measure7 the branching fraction for each of the decays Do + K0K-r+, Do + K°K+.rr- and Do + E°K+K-

Table 3. Summary of measurements from BABAR and other experiments.

307

Table 4.

Systematic Monte Carlo Statistics

Particle Identification f0.2 Background f0 .2 f 0 . 6

+0.2 +0.3

Quadrature Sum n ? - 1 "

Sources of systematic uncertainty on y.

Tracking f0 .2 f0.9

Alignment -0.1 -0.1

Table 5. Ratios of branching fractions relative to the decay Do + FO,+A-. Channel B a r n preliminary PDG world average12

Do --t K°K-a+ (8.32 f O.29(stat) f 0.56(syst))% (11.7 f 1.7)% DO -+ E O K + ~ - Do + K°K+K-

(5.68 f o.x(statj f 0.4i(~&jj% (16.30 f 0.37(stat) f 0.27(syst))%

(8.9 rt 1.7)% (17.2 f 1.4)%

relative to that for the decay Do + Zo.rr+.rr- as shown Table 5. In these ratios, many systematic errors cancel.

We perform an amplitude analysis7 of the Dalitz plot distributions in Figs. 2(a-c) to determine the relative fractions and phases of intermediate resonant and non-resonant amplitudes in Do decays. The PDF consists of a signal and a constant background term, each properly normalized. The signal term includes only those amplitudes containing known states and a non-resonant term with a fixed modulus and free phase.

The vertical band in Fig. 2(a) and the results of the amplitude analysis indicate that the Do decays to K°K-.rr+ primarily through the Ky+(892)K- intermediate state. Only a small non-resonant contribution is required.

K°K+.rr- is shown in Fig 2(b). The amplitude analysis indicates that this decay contains several interfering amplitudes: K*-(892)K+, K,'O(1430)R0 and a$(980).rr-. A significant non-resonant term is required.

The Dalitz plot for the decay Do + K°K+K- is shown in Fig. 2(c). In the K+K- system, a strong 4(1020) signal is seen interfering with a threshold scalar. A clustering of events at low K°K+ mass due to the aZ(980) can also be seen. In the Dalitz analysis, the dominant amplitudes are K0u00(980), K04(1020) and a$(980)K-. A small KOfo(980) amplitude is also required. There is no significant non-resonant contribution.

The Dalitz plot for the decay Do + zo.rr+7r- is shown in Fig. 2(d). Many intermediate resonances are evident, including the p(770), fo (980) and K* (890). An amplitude analysis of this decay is underway.

The Dalitz plot for the decay Do

--+

308

2 ,

v - - - \ %1.5

0 . v -

1 - Y v -

E : 0.5 -

1

rnz(Ko rr') (GeV'/c')

2 r

t t , * > # I 1 2

rn*(K' K-) (GeV*/c')

2 1

m2(?' rr-) (GeV'/c')

2 ,

" 0 2 rn'(i7" rr*) (GeV'/c')

Figure 2. Dalitz plots of the decays (a) Do + K°K-r+, (b) Do -+ F°K+r- , (c) Do -+ z ° K + K - and (d) Do + Eor+r-. In (a), (b) and (c), the estimated Do signal purities are (95.5 f 0.4)%, (95.5 f 0.4)% and (97.5 f 0.2)%, respectively.

References

1. A. F. Falk, Y. Grossman, Z. Ligeti and A. A. Petrov, Phys. Rev. D65, 054034

2. H. N. Nelson, in Proc. of the 19th Intl. Symp. on Photon and Lepton Interac- tions at High Energy LP99, ed. J.A. Jaros and M.E. Peskin, hep-ex/9908021.

3. G. Blaylock, A. Seiden and Y. Nir, Phys. Lett. B355, 555 (1995). 4. B. Aubert et al. [BABAR Collaboration], Nucl. Instrum. Meth. A479, 1

5. B. Aubert et al. [BABAR Collaboration], hep-ex/0304007. 6. A. Pompili [BABAR Collaboration], hep-ex/0205071. 7. B. Aubert et al. [BABAR Collaboration], hep-ex/0207089. 8. K. Abe et al. [Belle Collaboration], Phys. Rev. Lett. 88, 162001 (2002). 9. D. Cronin-Hennessy et al. [CLEO Collaboration], hep-ex/0102006. 10. E. M. Aitala et al. [E791 Collaboration], Phys. Rev. Lett. 83, 32 (1999). 11. J. M. Link et al. [FOCUS Collaboration], Phys. Lett. B485, 62 (2000). 12. K. Hagiwara et al. [Particle Data Group Collaboration], Phys. Rev. D66,

(2002).

(2002).

010001 (2002).

SEARCHES FOR NEW PHYSICS AT HERA

N. M. MALDEN* Department of Physics and Astronomy, Schuster Laboratory, Brunswick Street,

Manchester University, Manchester, M13 SPL, UK E-mail: [email protected]

HERA is the only high energy electron-proton collider in the world today and hence has unique opportunities to search for physics beyond the Standard Model. Results are presented for searches for processes involving direct electron-quark interactions (leptoquarks and R-parity violating SUSY), generic coupling models (contact interactions and large extra dimensions) and exclusive final states (isolated leptons and missing PT, and single top production). Exclusion limits on proposed models are set where no deviation from Standard Model predictions are found.

1. Introduction

Between 1994 and 2000 HERA collided 27.5 GeV electrons or positrons and 920 GeV protonsa, delivering an integrated luminosity of over 130 pb-l to each of its ep collision experiments H1 and ZEUS. Thus ep collisons at HERA have a centre of mass of 318 GeV with squared four momentum transfers (Q2) reaching 3.104 GeV2, allowing competitive searches for exotic heavy particles and small scale physics to be performed.

2. Direct electron-quark interactions

2.1. Leptoquarks

Both Neutral Current (NC) and Charged Current (CC) high Q2 data are examined for evidence of leptoquark (LQ) production via either s or u channel exchanges. This is done in the framework of the BRW' model which predicts 7 scalar and 7 vector LQs. The eq coupling is parameterised by the Yukawa coupling X and the branching ratios are fixed. The data2>3 show

*On behalf of the H1 and ZEUS collaborations a820 GeV before 1998

309

310

good agreement with the Standard Model (SM) prediction and exclusion limits in terms of X and LQ mass MLQ are set. One such result is shown in figure 1, with the complementary LEP and TeVatron results.

SCALAR LEPTOQUARKS WITH F=O { 5 ,*, ) x

1

-1 L3 indir. limit 10

H1 direct limit -2

10 1 TEVATRON lim.

150 175 200 225 250 275 300 325 350 375 400

LQ (GeV)

Figure 1. MLQ .

Exclusion limits on the Yukawa coupling X as a function of leptoquark mass

2.2. R-parity violating SUSY

Since R-parity (Rp) is even (+1) for all SM particles and odd (-1) for their supersymmetric (SUSY) partners, its violation implies that SUSY particles may be singly produced and that the lightest SUSY particle (LSP) is not stable. Resonant squark production is searched for in the framework of both the minimally SUSY SM (MSSM) and the minimal supergravity (mSUGRA) models. Some cascade decays result in background-free channels. No e ~ i d e n c e ~ ? ~ for such processes is found allowing mass and coupling limits to be set with the free variation of the MSSM parameters p, M2 and tanp. One such result is shown in figure 2.

31 1

Search for R, viol. SUSY

Figure 2. Exclusion limits on the Yukawa coupling as a function of squark mass.

3. Generic coupling models

3.1. Contact interactions

These models parameterise a coupling for the virtual exchange of particles with masses beyond the direct access of the collider, but whose interference with SM exchanges (y, 2” and W*) could nevertheless be measureable. No deviations in the agreement of the highest Q2 NC data and the SM expectation are observed. These results also set limits on finite quark radii. The ZEUS collaboration set an upper limit of 0.73.10-lsm at 95% C.L.

3.2. Large eztm dimensions

High Q2 data may also be examined in the context of large extra dimensions (LEDs). It has been suggested6 that whilst SM particles propagate in 4-D, gravitons may inhabit (4+n)-D. These extra dimensions are proposed to be “curled up’’ such that their presence might only become apparent at large mass scales. Fits to NC data have produced 95% C.L. exclusion limits on the mass scale of the order of 0.8 TeV.

312

4. Exclusive final states

4.1. Isolated leptons and missing PT

The HI Collaboration has recently reported7 an excess of events containingan isolated electron or muon and missing transverse momentum. Withinthe SM such events of this topology are expected to be mainly due to theproduction of a W boson and its subsequent leptonic decay, particularlywhen the hadronic system has high PT (large P*)- Recent work8 hascalculated the dominant QCD corrections to the SM prediction at next-to-leading order (NLO). The ZEUS Collaboration has also performed a searchfor such events9. The results of these searches are presented in table 1.

Table 1. Observed and expected number of events with an isolated elec-tron or muon and missing transverse momentum. The percentage of theSM expectation composed of W production is also given.

HI94-00 e+p 105 pb"1

25 < Pf < 40 GeVP$ > 40 GeV

ZEUS preliminary94-00 e±p 130 pb"1

P* > 25 GeVP* > 40 GeV

ElectronsObserved/exp'd (W)1 / 0.95±0.14 (86%)3 / 0.54±0.11 (83%)

ElectronsObserved/exp'd (W)2 / 2.90^'^ (45%)0 / 0.94^;Ji (61%)

MuonsObserved/exp'd (W)3 / 0.89±0.14 (87%)3 / 0.55±0.12 (93%)

MuonsObserved/exp'd (W)5 / 2.75+^'^ (50%)0 / 0.95i£}3 (61%)

The number of events with an isolated electron or muon observed by HIovershoots the SM prediction, in particular at high P* • The distributionof events observed by HI is shown in figure 3 (left) with respect to P*.Additionally, the ZEUS Collaboration has searched in the tau channel,finding 2 candidate events at P* > 25 GeV compared to a SM expectationof 0.12 ±0.02.

4.2. Single top production

An event topology of an isolated lepton, missing PT and a high PT hadronicjet may also be the signature of single top production, where the top quarkdecays to a b quark and a W. This rate of process is, however, negligiblein the SM, due to the flavour changing neutral current (FCNC) vertex re-quired. The anomalous coupling at the two relevant vertices tuj and tuZ,is parameterised by the magnetic coupling Ktm and the vector couplingVtuz respectively. Both collaborations have also searched for hadronic de-cays of single top quarks, but the large background from other multi-jetprocesses severely restricts the contribution of this channel to the analysis.

313

ZEUS Combined Electron and Muon

i n

2 N,,,=18 8 H1 Data N,, = 12.4H.7 0 AllSMprocesses j

I SMerror i i

t t

0 10 20 30 40 50 60 70 80

4 I GeV

1 $3 s 0.8

0.6

0.4

0.2

n 0 0.2 0.4 0.6 0.8 1

Figure 3. (Left) Number of events with isolated leptons (electrons or muons) and missing transverse momentum as a function of P$, the transverse momentum of the hadronic system. (Right) Excluded regions of the anomalous coupling ~ t u y - v t u Z plane.

The combined result^^^>^, in terms of exclusion limits for the anomalous couplings ntu7 and v t , ~ , are shown in figure 3 (right).

References 1. 2. 3. 4.

5. 6. 7.

8.

9.

W. Buchmiiller, R. Ruck1 and D. Wyler, Phys. Lett. B191 (1987) 442. H1 Collaboration, ICHEP 2002 contributed paper, abstract 1027. ZEUS Collaboration, ICHEP 2002 contributed paper, abstract 907. C. Adloff et al. [Hl Collaboration], Eur. Phys. J. C20 (2001) 4, 639, [hep- ph/0102050]. ZEUS Collaboration, ICHEP 2000 contributed paper, abstract 1042. N. Arkani-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. B429 (1998) 263. C. Adloff et al. [Hl Collaboration] “Isolated electrons and muons in events with missing transverse momentum at HERA”, accepted by Phys. Lett. B, [hep-ex/0301030]. K. Diener, C. Schwanenberger, and M. Spira, Eur. Phys. J . C25 (2002) 405, [hep-ph/0203269]. S. Chekanov et al. [ZEUS Collaboration] “Search for single-top production in ep collisions at HERA”, accepted by Phys. Lett. B, [hep-ex/0302010].

10. H1 Collaboration, ICHEP 2002 contributed paper, abstract 1024.

QUANTUM CHAOS IN THE GAUGE FIELDS AT FINITE-TEMPERATURE

D.U.MATRASULOV AND F.C.KHANNA Physics Department University of Alberta

Edmonton Alberta, T6G ZJ1 Canada and TRIUMF, 4004 Wersbrook Mall,

Vancouver, British Columbia, Canada, V6TZA3

U.R.SALOMOV Heat Physics Department of the Uzbek Academy of Sciences,

28 Katartal St., 700135 Tashkent, Uzbekistan

A.E.SANTANA Instituto d e Fisica, Universidade Federal, Campus de Ondina, 402-10 340,

Salvador, Bahia Brazil

The quantum chaos in the finite-temperature Yang-Mills-Higgs system is studied. The energy spectra of a spatially homogeneous SU(2) Yang-Mills-Higgs is calculated within thermofield dynamics. Level statistics of the spectra is studied by plotting nearest-lelel spacing distribution histograms. It is found that finite temperature effects lead to the strengthening of chaotic effects.

1. Introduction

In recent years there has been considerable interest to dynamical chaos in field theories '-3. Chaotic properties of Yang-Mills' , Yang-Mills-Higgs 2 7 3

and Abelian Higgs have been considered. The Hamiltonians of Yang-Mills and Yang-Mills-Higgs fields can be written in the same form as those for the coupled nonlinear oscillators. This allows the use of conventional methods. Quantum chaos in Yang-Mills-Higgs system was also studied recently 3 .

Quantum chaos is a relativley new area in physics and has been the subject of extensive studies 4 9 5 in atomic and molecular physics, nuclear physics and condensed matter physics. There is growing interest in quantum chaos in particle physics, too. The present study extends the quantum chaos to finite temperature. The thermofield dynamics (TFD) f ~ r r n a l i s m ~ ? ~ is used

314

31 5

to introduce temperature. Section 2 gives an outline of quantum chaos at zero temperature. Section 3 extends the formalism to finite temperature. Section 4 presents some concluding remarks.

2. Zero temperature case

The Lagrangian for YMH system with SU(2) symmetry is given as 1 1

L = -4F;”Ff’ + z(Dp4)+(Dp4) - V(4)

where

F;” = &A: - &A: + gALAE

( D p 4 ) = ap4 - igALTb4

with T b = coupling constant. The potential of the scalar (Higgs) field is

/2, b = 1 ,2 ,3 generators of the SU(2) algebra a

~ ( 4 ) = P2i4i2 + w4.

d g i s a

Here we give a brief description of the non-thermal case 3. In (2 + 1)- dimension Minkowski space and for spatially homogeneous Yang-Mills and Higgs fields which satisfy the conditions

aiAf = ai4 = 0, i = 1 ,2 , ; and in the gauge A,” = 0, the Hamiltonian corresponding to the Lagrangian is written as

+ where 40 = (O,O,v) q1 = A!, q2 = A; (other components of the Yang- Mills fields are zero) pl = q1 and p2 = 42, and with w2 = 2g2w2 being the mass term of the Yang-Mills fields. In terms of annihilation and creation operators, which are defined as

the Hamiltonian can be written as

(3) H = w(a1af + u2u,’) + -(a1 g 2 + u 9 2 ( a 2 + u,’)2, 8w2 where w2 = 2g2v2 and [ i i k , &:] = 6 k l , I C , 1 = I, 2.

The eigenvalues of this Hamitonian can be calculated by numerical diagonalization of the truncated matrix of the quantum Yang-Mills-Higgs Hamiltonian in the basis of the harmonic oscillator wave functions 3 .

316

3. Finite- temperature case

To treat quantum chaos at finite-temperature in Yang-Mills-Higgs system we apply Thermofield Dynamics(TFD). TFD is a real time operator formalism of quantum field theory at finite temperature with a temperature dependent vacuum (O(p) > which is a pure state. The thermal average of any operator is equal to the expectation value in the state lo(,@ >. The Fock space of the original field is doubled The Bogoluybov transformation introduces a rotation in the tilde and non-tilde variables and tranforms the non-thermal variables into a temperature-dependent form. The YMH Hamiltonian in TFD is given as

f i = H - H (4) where H is given as

2 H = W ( 6 1 6 ; t + 6 2 6 9 + 8w2(al 9 - + 6 3 2 ( 6 2 + 6;)2

First we need to rewrite the non-tilde part of the Hamiltonian in the temperature-dependent form using the Bogolyubov transformations given as

ak = ak(P)coshe + 6;(p)sinhe7 = a;(p)coshe + ak(p)sinhe7

where

where tilde and non-tilde creation and annihilation operators satisfy the following commutation relations:

[ak ( P ) 7 a? (@)I = 6k3

1, Ic = 1,2, and sinh20 = (eP - 1)-l.

[ck ( P ) 7 6; (@)I = bkl

Then the temperature-dependent form of HO is

H~ = w { ( F ~ + F2)cosh2e + ( L ~ + ~ ~ ) ~ i ~ h ~ e + (sl + ~ ~ ) ~ ~ ~ h e

where

Fk = ak (P),; (p) 7 Lk = 6; (P)ak (P ) 7

317

ck = (G; (P) + &c(P))2- Then energy eigenvalues can be calculated by diagonalizing the matrix

(5) I - I - I R =< 4 n 2 , nln21Ho + Vlnln2, fiilfiz > .

Diagonalizing the matrix R numerically we obtain the energy eigenvalues of the finite-temperature Yang-Mills-Higgs system.

As spectrum is found we can calculate its statistical properties. One of the main characteristics of the statistical properies of the spectra is the level spacing distribution 4 7 5 function. In this work we calculate the nearest- neighbor level-spacing distribution4i5. The nearest neighbor level spacings are defined as Si = Ei+1 - Ei, where Ei are the energies of the unfolded levels, which are obtained by the following way: The spectrum {Ei} is separated into smoothed average part and fluctuating parts. Then the number of levels below E is counted and the following staircase function is defined:

N ( E ) = No, (E) + Nfluct (El.

E i = Nav(Ei).

The unfolded spectrum is finally obtained with the mapping

Then the nearest level spacing distribution function P(S) is defined as the probability of S lying within the infinitesimal interval [S, S + dS].

For the quantum systems which are chaotic in the classical limit this distribution function is the same as that of the random matrices '. For systems which are regular in the classical limit its behaviour is close to

For V we have

where

318

R I

P (8)

s

Figure 1. of parameter w = 0.01.

The level spacing distributions for for Yang-Mills-Higgs system for the value

31 9

a Poissonian distribution function. For systems whose classical motion is chaotic the distribution will be Gaussian.

In Fig. 1 we plot the level spacing distributions for different values of 8 at w = 0.01. It is clear from this figure that for 8 = 0 it is the same as the results of non-thermal calculations 3. By increasing the temperature it becomes closer to a Gaussian distribution that means strengthening of chaos in the thermal case. However the heating leads to chaotization of the system and P(S) becomes closer to a Gaussian distribution. Thus increasing the temperature leads to a smooth transition from Poissonian to a Gaussian form in the level spacing distribution.

4. Conclusion

We have studied quantum chaos in gauge fields at finite temperature using a toy model, SU(2) Yang-Mills-Higgs system. Finite-temperature effects are introduced using the thermofield dynamics technique. The need for simul- taneous exploration of level fluctuations and the finite-temperature effects is dictated by recent advances in relativistic heavy ion collisions experiments, that allows one to create hot and dense quark-gluon and hadronic matters .

Acknowledgements

The work of DUM is supported by NATO Science Fellowship of Natu- ral Science and Engineering Research Council of Canada (NSERC). The work of FCK is supported by NSERC. The work of AES is supported by CNPq(Brazi1).

References 1. G.K.Savvidy, Phys. Lett. 159B 325 (1985). 2. Luca Salasnich, Phys.Rev.D, 52 6189 (1995). 3. Luca Salasnich, Mod.Phys.Lett. A 12 1473 (1997). 4. T.A.Brody et al, Rev.Mod.Phys. 53 358 (1981). 5. M.C.Gutzwiller,Chaos in classical and quantum systems. New York, Springer

Verlag 1990. 6. H.Umezawa, H.Matsumoto and M.Tachiki Thermofield Dynamics and con-

densed states.(North-Holland. Amsterdam, 1982). 7. Y,Takahashi and H.Umezawa, Collective Phenomena 2 55 (1975) (Reprinted

in 1nt.J. M0d.Phys.B 10 1755 (1996)).

GALACTIC DARK MATTER SEARCHES WITH GAS DETECTORS

B. MORGAN (ON BEHALF OF THE DRIFT AND UK DARK MATTER COLLABORATIONS) University of Shefield,

Department of Physics and Astronomy, Hacks Building,

Hounsfield Road, Shefield S3 7RH, England

E-mail: b.morganOshefield.ac.uk

The search for non-baryonic dark matter in our galaxy is one of the greatest challenges facing particle physics at present. Low event rates and backgrounds are particularly problematic. Gas Time Projection Chambers (TPCs) offer several advantages in these areas. Here I discuss the use of TPCs in dark matter searches and recent advances in TPC readout devices with regard to the DRIFT experiment.

1. Introduction

The search for dark matter is perhaps the greatest challenge facing particle physics at present. Astronomical observations continue to demonstrate the presence of dark matter on scales from our own galaxy up to the largest superclusters of galaxies. Measurements of the total and baryonic matter densities of the universe, most recently by the WMAP satellite', show however that - 86% of the matter in the universe is in the form of some unknown elementary particle(s).

Weakly Interacting Massive Particles (WIMPs) are the currently favoured candidates for the dark matter, and Supersymmetry provides a potential candidate for dark matter in the form of the neutralino, a linear combination of the superpartners of the Standard Model gauge bosons. The inferred dark matter halo of our own galaxy provides great motivation for direct searches for these particles via the nuclear recoils produced by elastic scattering of WIMPs off atomic nuclei in a suitable detector. These recoils can be detected through the scintillation, ionisation or thermal phonons produced. However, the kinematics of WIMPs in the galactic halo and

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32 1

the predicted neutralino mass of w lOOGeV mean that the recoil energy is < 1OOkeV. In addition, the predicted neutralino-nucleon elastic scattering cross-sections of < B < 10-6pb mean that the expected recoil rate is < lkg-'day-'. Such low rates and energies mean that the reduction of background electron and alpha recoils is critical. It is therefore important to also look for characteristic features of the WIMP signal that positively identify it as galactic in origin.

This article discusses the advantages of measuring the directions of WIMP-induced nuclear recoils to identify a WIMP signal. Low pressure gas Time Projection Chambers offer a way to measure low energy recoil directions, and the DRIFT-I (Directional Recoil Identification From Tracks) TPC is described. Finally, the use of new gas detector readouts such as the Gas Electron Multiplier (GEM) and Micromesh Gaseous Structure (MI- CROMEGAS) in future DRIFT detectors is discussed.

2. Modulations in the WIMP Recoil Signal

Models of the dark matter halo believed to surround our galaxy predict it to be non-rotating, or a least very slowly rotating, in the galactic rest frame. In contrast, the solar system orbits the galactic centre at a speed of - 220kms-l. The simplest model of the WIMP velocity distribution is an isotropic Maxwell-Boltzmann distribution with a mean speed of - 270kms-l. In consequence, the velocity distribution of WIMPS in the Earth's rest frame is strongly peaked in the direction of the solar motion.

Figure 1. WIMP flux in galactic coordinates for the standard Maxwellian halo ?-.

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As the Earth's orbital plane is inclined at N 60" to the galactic plane, its speed through the halo modulates as its velocity component parallel to the solar motion adds to, and then subtracts from, the solar velocity. This leads to an annual modulation in the WIMP-induced recoil rate of 5-7% over the year. Such a small change in an already small signal is very difficult to measure, although the DAMA group do claim to have seen such a modulation. More problematic is the difficulty in ruling out unknown seasonal modulations in the background rate (e.g. Radon concentration) and ensuring stability in the detector response.

A far stronger signal becomes available if the directions of recoils can be measured. The anisotropic WIMP velocity distribution means that the distribution of recoil directions will be strongly anti-correlated with the solar motion direction. Two distinct signals arise from this anisotropic angular distribution. Firstly, a detector fixed on the Earth at mid-Northern latitudes will see the mean recoil direction rotate from downwards to south- wards and back again over one sidereal day. Alternatively, one can transform the recoil directions to the galactic frame and look at the resultant direction distribution for deviations from isotropy. Monte Carlo simulations indicate that as few as 100 events might be needed to identify a non-isotropic signal at 90% confidence. A further advantage of both these signals is that they cannot be mimicked by background signals.

Measuring recoil directions may also allow the formation history of the WIMP halo to be determined. Evidence from astronomical observations suggests that the halo may be flattened3, and N-body simulations of halo formation indicate that there could be distinct tidal streams of WIMPS flowing past the Sun4. In both cases, distinct features could be present in the recoil direction distribution.

3. The DRIFT Concept

The sub-100keV energy scale of WIMP induced nuclear recoils means that their ranges are very short (of order a few hundred Angstroms) in solids and liquids rendering directional detection near impossible. DRIFT therefore utilises a gas Time Projection Chamber (TPC) operated at low pressure to extend the recoil range to a few millimetres.

In order for DRIFT to see a signal background must also be suppressed. Fortunately, DRIFT'S ability to visualise the range of particle tracks also allows for excellent background rejection. As shown in Figure 2 below, the range difference between electrons, alphas and recoils at a given ionisation is

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such that rejection efficiencies of at least 99.9% are possible at 6keV5. This allows a lm3 detector operating with Ar at a pressure of 40torr to produce a limit competitive with the ZEPLIN-I and EDELWEISS experiments.

1 - b?

, . . . . . .-

!.

I . . . . ,

.U

Figure 2. Simulated recoil, a and electron tracks of the same ionisation in Ar at 40torr.

To optimise the spatial resolution of such a detector, the diffusion of charge in the particle tracks must be minimised. An underground experiment rules out the use of a large magnet, so instead DRIFT uses CS2 as an electronegative target gas to capture the ionisation electrons. The resultant negative ions are drifted to the readout plane, reducing diffusion to thermal levels. Experiments have shown that the diffusion can be reduced to 0.5mm over drift lengths of 50cm using CSz6.

4. The DRIFT-I Detector

DRIFT-I is the first full scale DRIFT detector to be operated at a deep underground, low background site. The detector consists of two 0.5m3 fiducial volumes defined by 0.5m long field cages mounted either side of a common cathode plane consisting of 512 20pm stainless steel wires. Particle tracks are read out with two lm2 MWPCs, one at each end of the field cages. The MWPCs are made up of an anode plane instrumented with 512 20pm stainless steel wires at a pitch of 2mm, with grid planes of lOOpm stainless steel wires either side. All field cage and MWPC structural components are constructed from Lucite to ensure a low contamination of U/Th. Although the DRIFT-I MWPCs only permit a 2D track projection to be measured from reading out signals on the anode wires, background rejection efficiencies > 99.9% are still possible via the range/ionisation measurement. The detector is housed in a large stainless steel vacuum vessel.

The DRIFT-I detector is now installed l.lkm underground at the Boulby Mine in England. Data collection is underway, and some results

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from preliminary engineering runs are discussed in Lawson7.

5. Gas Electron Multipliers and MICROMEGAS

Whilst DRIFT-I is expected to produce a limit down to lOPpb, higher target masses are needed to fully explore the predicted SUSY parameter space. DRIFT-I1 is proposed to have a target mass of N 3kg through increasing the gas pressure and TPC volume by factors of 4. The increased gas pressure requires higher spatial resolution charge readout in order to cope with the reduced track length and acheive the design goal of a 50x increase in sensitivity. Although DRIFT-I1 is proposed to use new grid readout MWPCs, GEMs and MICROMEGAS are also being explored.

GEMs consist of a thin (-50pm) Kapton film coated with a -5pm layer of Cu on both sides. A matrix of holes is etched through the Cu/Kapton sheet using standard photoresist techniques, the holes generally being -80pm in diameter with a pitch of ~ 1 4 0 p m . Applying a high voltage (- 500V) across the Cu layers produces a strong E-field in the GEM holes, giving avalanche charge multiplication with gains of up to lo5. Higher gains are possible by stacking two or more GEMs together. The confinement of the avalanche to the small holes combined with the small pitch allows high spatial resolutions. The charge produced by GEM avalanches can be detected with a variety of anode readout devices placed below the final GEM sheet. Both 2D microstrip and micropixel readouts have been demonstrated, allowing full 3D track reconstruction down to - 100pm8.

MICROMEGAS (MICROMEsh GASeous Structure) is another recently developed microstructure device?. It consists of a 50-100pm Kapton film coated with a - 5pm Cu or Ni film on one side. Holes - 39pm square at a pitch of N 50pm are etched or electroformed in the Cu/Ni mesh, with the remaining Kapton being etched away to leave a series of 50-100pm high pillars or strips at a pitch of N 2mm. This micromesh is placed on top of an anode readout device, with a microgap between the mesh and anode defined by the Kapton spacers. Applying a high voltage (- 500V) to the mesh generates a high E-field in the microgap between the mesh and anode, giving charge gains of up to lo5. As with GEMs a wide variety of anode readouts can be used.

The microgap structure of MICROMEGAS has several advantages for TPC detectors. Very fast pulses (- ns) are produced, giving high spatial resolution in the drift direction. High energy resolutions are possible down to keV energies, and resolutions of 11% at 8keV have been demonstratedg.

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The high gain raises the possibility of energy thresholds at the sub-keV scale. A particular advantage for dark matter detection is that the materials used in MICROMEGAS have very low backgrounds and are also used in small amounts. Large area detectors can be constructed, with 40x40cm2 MICROMEGAS detectors used in the COMPASS experiment. Studies are now underway to test the feasibility of MICROMEGAS for DRIFT with regard to its spatial resolution and performance in low pressure CS2 gas.

6. Conclusions

Galactic dark matter searches are now entering an exciting phase as they begin to explore the regions of parameter space predicted by SUSY for neutralino dark matter. Measuring the directions of nuclear recoils produced by neutralinos provides a powerful method for positively identifying a neutralino signal. Low pressure gas TPCs allow these recoil directions to be measured, although the spatial resolution must be optimised. DRIFT-I is the worlds first TPC dark matter detector and is now collecting data. Im- provements in readout with GEM and MICROMEGAS systems are under investigation.

Acknowledgements

This work was performed within the framework of the DRIFT Collabo- ration (University of Sheffield, Rutherford Appleton Laboratory, Imperial College, Temple University, Occidental College, Lawrence Livermore Na- tional Laboratory) and contributes to to collaboration-wide detector development efforts.

References 1. D. N. Spergel et al, astro-ph/0302209. 2. G. Gelmini and P. Gondolo, Phys. Rev. D 6 4 , 023504 (2001). 3. A. M. Green, Phys. Rev. D 6 6 , 083003 (2002). 4. B. Moore et al, Phys. Rev. D 6 4 , 063508 (2001). 5. D. P. Snowden-Ifft et al, Phys. Rev. D 6 1 , 101301 (2000). 6. T. Ohnuki et al, Nucl. Instrum. Methods A 463, 142 (2001). 7. T. Lawson. , ‘DRIFT-I, A Direction Sensitive Dark Matter Detector: Current

Status’, Proceedings of the 4th International Workshop on the Identification of Dark Matter, 2-6th September 2002, York, England (To be Published).

8. R. Bellazzini, G. Spandre and N. Lumb, Nucl. Instrum. Methods A 478, 13

9. G. Charpak, et al, Nucl. Instrum. Methods A 478, 26 (2002). (2002).

MEASUREMENT OF W POLARISATION WITH L3 AT LEP

RADOSLAW A. OFIERZYNSKI CERN, EP Division, 121 1 Geneva 23, Switzerland

E-mail: Radoslaw.OfierzynskiOcern.ch

The three different helicity states of W bosons produced in the reaction e+e- + W+W- + tuq$ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies fi = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 f 0.027 f 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation. The helicity information is used to determine spin correlations between W bosons w.r.t. the W flight direction. Combining all data, WW spin correlations are seen with a significance of up to 3 standard deviations in the forward and backward scattering regions. The difference between data and the Standard Model is at the 2 standard deviation level.

1. Introduction

In the Standard Model, the masses of the W and the Z boson are generated by the Higgs mechanism. The massless W, which has only two spin degrees of freedom, becomes massive through the combination with a scalar Gold- stone boson. At the same time, the third spin degree of freedom appears, corresponding to longitudinal polarisation. Still the unphysical Goldstone boson controls the amplitude for emission or absorption of the longitudinal W boson. At high energy, this amplitude becomes equal to the amplitude for emission or absorption of the Goldstone boson '. Hence the measurement of the fractions of longitudinally and transversely polarised W bosons constitutes an important test of the Standard Model.

In this analysis, semileptonic W pair events generated at LEP are studied, i e . events of the type e+e-+W+W-+lvqq' , with l denoting either an electron or a muon 2.

The W helicity states are extracted in a model independent way from the shape of the distributions of the polar decay angle, O t , which is the angle in the W rest frame between the charged lepton and the W flight direction. Transversely polarised W bosons have angular distributions (1 T cos 8;)2

326

327

for a W- with helicity f l , and (1 fcos8;)2 for a W+ with helicity f l . For longitudinally polarised W bosons, a sin2 0; dependence is expected. For simplicity, we refer in the following only to the fractions f-, f+ and fo of the helicity states -1, +1 and 0 of the W- boson, respectively. Assuming CP invariance these equal the fractions of the corresponding helicity states +1, -1 and 0 of the W+ boson.

The differential distribution of leptonic W- decays at Born level is: 1 dN 3 3 3 -f-- (i+cos8;)2+f+- (1-cose;)2+f0-sin28;. (I) N d cos 8; 8 8 4

For hadronic W decays, the quark charge is difficult to reconstruct experimentally and only the absolute value of the cosine of the decay angle, I cos 8; 1, is used:

After correcting the data for selection efficiencies and background, the different fractions of W helicity states are obtained from a fit to these distributions.

A total of 685 pb-l of data, collected at different centre-of-mass energies between 183 GeV and 209 GeV, is analysed. After a simple selection, which ensures a good angular resolution, we obtain 1088 W+W-+euqq' candidates and 922 W+ W- +puq$ candidates, with an efficiency of 65.7% and a contamination from W+W--+ruq$ and e+e-+qq(y) of 3.7%. For the selected events, the rest frames of the W bosons are calculated from the lepton and neutrino momenta, the latter being approximated by the missing momentum vector of the event. The polar decay angles 8; and 8; of the lepton and the quarks are then determined. The angle 8; is approximated by the polar angle of the thrust axis with respect to the W direction in the rest frame of the hadronically decaying W.

The fractions of the W helicity states are obtained from the event distributions, dN/d cos 8; and dN/dl cos 8;l. These distributions are corrected at each energy point for background and selection efficiencies. The corrected distributions at the different centre-of-mass energies are combined into single distributions for leptonic and hadronic decays. A binned fit to the functions (1) and (2) is performed on the normalised distributions. For leptonic decays, f- and fo are used as the fit parameters and f+ is obtained by constraining the sum of all three parameters to unity. For hadronic decays, fo is used as the fit parameter and the sum of f+ and f- is obtained from the unity constraint. The fit results are corrected for a small bias

328

0.4

0.3

03 - 8 5 P

o.2-

0.1

+ Data, 183-209 GeV

r] KoralW MC, 183-209 GeV

- Fit Helicity (*1,0) -

.... Fit Helicity (k1) .... .... ....

_._....- ._.._... ...

~

(b) W-+ hadrons L3

-. Figure 1. Corrected decay angle distributions for (a) leptonic .W decays and (b) for hadronic W decays at fi = 183 - 209 GeV. Fit results for the different W helicity hypotheses are also shown.

W- Data W+ Data W* Data

Monte Carlo

due to migration effects introduced by detector resolution. The Standard Model predictions for f-, f+ and fo are obtained from Monte Carlo samples by fitting the generated decay angular distributions for each value of &. The expected fraction of longitudinally polarised W bosons depends on the centre-of-mass energy, e.g. it changes from 0.271 at & = 183 GeV to 0.223 at & = 206 GeV.

f- f+ f o 0.555f0.037f0.016 0.200f0.026f0.015 0.245f0.038f0.016 0.634f0.038f0.016 0.181f0.024f0.015 0.185f0.039f0.016 0.592f0.027f0.016 0.190f0.017f0.015 0.218f0.027f0.016

0.590 f 0.003 0.169 f 0.002 0.241 f 0.003

2. Polarisations of the Individual W Bosons.

Figure 1 shows the results of the fits to the normalised decay angle distributions for leptonic and hadronic W decays. The data are well described only if all three W helicity states are used. For leptonic W decays, if the helicity 0 state is omitted the x2 of the fit increases from 12.7 for eight degrees of freedom to 56.2 for nine degrees of freedom. For hadronic decays, the x2 increases from 6.6 for four degrees of freedom to 59.1 for 5 degrees of freedom if we use only f l helicities.

Table 1. W- helicity fractions, measured combining leptonic and hadronic decays. All the helicities are converted to W- parameters using CP invariance. The first uncertainty is statistical, the second systematic. The corresponding Standard Model expectations are also given with their statistical uncertainties.

329

0 -

MC (-1) A Data(+l) .......... MC (+1)

100 ~3 V Data(-1) -

I I I1

::.:.:.:.:..4:.<:.<:::.:.; -41 + ................... 4. .................. ........... + ........ I ‘ I ‘ I

Figure 2. W helicity fractions f-, f+ and fo and their statistical uncertainties for four different bins of cosOw- in the combined data sample and in the KORALW Monte Carlo for ,h = 183 - 209 GeV.

The measured helicity fractions, at an average centre-of-mass energy fi = 196.7 GeV, are presented together with the Standard Model expectations in Table 1. The measured W helicity fractions agree well with the expectations. We observe longitudinal W polarisation with a significance of seven standard deviations, including systematic uncertainties.

Because of CP symmetry, the helicity fractions f+, f- and fo for the W+ are expected to be identical to the fractions f-, f+ and fo for the W-, respectively. We test CP invariance by measuring the helicity fractions for W+ and W- separately. The charge of the W bosons is obtained from the charge of the lepton. We select 1020 W++l+v, and 990 W - 4 - D events. Table 1 shows the results for separate fits to the W+ and W- distributions. The results are consistent with CP invariance.

To test the variation of the helicity fractions w.r.t. the W- production angle, OW-, the data have been grouped into four bins of cos Ow-. The ranges have been chosen such that large and statistically significant variations of the different helicity fractions are expected. The fit results combining leptonic and hadronic W decays are shown in Figure 2 together with the Standard Model expectations. The results are in agreement with the Standard Model expectation and demonstrate a strong variation of the W helicity fractions with the W- production angle.

330

w+lV 0.3 I cos 0,- 50.9 0.6 I W+qq (kl) depleted I 0.5 x

\ * 0.4 5 8 0.3 9

v)

5 0.2

5 0.1

0

. 0 Data I-: MC

W+qq (kl) enriched Data + MC -

........... , +

0 /-.$--: .............. 0 i""F"'

.......... w L3 preliminary

-1 -0.5 0 0.5 1

w-+h -0.9 I cos 0,- 2-0.3

cos 0; cos 0;

Figure 3. Corrected cos 8; distributions for W + tv decays for data and the KORALW Monte Carlo in the intervals 0.3 < cosOw- < 0.9 (left) and -0.9 < cosOw- < -0.3 (right) at &=183-209 GeV. The distributions are shown for the subsamples with f l helicities depleted and enriched in W-ihadron decays.

3. Spin Correlations between W Bosons. (or: does one of the W bosons scream when we squeeze the other one ?)

To answer this question, we consider two subsamples of W pair events: in the first the fraction of hadronically decaying W bosons with helicity f l is enlarged, in the second reduced. This enrichment and depletion is performed by cuts on the angular distribution of the hadronically decaying W bosons. For small polar decay angles (as follows from Eq. (2)), the sample consists of much fewer f l states, while for large polar decay angles the opposite is the case. For our analysis the slices 0 < I cosOG1 < 0.33 for f l depleted and 0.66 < I cosOG1 < 1.0 for f l enriched samples were chosen. The corresponding leptonically decaying W boson samples are compared to determine the correlation effect.

In order to enlarge possible effects the W- scattering angle, cos Ow-, is used. As was shown in the first part, the W helicities vary with cos OW-, as do the helicity combinations. One can thus use this angle to select particular W pair helicities. For this analysis, two intervals of the W scattering angle are used: In the forward bin, 0.3 < COSOW- < 0.9, the fraction of the helicity combination XW- = -1, XW+ = +1 is increased to about 63% of all W pairs compared to 43% average over the whole COSOW- range. In the backward bin, -0.9 < cosOw- < -0.3, the fraction of the helicity combination XW- = O,Xw+ = 0 is increased to about 25% compared to the average value of 9%. In each of these two COSOW- bins, the proce-

33 1

w+ qc

Table 2. The W helicity fractions measured with leptonic W decays for different intervals of cosOW-. The results are shown for different subsamples with enriched or depleted helicity f l component of the hadronically decaying W boson.

f- f+ fo 0.3 < cos 0,- < 0.9: W-t eu helicity fractions

f l enriched difference data difference MC

w+ S B f l depleted f l enriched

difference data difference MC

0.832f0.061f0.004 0.092&0.033f0.030 0.076f0.081f0.030 -0.376f0.105f0.060 0.005f0.067f0.047 0.372f0.142f0.075

-0.120 0.048 0.072 -0.9 < cos 0,- < -0.3: W+ lv helicity fractions

0.327f0.112f0.089 0.296f0.112f0.076 0.377f0.259f0.112 0.134f0.075f0.075 0.472f0.107f0.104 0.394f0.197f0.136 0.193f0.135f0.116 -0.176f0.155f0.129 -0.017f0.325f0.176

0.039 -0.163 0.124

f- f+ fo

dure of enrichment/depletion of the hadronically decaying W bosons with helicity f 1 is performed and the helicity composition of the corresponding leptonically decaying W bosons is compared.

The polar decay angle distributions of the leptonically decaying W bosons in the data and the Monte Carlo, combined for all centre-of-mass energies, are shown in Figure 3. We see a clear difference between the distributions for f l depleted and enriched samples. The results of the fits to these distributions are summarised in Table 2. The data demonstrate the existence of WW spin correlations along the W flight direction, with a significance of up to 3 standard deviations in the forward and backward scattering regions, 2 standard deviations stronger than expected.

4. Conclusions

Studies of W polarisation in the reaction e+e---+W+W-+Cuqq' have been presented. All three possible W helicity states are required to describe the data. The helicity fractions and their variations as a function of cos Ow- are in agreement with the Standard Model expectation. The helicity fractions of W+ and W- considered separately are in agreement with CP invariance. The data also show significant correlations between W+ and W- helicities, 2 standard deviations stronger than the Standard Model expectation.

References

1. see e.g. M.E.Peskin, D.V.Schroeder, An Introduction to Quantum Field The- ory, Addison-Wesley, 1995.

2. L3 Collab., P. Achard et al., Phys. Lett. B 557 (2003) 147.

A SEARCH FOR CP VIOLATION IN, AND A DALITZ ANALYSIS OF Do + n-n+no DECAYS IN CLEO 1I.V *

CHARLES PLAGER THE CLEO COLLABORATION

E-mail: cplager+lakelouiseOuiuc.edu

Using the 9fb-1 data sample collected with the CLEO 1I.V detector at the Cor- nell Electron Storage Ring, we study the resonant substructure of the Cabibbo suppressed decay Do + T - T + T O . We observe significant contributions from the p-?r+, p + ~ - , p o r o , and non-resonant channels, and present preliminary results of the amplitudes, phases, and fit fractions for these sub-modes. No significant evidence for the (~(500) or any other heavy resonance was found. The preliminary measurement of ACp is consistent with 0 at 0.01'",:~ f 0.09.

1. Introduction

1 .l. Motivation

We are studying the resonant substructure of the Cabbibo suppressed decay Do + 7r-7r+7ro using the Dalitz Plot Analysis technique. There are two recently published Dalitz analyses to which it would be interesting to compare to the one presented here: CLEO'S Do + K-7r+7r01 and E791's D+ + ~ - 7 r + 7 r + . ~

Studying the Cabbibo favored decay Do + K-7r+7ro at CLEO uses much of the same machinery needed to investigate Do + 7r-7r+7ro. Since Do -+ 7r-7r+7ro is Cabbibo suppressed, the expected number of signal events should be smaller than Do + K-7r+7ro, also suggesting that the signal fraction will be smaller.

The E791 Dalitz analysis of D+ + ~ - 7 r + 7 r + found significant evidence for a new broad scalar neutral resonance (a(500)). With a mass around 500 MeV/c2 and a width of about 300 MeV/c2 , this new reso-

'This material is based upon work supported by the National Science Foundation under Grant PHY 9553157 FFW and the Department of Energy under Grant DE FG02 91ER40677.

332

333

nance accounted for a fit fraction over 45%. If such a scalar exists and D+ -+ a(500)n+ has been seen at such significant levels, it would be very interesting to see how important Do -+ a(500)nO is in our case.

Finally, since Do -+ 7r-7r+no is a CP eigenstate, we can also look for CP violation. With no CP violation, Do -+ p+n- should have the same amplitudes and phases as -+ p-n+. Recent theoretical works suggest that CP violation in Do -+ n-n+nO may be as large as 0.1%. 3 9 4 , and this is one of the main motivations for doing this analysis.

1.2. Three Body Decays

When discussing three body final states, it is important to distinguish between the two different decay modes: resonant and non-resonant. In the former, the Do decays into an intermediate resonance and one final state daughter and the intermediate resonance then decays into the two other daughters. In the latter, the Do decays directly into the three daughters.

0 Examples of Resonant Decays: Do -+ poxo DO -+ p+n- Do -+ p - n +

L n - n+ 4 n + no 4 n - no 0 Non Resonant decay

Do -+ n-nIT+no

In this analysis we are looking at a spin 0 particle decaying into three spin 0 particles. Since there is no spin in either the initial or final states, only two degrees of freedom are needed to describe this ~ y s t e m . ~ Choosing two of the nn invariant mass squared terms (e.g. m:-lr+ and mi+xo) as our parameters turns out to be an appropriate choice since, when averaged over intermediate spin states, the partial width is proportional to the matrix element squared (i.e. it does not depend on its position in mi-x+ - space):

1 256 n3 mL0

dr = JMI2 dm:-,+ dm:+,o

A “Dalitz Plot” is simply a scatter plot of all candidates in the mz-lr+- m:+xo plane. The reason that Dalitz Plots are so useful is apparent from Equation 1. Any structure that shows up in the Dalitz plot is due entirely to M . Intermediate resonances will show up as bands on the plot.

334

1.3. Resonances

The technique used in this analysis is to fit this distribution in data with representations of different possible resonances as well as a non-resonant piece (i.e. flat over the Dalitz Plot). All resonances are represented by a Breit-Wigner and a numerator that conserves angular momentum:

(2) F D O ( ~ ~ ) and Fr,,(q2) are functions which represent that these mesons

are not point-like and do have finite size.6 We also use a mass-dependant function for the resonance's width (I'(q)) that depends on its spin.7

It is unknown, a priori, how much of each resonance we have. We therefore weigh each piece of the matrix element with an amplitude and a phase. The total matrix element is simply the sum of all of the pieces:

M D o + ~ - ~ + ~ o = A,,, . ei + Ap+=- ' ei 4 ~ + m - - . MDO+.,,+~- +

. ei @ P - - + . M D o + ~ - ~ + + (3) ApoKO . ei ~ P O ~ O . M Do-+p07r0

+.. . In order to decide which resonances were used, we tried adding different

resonances one at a time to see if it improved the overall fit or not. We only kept resonances that significantly improved the fit.

A final note about resonances. The long lifetime of the Kg means that the two-body decay Do + Kgno will not interfere with any other resonances. Because of this, the Kg is described as part of the background instead of part of the signal.

2. Analysis

2.1. General Overview

We are searching for the following decay chain (particles in red are directly observed; those in black are constructed from the observed particles):

335

In this analysis, like most CLEO charm analyses, we are using a D*+ tag (i.e. only using Do particles that decay from D*+ mesons). This allows us to both greatly reduce the background without a large signal loss and differentiate between Do + 7r-7r+7ro and + 7r+7rIT-7ro. We first construct no candidates from photon candidates in the electromagnetic calorimeter. Next, we construct Do candidates from two oppositely charged tracks and one of the 7ro candidates. By adding suitable T:,,~ Candidates", D*+ candidates are created. To increase our ability to distinguish signal from background, we refit the slow pion using the beam spot and the Do using a vertexing package. For every candidate passing our event selection criteria, we calculate m:-,+ and m:+,o.

2.2. Dalita Fitter

To fit the data to our representation, we used a MINUIT-based unbinned maximum likelihood fitter, minimizing

events

where

0 F is fraction of signal events in the sample. This quantity is called "Signal Fraction".

0 E(m2,-,+,m:+,o) is the efficiency for an event falling at point (m$,+, m:+,o) in the Dalitz plot to be detected by CLEO and to pass all of our analysis cuts. This shape was determined by fitting a 2 0 cubic polynomial to reconstructed signal MC. mm:-,+,m:+,O) is the background level at point (mz-,+,mz+,o). This background shape was calculated by fitting the same 2 0 cubic polynomial as the efficiency

"The slow pion has its name for two reasons. First, it has a very low momentum in the D' rest frame (39 M e V / c ) . Second, we want to differentiate this pion from the other final state daughters.

336

Resonance

P+ PO

P non res .

-

with additional terms representing real KZ and real p's to two different sidebands in Do m a s - D*+ - Do mass difference space. Nsignal = JE(m$.?r+, m:+?ro) I M D o + ~ - ~ + ~ o I dDP is the signal normalization. Nbackground = Jt?(m$,+, m:+?ro)dDP is the background normal- izat ion.

2

Amplitude Phase(") Fit Fraction(%) 1. (fixed) 0. (fixed) 76.5 f 1.8 f 4.8

23.9 f 1.8 f 4.6 32.3 f 2.1 f 2.2

2.7 f 0.9 f 1.7

0.56 f 0.02 f 0.07 0.65 f 0.03 f 0.04 1.03 f 0.17 f 0.31

10 f 3 f 3 176 f 3 f 4 77 f 8 f 11

3. Results

3.1. Systematic Errors

We calculated systematic errors by varying parameters of concern and re- running the Dalitz Fitter to assess how sensitive the final answers were. Specifically, this was done for our parameterizations of efficiency and background, our determination of signal fraction, and our event selection criteria. We are not yet finished with our systematic studies and these numbers are expected to change.

3.2. Preliminary Numbers

The preliminary results presented here use the full CLEO 1I.V *i9 dataset (9fb-l). Only the three light p resonances were found to have significant contributions to the Dalitz Plot fit (i.e. Do + p+7r-, Do + p-7r+, and Do + po?ro). There was no evidence for any CP asymmetry, either in any of the final parameters of fitting Do +- 7r-7r+7ro and -+ 7r+7r-7ro samples separately, or in the single figure of merit A C P :

dcp = 0.01'8:;~ f 0.09 where

337

4. Conclusions

We have reported on our preliminary results of our Dalitz Analysis of Do + 7r-&7r0. While we find large fit fractions for the three light p resonances (Do + p+7r-, Do + p-7r+, and Do + po7ro) as well as a small but significant non-resonant contribution, we do not find any significant contributions from any other resonances (including the ~ ( 5 0 0 ) and the heavy

The ~ ( 5 0 0 ) is a controversial particle whose existence has not yet been confirmed. E7912 found strong evidence for it in their D+ -+ ~ - 7 r + 7 r +

analysis (they found a fit fraction of almost 50%), but we see none here. Whether the lack of evidence for the ~ ( 5 0 0 ) in this analysis indicates a lack of sensitivity or suggests that this particle does not exist is very interesting question which deserves further study.

The lack of the heavy ps is also interesting. In CLEO'S analysis Do -+ K-.rr+7r0,l the p+(1700) was needed for the final fits. If Do -+ K-p+(1700), one might expect to see the Do -+ 7r-p+(1700) as well. It is interesting to note that in the Do + K-7r+7ro analysis, the nominal peak location of the p+(1700) was not on the Dalitz plot so this analysis was only sensitive to the tail of this resonance. In Do + T-T+T', the peak of the ~(1700) resonances would all be contained in our Dalitz plot, making Do -+ 7r-7r+ro a more suitable laboratory for studying these heavy resonances. Again, this begs for further study as more statistics become available.

Finally, we saw no evidence for CP violation, either from comparing the amplitudes, phases, and fit fractions from the separate Do -+ 7r-7r+7ro and Do + 7r+7r-7r0 fits or in the single ACP number. The recent theoretical work expects violation on the order of 0.1%. 394 but we do not yet have enough sensitivity to confirm or refute these findings.

PSI.

-

References

1. S. Kopp et al., Physical Review D 63, 092001 (2001). 2. C. Gobel, arXiv:hep-ex/0012009. 3. F. Buccella, M. Lusignoli, and A. Pugliese, Phys. Lett. B 379, 249 (1996). 4. P. Santorelli, arXiv:hep-ph/9608236. 5. C. Plager, thesis. 6. J. Blatt and V. Weisskopt, Theoretical Nuclear Physics, New York, John Wiley

and Sons (1987). 7. H. Pilkuhn, The Interactions of Hadrons, Amsterdam: North-Holland(l967). 8. Y . Kubota et al., Nucl. Instrum. Methods Phys. Res., Sect. A 320, 66 (1992). 9. T.S. Hill, Nucl. Instrum. Methods Phys. Res., Sect. A 418, 32 (1998).

MEASUREMENT OF HIGH-PT AND LEPTONIC OBSERVABLES WITH THE PHENIX EXPERIMENT AT

RHIC

T. SAKAGUCHI* FOR THE PHENIX COLLABORATION

Center for Nuclear Study, Graduate School of Science, University of Tokyo RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan

The PHENIX experiment at Relativistic Heavy Ion Collider has successfully been operated in Year-1 and Year-2 Runs. The recent results on the measurement of high transverse momentum hadrons, J / $ , and single electrons and photons are presented.

1. Introduction

It is predicted from lattice QCD calculations L a t at igh energy density, a phase transition from hadronic matter to a plasma of deconfined quarks and gluons may occur to form a Quark Gluon Plasma (QGP) similar to that found in the early universe a few microseconds after the Big Bang. Rela- tivistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) are expected to produce a similar phase transition.

2. Experimental Setup

Figure 1 shows the PHENIX’ detector at RHIC. Beam-beam counters and zero-degree calorimeters provide the minimum bias trigger, measure the vertex position, and are used for centrality selection. no’s are reconstructed via decay channel of no + yy with Electromagnetic Calorimeter (EMC). Charged particle tracks are reconstructed with drift chambers (DC) and three layers of pad chambers. Electrons are primarily identified with Ring Imaging Cherenkov detector, and selected by energy/momentum matching

*e-mail: takaot2phenix.cns.s.u-tokyo.ac.jp

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Figure 1. PHENIX detector. Views from beam axis (left), from top side (right).

using information from DC and EMC. The acceptance of the PHENIX detector is 1111 <0.35 in pseudo-rapidity (q), and T in azimuth (4). The PHENIX measured electrons, photons, hadrons and muons in 130 GeV Au- Au collisions in Year-1 and in 200 GeV Au-Au and p-p collisions in Year-2.

3. High p~ hadron measurement

Partons produced in initial Au-Au collisions will interact with hot dense medium formed after the collisions, loose their energy, and finally turn into jets. Since most of the high p~ hadrons are fragments of jets, the effect can be seen in terms of a suppression of yield on high p~ hadron spectra'. The left panel of Fig. 2 shows the PT spectra of 7ro for 60-80 % and 0-10 % central collisions at Jslvnr =130 GeV in Year-1 Au-Au Run3, and the middle and

IIIIIIIIJIIIIIIII 1 1 3 4 5 6 1 8 9

n@p,(GeV/c)

Figure 2. T O p~ spectra for 60-80% and 0-10% central collisions at ==130GeV (left), and 70-80 % (middle) and 0-10 % (right) central collisions at -=200 GeV. Reference p-p data scaled by NcOll are also shown.

right panels show 70-80 % and 0-10 % central collisions at ,/GG =200 GeV in Year-2 Au-Au Run4, respectively. The reference p-p data scaled by corresponding number of binary nucleon-nucleon collisions (N,,n) are overlayed

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onto the data as well. Since p-p Run were not carried out in Year-1, the reference p-p data for 130 GeV were obtained by interpolating ISR, CDF and SpPS data to RHIC energy3. At both beam energies, the peripheral (60-80 or 70-80 %) data are consistent with the reference p-p data scaled by Ncoll, while the central (0-10%) data are clearly suppressed. To quantify the suppression, the nuclear modification factor is introduced as follows:

(Yield per A-A collision) - - 1/N=,t &NAA/dpTdv (N,,ll)(Yield per p-p collision) (Nc,11) (d2aPP/dpTdrl ) /aRAA(PT) =

The left panel of the Fig. 3 shows the nuclear modification factors for 130 GeV central Au-Au and 17.3GeV Pb-Pb collisions5. The 130 GeV data is suppressed, and clearly different from the 17.3GeV data that indicates parton multiple scattering effect. From the right panel of the figure showing

PHENIX Prelimin.

0 1 2 3 4 5 6 ' 7 8 0 1 2 3 4 5 6 7 8 p, (CNh) n'p,(CeV/c)

Figure 3. collisions (left), and 70-80 % and 0-10 % central collisions at 200 GeV (right).

Nuclear Modification factors for 130 GeV 0-10 % central and 17.3 GeV Pb-Pb

the nuclear modification factors for 200 GeV Au-Au, it is clearly seen that the peripheral data is consistent with unity within errors, while the central data is suppressed as is seen in 130 GeV. While the inclusive charged hadron spectra show the same tendency in 200GeV6, the ratio of TO to noniden- tified charged hadrons ((h+ + h-)/2) reaches constant of -0.4 instead of unity as is shown in Fig. 4. The result is rather different from hard processes measured in e+e- collisions7. There may be other mechanisms for enhancing the high p~ yield for protons and/or kaons in Au-Au collisions.

4. J/+(M=3.1 GeV/c2) measurement

In case of deconfinement, the color screening may result in a dissociation of cE and thus a decrease in the production of charmonium'. There are also models that predict an enhancement of charmonium due to cZ coalescence

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0.4

0.3 0.2 0.1

PnENlX Freliminary

"0 1 2 3 4 5 6 7 8 9 10 pT ( G e W

Figure 4. Ratio of ro to (h+ + h - ) / 2 in 200 GeV Au-Au minimum bias collisions.

as the collision volume coolsg. Therefore, the measurement of J / $ which is a bound state of cC has been an interesting topic. Figure 5 shows the e+e- invariant mass spectra around J / $ mass region in p-p and Au-Au collisions at ==200GeV. This is the first measurement of J / $ --+ e+e- in heavy

16

2 3 4 s Invariant Mass e'e- (GeVlc')

PHENIX Preliminary] Minbias Au Au

is 3 3.2 3.4 Inv. Mass e'e- (GeVk')

Figure 5. (right) collisions at ==200 GeV.

e+e- invariant mass spectra around .I/$ mass region in p-p (left) and Au-Au

ion collisions. Although the statistics are poor, the yield of J / $ per Ncoll

are evaluated in three centralities as shown in Fig. 6. The result shows that models assuming nuclear absorptions fit the data, but the simple binary scaling model does not.

5. Leptonic and Photonic Observables

The leptonic and photonic observables have long been considered to be an excellent probe because they do not strongly interact once produced. The thermal radiation turns into both electrons and photons, the heavy quarks produced in the collision's earliest stages decay into electrons, and the initial hard scattering produces photons.

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5 0.25

8 $ 0.2

b 0.15

- -

- - z s 0.05

0 50 XI0 150 Mo 254 9W JJQ Number of Parlicipants

Figure 6.

5.1. Electron measurement

Single electrons are measured both at -=130 and 200GeV. The left panel of Fig. 7 shows the single electron spectra at 130 GeV for central and peripheral collisions. The spectra were obtained after subtracting back-

J/$J yield per Ncoll as a function of centrality.

central,min.biar

"*O 0.5 1 15 2 2.5 3 PJGeV/C)

Figure 7. (left) and both beam energies (right).

Single Electron spectra for both peripheral and central collisions at 130 GeV

ground electrons from known hadronic sources. The result shows that the electron spectra are consistent with ones from charm quarks calculated with PYTHIA scaled by Ncoll. In contrast to the high p~ hadron measurement, the suppression of the yield in the central collisions is not seen, suggesting possible smaller energy loss of charm quarks. The yield of electrons is sensitive to the beam enegies as shown in right panel of Fig. 7, indicating that electrons may play a role as a thermometer of the system.

5.2. Photon measurement

Photons have been measured at both beam energies and both peripheral and central collisions. Figure 8 shows the ratio of the measured

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inclusive photons to the calculated photons from hadronic sources at -=130GeV and 200GeV1°. So far, no significant excess are seen in either centralities or beam energies within current errors.

pT WeV) P ( G W

Figure 8. hadronic sources in Au-Au collisions at -=130 GeV and 200 GeV.

Ratio of the measured inclusive photons to the calculated photons from

6. Conclusion

The PHENIX experiment at RHIC has successfully been operated in Year-1 and Year-2 Runs. The recent results on the measurement of high transverse momentum hadrons, J/$, single electrons and photons were shown.

References 1. PHENIX Collaboration, Nucl. Inst. to be published. 2. X.N. Wang, Phys. Rev. C58, 2321 (1998). 3. K. Adcox et al.(PHENIX Collaboration), Phys. Rev. Lett. 88, 022301 (2002). 4. D. d’Enterria, for the PHENIX Collaboration, hep-ex/0209051 (2002). 5. M.M. Aggarwal et al.(WA98 Collaboration), Eur. Phys. J. C23, 225 (2002). 6. S. Mioduszewski, for the PHENIX Collaboration, nucl-ex/0210021 (2002). 7. P. Abreu et al.(DELPHI Collaboration), Eur. Phys. J. C17, 207 (2000). 8. T. Matsui and H. Satz, Phys. Lett. B178, 416 (1986). 9. R.L. Thews et al., Phys. Rev. C63, 054905 (2001).

10. K. Reygers, for the PHENIX Collaboration, nucl-ex/0209021 (2002).

NONEQUILIBRIUM EVOLUTION OF CORRELATION FUNCTIONS

S. SENGUPTA AND F.C. KHANNA Theoretical Physics Institute, Department of Physics

University of Alberta Edmonton, AB X6G 2J1, Canada. E-mail: [email protected]

S.P. KIM Department of Physics

Kunsan National University Kunsan 573-701, Korea

Nonequilibrium evolution equations for the n-point correlation functions are obtained using a canonical approach, for a self-interacting quantum field theory. Non-equilibrium evolution of the 9* field theory is investigated in the Hartree approximation. To take into account next-to-leading order effects, the time evolution equations for the equal-time, connected correlation functions are derived by including the connected 4-point functions in the hierarchy. The resulting coupled set of equations form a part of infinite hierarchy of coupled equations relating the various connected n-point functions.

1. Introduction

Recently, a lot of attention has been focussed on the investigation of classical and quantum fields evolving out-of-equilibrium. The motivation for such an interest is plentifold. The very early history of the universe provides many scenarios where nonequilibrium effects may have played an important role. The reheating of the universe after inflation, formation and growth of domains in any generic spontaneous symmetry breaking phase transition, the formation of topological defects and possible formation of Quark-Gluon Plasma during the deconfinement transition or Disoriented Chiral Conden- sates during the chiral phase transition are just some instances where our knowledge of the physical process may crucially depend on our understanding of nonequilibrium quantum fields. The development of facilities like RHIC and LHC makes the study of non-equilibrium phenomenon occuring

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345

at high energies, experimentally accessible. An important aspect of non-equilibrium phenomenon is the study of

thermalization in closed systems. We need to understand how it is possible for macroscopic irreversible behavior to emerge from microscopic reversible (unitary) quantum dynamics. We also need to know the precise role of interactions (non-linearities) in bringing about thermalization. Some of these issues have been explored theoretically and numerically using the path- integral formalism 1 3 2 , 3 7 4 . Our aim in this talk is to make use of a canonical formalism to study the nonequilibrium evolution of quantum fields. We first outline the key features of the canonical Louiville-von Neumann (LvN) formalism and use it to obtain the vacuum and thermal evolution equations in the Hartree approximation. After pointing out the limitations of the Hartree approximation scheme, we use the Heisenberg formalism to go beyond the Hartree approximation to obtain a set of coupled evolution equations for the 2-point and 4-point correlation functions which are a part of an infinite hierarchy of equations for the equal-time connected n-point functions 5 .

2. Evolution Equations for Correlation Functions in the Hartree Approximation

We first apply the LvN method to obtain the evolution equations for the connected, equal-time, 2-point functions. The symmetric q54 field theory is described by the Hamiltonian

m2 2 + -4' +

where %(x, t ) = $(x, t ) is the conjugate momentum operator. The Hartree approximation amounts to making the substitution J4 -+ 6(J2)>i2

The Hamiltonian in the Hartree approximation written in terms of the r 1

Fourier modes is &A(t) = J & 1 afi:(t) + a!l:(t)&:(t)]

In the LvN formalism 6; the field and conjugate momentum operators are expressed in terms of annihilation and creation operators as follows

&k = fi[(Pk(t)hk(t) + &(t)&(t)] fik = fi[$k(t)hk(t) + $l(t)&(t)]

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The requirement that the annihilation and creation operators satisfy the LvN equations

lead to the equations for the auxilliary field variables p k ( t ) and &(t)

It is more advantageous to work with the evolution equations for correlation functions, rather than the field equations for two reasons. In thermal equilibrium, the 2-point correlation functions can be related to the Bose-Einstein distribution function (for a quantum theory) and the temperature of the system (for a classical theory) in a fairly simple way; thereby allowing us to use them as benchmarks to track the evolution of the system towards thermal equilibrium. Secondly, it is more convenient to make systematic improvements to the mean field description, by working with equations for the correlation functions. We define the 2- point functions for the fields as g i j ( z 1 , z 2 ; t ) = (&(xi; t ) & ( z 2 ; t ) ) such that 9 1 2 ( 2 1 , 2 2 ; t ) = ($(XI; t)7?(22; t ) ) ; where the expectation value is taken with respect to the vacuum state.

The fourier transforms of the 2-point correlators can then be expressed in terms of the auxilliary field variables

G i j ( k , t ) = h2pTk(t )pjk(t ) (3) where i,j = 1,2. Using Eqs.(2), it is easy to show that the equations for the 2-point correlators in momentum space are

Gii (k, t ) = (712 (k, t ) + G21 (k, t )

It is important to note that the above equations form a closed set which is a characteristic feature of the Hartree approximation in which the dynamics is completely determined by specifying the 2-point functions. It is

347

also possible to define the thermal 2-point functions by taking the expectation value of the field operators with respect to an initial thermal Gaussian state

<&x, t)&x‘, t))T = -Tr[e-PO*HA&x, t)&x’, t)l

where ,f30 is the initial inverse temperature of the system and

( 5 ) 1 2

00

2 T ~ [ ~ - P o H H A ] = (nk,t(e-80tLO~(iL:Bk+4) Ink, t>. ( 6 ) nk=O

The Fourier transform of the 2-point thermal correlation functions

G$(k, t ) = ti2vrkvjk coth where i, j = 1 , 2 It is interesting to

note that GT2(k,t) = tiwk(nk + 4); which corresponds to the energy of a state with nk quanta, where nk is given by the Bose-Einstein distribution function. In the classical limit ti + 0, this reduces to the temperature (2‘) of the system ’. The dynamical evolution of the 2-point correlation function therefore provides a useful benchmark for tracking the evolution of the system towards thermal equilibrium.

3. Evolution Equations Beyond the Hartree Approximation

Although the mean-field (Hartree) approximation is effective in describing the initial evolution, it breaks down at late times. Moreover the Hartree approximation does not take into account direct scattering effects which is essential to ensure the thermalization of the system. This is manifest in the closed form of the equations for the equal-time, 2-point functions. Effects of scattering manifest themselves through the appearance of 4-point functions in the evolution of the 2-point functions. In fact the evolution equations for the equal-time connected n-point functions form an infinite hierarchy. The next-to-leading-order (NLO) equations which go beyond the Hartree approximation are obtained by truncating the hierarchy at the 4-point level, which amounts to ignoring the connected 6-point functions in the evolution equation for the connected 4-point function. The canonical Heisenberg formalism provides a convenient method of obtaining this hierarchy of equations for the connected, equal-time, n-point correlation. The evolution equation for the ordinary n-point functions defined as

( 7) ga, (n) ... , b ( ~ 1 , . . * > xn; t ) = (Ja(x1, t ) . . .&(Xn, t))

are obtained by taking the vacuum expectation value of the Heisenberg equations of motion of the appropriate product of field operators

348

where the subscript indices a, b, . . . = 1,2 for our model Hamiltonian and $a is to be understood as the field operator $(x,t) ( a = 1) or the conjugate momentum operator i i(x, t)(a = 2) in the Heisenberg picture. For the unbroken symmetry case, only correlation functions of even order are non-vanishing. Using the cluster expansion * to express ordinary n-point functions in terms of the equal-time, connected n-point correlators, it is possible to obtain a set of evolution equations for the connected correlators. Because of the presence of-the quartic coupling, the equations for the 2-point functions would depend upon the connected 4-point functions; the equations for the 4-point functions would depend upon the 6-point functions and so on, thereby yielding an infinite hierarchy of evolutions equations for the n-point correlators. To go beyond the Hartree approximation requires, at least, inclusion the cluster expansion of the 6-point function in terms of products of connected n-point functions of lower order. The effect of the connected 6-point function in the expansion is neglected. This provides a systematic way of going beyond the leading-order mean field expansion ‘. This then yields a set of closed equations which have been truncated at the 4-point level. In this scheme, incorporating NNLO effects would then amount to truncating the hierarchy of evolution equations at the 6- point 1evel.The evolution equations for the connected 2-point and 4-point functions can be written symbolically as

The equations for the 2-point functions in configuration space are given below.

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The numbers in parenthesis correspond to position coordinate indices. The equations for the connected, equal-time, 4-point functions can be obtained in a similar manner ’. Truncation of the hierarchy beyond 4-point level, allows for improved treatment of scattering effects but is much more complicated to handle.

4. Conclusions

In this talk, we have developed a canonical formalism which allows us to obtain the non-equilibrium evolution equations for the connected, equal- time, n-point correlators in the Hartree approx. as well as in the NLO approximation. This provides a self-consistent method of incorporating higher-order scattering effects by inclusion of higher order connected n- point functions in the hierarchy of equations for the equal-time correlation function. Solving this set of equations numerically, may provide valuable insights into the effect of various types of scattering processess on the nonequilibrium evolution and approach to thermalization of quantum fields.

References 1. M. Gleiser and R.O. Ramos, Phys. Rev. D 50, 2441 (1994). 2. D. Boyanovsky, H. J. de Vega, R. Holman, D.S. Lee, and A. Singh, Phys. Rev.

D 51, 4419 (1995). 3. C. Greiner and B. Muller, Phys. Rev. D 55, 1026 (1997). 4. J. Berges and J. Cox, Phys. Lett. B517, 369 (2001); G. Aarts and J. Berges,

Phys. Rev. Lett. 88, 041603 (2002). 5. S.Sengupta, S.P. Kim and F.C. Khanna, hep-ph/0301071. 6. S.P. Kim and C.H. Lee, Phys. Rev. D 82, 125020 (2000). 7. G. Aarts, G.F. Bonini, and C. Wetterich, Phys. Rev. D 63, 025012 (2001). 8. J.M. Hauser, W. Casing, A.Peter, and M.H. Thoma, Z. Phys. A 353, 301

(1996); A. Peter, J.M. Hauser, M.H. Thoma, and W. Casing, Z. Phys. C 71, 515 (1996).

RECENT RESULTS FROM BELLE

R. SEUSTER University of Hawaii,

Departement of Physics and Astronomy, 2505 Correa Road,

Honolulu, H I 96822, U S A E-mail: [email protected]

This short review covers four different measurements performed at the Belle collider. The electroweak penguin decay B + XJ1 might exhibit the first signs of physics beyond the Standard Model, establishing this decay mode is therefore is a first step in search for these signs. CP measurements are the main goal of current B-factories, increasing the knowledge about all processes involved can help reduce systematic uncertainties; a branching ratio measurement therefore is an important step. Baryon production is still not well understood, neither in B decays nor in fragmentation; establishing a baryonic two body decay gives valuable insight into this topic. Belle performs analysis also in fields other than B physics, one of the most interesting topics being the surprisingly large contribution of double cE production at center-of-mass (CMS) energies around the T(4S) to inclusive J/* production, which is still not understood theoretically.

1. Introduction

The current B-factory experiments BaBar at the PEP-I1 collider and Belle at the KEKB ring have accumulated data samples around 100 fb-'.

This huge dataset allows not only for more refined analysis of existing measurements, but also for many new observations and determinations of branching ratios. In this article, four recent measurements performed at the Belle detector are described briefly, a more detailed description can be found in the corresponding papers'.

1.1. The KEKB Accelerator and the Belle Detector

An important pre-requisite of all measurements described here, is the excellent performance of the KEKB accelerator. An integrated luminosity of well over 100 ft-' has been delivered and recorded by the Belle detector in February 2003. KEKB is an asymmetric e+e- collider, electrons and

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35 1

positrons are accelerated to energies of 8 GeV/c2 and 3.5 GeV/c2, respectively. The available CMS energy equals the mass of the T(4S). A detailed description can be found in 2 .

The Belle detector covers a solid angle of almost 47r. Closest to the interaction point is a high resolution silicon micro vertex detector (SVD). It is surrounded by the central drift chamber (CDC). Two dedicated particle identification systems, the aerogel cherenkov counter (ACC) and the time- of-flight (TOF), are mounted between the CDC and the electromagnetic calorimeter consisting of CsI crystals (ECL). All these subdetectors are located inside a superconducting coil which provides a magnetic field of 1.5 T . The return yoke of the coil is instrumented as a KL and p detector. A detailed description can be found in 3 .

2. B + X,11 The first b decay mediated via a pure electro-weak penguin graph was discovered by the CLEO collaboration in 19934, a b + sy transition. These types of decays are well suited for searching for physics beyond Standard Model, since contributions of new physics will already appear at Born level. Recently, observation of the exclusive mode B + K11 was claimed by the Belle collaboration5, being confirmed later by the BaBar collaboration6. The exclusive measurement suffers from theoretical uncertainties of modeling of the final state. The inclusive mode B + X,11 has smaller theoretical uncertainties, but is experimentally more difficult to access.

Interesting quantities which might show deviations when new particles are included are the mass of the hadronic system or the invariant mass of the di-lepton system. In the following, leptons mean only the stable or long lived leptons, namely electrons and muons a .

Crucial for this measurement is an excellent performance of the lepton identification system. For this analysis, minimum momenta in the laboratory rest frame for electrons and muons of 0.5 and 1.0 GeV/c2, respectively, are required. The efficiency has been measured to be 92.5% for electrons and 91.3% for muons with very low misidentification probabilities of 0.2% and 1.4%. The X, systems is constructed from a charged or neutral kaon, combined with up to 4 pions; at most 1 neutral pion is allowed.

To remove contribution from b + sy* , y* + e+e- , a minimum invariant mass of the dilepton system of 200 MeV/c2 was required. To remove com-

'Unless stated explicitly, charge conjugation is implied throughout this article.

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binatorial background from light quark events, the so called continuum, a maximum invariant mass of the X, of 2.1 GeV/c2 was required. This background was further reduced significantly by a Fisher discriminant.

A J/!P veto removed decay channels with the same final state. Other background events with two mis-identified leptons were removed by repeating the analysis without lepton identification and subtracting the yield multiplied by the mis-identification probability from the signal.

The signal yield was obtained by a fit to the beam constrained mass Mbc = ,/(Egr:m)2 - (pBms)2. Egr’m is the beam energy in the T(4S) CM- frame and pBms the 3-vector of the reconstructed B candidate. Together with the efficiency determined by a MC study, the branching ratio has been calculated to be

D(B + X,ll) = (6.1 f 1.4Ti:t) x lop6 (1)

with a significance of 5 . 7 ~ . This is in good agreement with the theory prediction7 of B = (4.2 f 0.7) x lop6. The invariant masses of the dilepton system and the X, system do not show a significant deviation from the theoretical calculation.

Including more data will increase the precision of this measurement and together with improvements in the theory prediction, one might see first hints towards physics beyond the Standard Model soon.

3. B + vcK(*)

The “golden” channel at current B-factories for performing measurements involving CP violation is Bo + J/QKt. Many other modes have been used to improve statistical precision, one of them being Bo + r],K;, like the golden mode a b + CES transition.

The goal of the analysis described here is not a CP measurement, but an improved determination of the branching ratio. Four decay channels of the r], are used here, r], + K;K+r-, K+Kpro , K*O(+ K+r-)K-n+ and pp. Both charged and neutral B mesons are reconstructed.

In all channels containing a non-excited kaon as the daughter of the B meson, signals with significances above 50 are observed, except for Bo + qcKg, qC + K*OK-n+ which has a significance of 1.6g. These results are obtained by fits to the beam constrained mass &. Fits to the difference of the energy of the reconstructed B candidate, ELmS, and the beam energy, Egr:m, both in the “(4s) CM frame, AE = ELms - Egr:m, gave consistent results.

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The sources of the systematic uncertainty include tracking, particle identification and possible non-resonant contributions to the Mb, distributions and are added in quadrature to give the total systematic uncertainty.

Since the branching ratios of the qc are only poorly known, only the channels q, -+ K:K+n- and q, -+ K+K-n0, which can be related via isospin, are combined:

B(B+ -+ qcK+) = (1.25 f 0.14+:::8 f 0.38) x B(Bo -+ qcKo) = (1.23 f 0.23::::; f 0.38) x

where the last uncertainty is due to the uncertainty in the qc branching ratio. For decay channels with an excited kaon, only the cleanest channel Bo + qcKo* with qc -+ K:K+n- is considered. An additional cut on the K* helicity angle is applied. The fit to Mb, yields a signal with a significance of 7 . 7 ~ ; the fit to AE is consistent. The branching ratio is calculated to be

B(Bo + qcK*') = (1.62 f 0.32+0,::: f 0.50) x

Both branching ratios with excited and non-excited kaons share the same systematic error in the branching ratio of the qc + K:K+n-, which cancels in their double ratio:

B(Bo + qcK*O) B(Bo 4 qcKo)

= 1.33 f 0.36::::; R% =

This ratio is consistent with expectation from factorization, 1.02 - 2.578

4. Bo += Acp

Baryon production in e+e- annihilation in general and in B decays in particular is still not well understood. Many models have already been ruled out by upper limits set by the CLEO collaborationg. With 29.1 fb-' the decays of B mesons into B + Acp nn with n=1,2 have been observed in Bellelo. The decay mode with two pions is almost one order of magnitude larger than the mode with one only pion. For the decay mode with no pion, the data sample used in lo allowed only for an improved upper limit.

We repeated the search for this two body baryonic decay mode in a data set almost three times larger, consisting of 78.2 fb-l. This update follows closely the analysis presented in lo. The few changes are releasing the cuts on the anti-proton from the B decay and aim at improving the efficiency of the selection.

For the A, only the decay channel into pK-n+ is used. In order to remove background from A's and Kg, a mass constrained vertex fit is per-

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formed for both Ac and the reconstructed B meson. The signal yield is determined by a two-dimensional fit in AE and Mbc to be 19.6t::: events with a significance of 5.81~. In this fit, the signal shape has been taken from Monte Carlo studies, the background parameters are allowed to float. The width of the signal peak is smaller in data compared to Monte Carlo. Various control samples do not exhibit such a behavior. We conclude that the difference is a statistical fluctuation with a probability of 0(1%) and treat it as a systematic uncertainty.

We assign additional systematic uncertainties of 10% for particle identification, 8% for tracking, 7.3% for fitting signal shape and 1.3% due to limited statistics. These add up to a total systematic uncertainty of 14.8%. Together with the detection efficiencyb derived from signal Monte Carlo, we obtain a branching ratio of

B(Bo + A,p) = (2.192:::; f 0.32 f 0.57) x

The branching ratio of this decay is about an order of magnitude smaller than the decay containing one pion and is in good agreement with theory prediction of the pole modelll .

5. Double cE Production

Although Belle is a dedicated experiment for physics in the b quark sector, it is very well suited to perform experiments including other quarks and leptons, e.g. charm physics. For inclusive J /Q production in continuum events, recently measured by Belle12 , non-relativistic QCD (NRQCD) predicts three main production processes. While e+e- -+ J/Qgg is believed be the dominant process, e+e- + J/QcC contributes with about O(lO%) and e+e- + J/Qqq is the smallest. Some models predict that another process, e+e- + J/Qg, dominates the momentum endpoint as it is a quasi-two-body decay. This expectation was not confirmed in a recent measurement13, which found the process e+e- + J/QcC to be dominant.

Belle updated this measurement with a larger dataset, now consisting of 86.7 fb-' taken at the T(4S) resonance and 60 MeV/c2 below. The approach taken is twofold. A search for charmonium states is performed in the recoil system against the fully reconstructed J/Q. The other approach involves the full reconstruction of almost all ground states of charmed mesons

was checked that the detection efficiency does not depend on the actual modeling of intermediate resonances in the decay.

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and baryons. This makes this approach less model dependent, since almost all charmed hadrons will eventually decay into one of these states.

Following this approach, the rate for double charm production over prompt J / 9 production has been measured to be

= 0.67 f 0.13

which is larger than 0.44 with 95% confidence level. This confirms the old result and contradicts the expectation from NRQCD. The old approach, i.e. using production rates of all reconstructed particles from MC, gives for the same quantity = 0.68 f 0.12. The consistent results for both approaches validates the previous approach which relied on the proper modeling of charm quarks fragmenting into the reconstructed D hadron.

6. Conclusion

Although the physics program at the Belle detector strongly focuses on B physics, it also includes other interesting topics. After identifying exclusive decay modes involving the electroweak penguin b -+ sll, a clear signal has now been found also for the inclusice decay. After being used in CP measurements, the branching ratios of the decays B -+ qcK(*) has been measured, increasing the knowledge about these decays. The baryonic two body decay into Bo -+ Acp has been observed for the first time, helping to understand baryon production. Double cE production in continuum events is still not understood, the new measurement confirms the old results. It is less model dependent and contradicts the expectation.

References

1. available at http://belle.kek.jp/belle/publications.html 2. M. Arinaga, et al. KEK-Report 2001-157 (2001). 3. Belle Coll., A. Abashian et al. Nucl. Inst. Meth. A479, 117 (2001). 4. CLEO Coll., R. Ammar et al. Phys. Rev. Lett. 71, 02674 (1993). 5. Belle Collaboration J.Kaneko, et al., Phys. Rev. Lett. 90, 021801 (2003). 6. Talk at ICHEP2002, hep-ex/0207082. 7. A.Ali, et al. Phys. Rev. D66, 034002 (2002). 8. M. Gourdin, Y.Y. Keum and X.Y. Pham Phys. Rev. D52, 1597 (1996). 9. CLEO Coll., S.A. Dytman et al. Phys. Rev. D66, 091101 (2002). 10. Belle Coll., N. Gabychev et al. Phys. Rev. D66, 091102 (2002). 11. H.Y. Cheng and K.C Yang Phys. Rev. D65, 054028 (2002);

12. Belle Coll., K.Abe et al. Phys. Rev. Lett. 88, 052001 (2002). 13. Belle Coll., K.Abe et al. Phys. Rev. Lett. 89, 142001 (2002).

erratum ibid. 099901(E).

RENORMALIZATION-GROUP IMPROVEMENT OF EFFECTIVE ACTIONS BEYOND SUMMATION OF

LEADING LOGARITHMS*

M. R. AHMADY AND A. SQUIRES Department of Physics,

Mount Allison University, Sackville, N B E4L 1E6, Canada

E-mail: aasqrsf2rnta.c.a (A . Squires)

V. ELIAS AND D.G.C. MCKEON Department of Applied Mathematics, The University of Western Ontario,

London, ON N6A 5B7, Canada

T. G. STEELE Departmetn of Physics and Engineering Physics,

University of Saskatchewan, Saskatoon, SK S7N 5E2, Canada

E-mail: tom.steeleOusask.ca

Effective actions are invariant under changes in the renormalization scale p. The renormalization group is seen to yield differential equations whose solutions are closed form expressions for successive sums of subleading logarithmic contributions to the effective action. This procedure can be applied to any order, provided the coefficient of the zeroth order logarithm has been previously calculated at that order in perturbation theory. We demonstrate this using the 4: model.

The classical action for a scalar field (f) theory with a trilinear self- coupling in six dimensions in Euclidean s p a ~ e ~ > ~ is

'See Ref. 1.

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Radiative corrections to Eq.(l) give us an effective action of the form

with L = log(m2/p2) and 0 0 0 0

A(X, L ) = C C am,nX2mLn, n=O m=n

0 0 0 0

B(X,L) = c c bm,,X2"L", n=O m=n

(3)

Renormalization scale invariance leads to the renormalization group equation

where

00 dm2 -rm(X)m2 = p- = -m2 c G2nX2n,

-W(X)f = p- = -f c D2,X2".

(6)

(7)

dP n=l 00

df dP n=l

Noting that for any function F(X, L ) , d

= -2-F(X, L) , d dF dL

p-F(X, L ) = p-- = p dP d L dp dL

and

we obtain the following RG-equations for A(X, L ) , B(X, L ) and C(X, L):

358

The key to our method is the resummation of the series A, B and C into subseries in powers of X2 L:

A(X, L ) 1 (A(X, L ) ) L L + ( A ( h L ) ) , t L + -.. = [a,,, + Ul,lX2L + a2,2(X2L)2 + a3,3(X2L)3 + ...I

+ [al,oX2 + a2,1X2(X2L) + a3,2X2(X2L)2 + ...I + ... oc)

e=o M

= 2 X2nRn(X2L), n=O

00

B(X, L ) = ... = c X2nSn(PL),

C(X, L ) = ... = c PTn(X2L).

n=O 00

n=O

In the following derivation, we will obtain relations between the first coefficient in each of the above subseries (e.g. a o , ~ , a1,o) and all subsequent coefficients of that subseries. This is what Elias et al. term “optimal RG- improvement” ?

Substituting Eq.(2) {(3), (4)) and Eqs.(5)-(7) into Eq.(8) {(9), (lo)}, respectively, and setting the aggregate coefficient of like powers of L and X2 equal to 0, we obtain the following recursion relations for & and R1 {(SO and Sl), (TO and TI)}, respectively:

0 = -2lae,e + [2(C - 1)Bs - 2 0 2 1 ae-l,e-1, O = -2(l - l)ae,e-I+ [2(l - I)& - 2021 ae-1,e-a

(11)

-(l - 1)G2ae-l,e-1 + [2(l - 2)B5 - 2 0 4 1 ae-2,e-n. (12)

(13) 0 = -2lbe,e + [2(C- 1)B3 - 2 0 2 - G2] be-l,e-l, 0 = -2 ( l - 1)beg-l + [2(C- I)& - 2 0 2 - Gz] be-i,e-:!

-(C - 1)Gzbe-l,e-1 + [2(l - 2)B5 - 2 0 4 - G4] be-2,e-a. (14)

0 = -2lce,e + [(2l - l)B3 - 3D2] ce-l,e-l, (15)

(16)

0 = -2(l - l )~e , e -~ + [(2C - l)B3 - 3D2] c~-~,e-2 -(l - 1)Gzce-l,e-1 + [ ( 2 l - 3)& - 3041 ct-2,t-z.

We define u = X2L, then multiply the recursion relations (ll), (13) and (15) by ue-l and sum over C from l = 1 to 00 to obtain differential

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equations for &, SO and TO:

03 03

e= 1 e=i

03 03 03

e= 1 e=i

'=1 e=i

Subject to the initial conditions &(O) = uo,o = 1, So(0) = bo,o = 1 and To(0) = CO,O = 1, we obtain solutions to Eqs.(l7), (18) and (19):

Multiplying the recursion relations (12), (14) and (16) by ue-2 and summing over t? from t? = 2 to 00 yields the following differential equations

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for R1, S1 and TI:

e=z e=z e=z

e=z t!=2

e=z e=2 e=2

e=z e=z e=z

e=2 e=z

Knowing the explicit solutions &, SO and TO and given the initial conditions &(0) = al,o, Sl(0) = bl,o, T1,o = q , ~ , the solutions to the differential equations (20), (21) and (22) are: (making the substitution w 1 - B ~ u )

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Comparing the p-dependence of the unsummed, truncated series {ALL, ANL, BLL, BNL, CLL, CNL} to that of the corresponding series {a, R1, SO, S1, TO, TI} , one finds that the latter exhibit much less p-dependence. This behavior reduces the theoretical uncertainty in the corrections A, B, and C , and should thus lead us to much more precise predictions. The procedure we have illustrated has also been (sucessfully) applied to the e+e--annihilation cross-section4 and to inclusive semileptonic B-decays5.

Acknowledgements

The author gratefully acknowledges the financial support of Mount Allison University’s VP-Academic, Dean of Science, and Student Administrative Council’s Academic Enrichment Fund, as well as NSERC for its support through a Summer Undergraduate Research Award.

References 1. M. R. Ahmady et al., Nucl. Phys. B 655, 221 (2003). 2. L. Culumovic, D. G. C. McKeon, T. N. Sherry, Ann. Phys. 197, 94 (1989). 3. D. G. C. McKeon, Int. J. Theor. Phys. 37, 817 (1998). 4. M. R. Ahmady et al., Phys. Rev. D 67, 034017 (2003). 5. M. R. Ahmady et al., Phys. Rev. D 66, 014010 (2002).

NEUTRAL CURRENT DETECTORS IN THE SUDBURY NEUTRINO OBSERVATORY

L. C. STONEHILL* Center for Experimental Nuclear Physics and Astrophysics

University of Washington Seattle, WA 98195 USA

The Sudbury Neutrino Observatory (SNO) is a heavy water solar neutrino Cherenkov detector with sensitivity to the neutral current, charged current, and elastic scattering reactions. The SNO experiment is poised to enter the neutral current detector (NCD) phase, during which 3He proportional counters will be deployed into the heavy water in order to detect neutrons liberated by the neutral current reaction. The NCD phase will provide a largely independent measurement of the total 8B solar neutrino flux as well as event-by-event discrimination between neutral current and charged current interactions in case of a supernova.

1. Introduction

The Sudbury Neutrino Observatory (SNO) is a unique heavy water Cherenkov detector designed to detect all three neutrino flavors via the neutral current (NC) reaction of neutrinos on deuterium:

2 H + u , +p+n+u, . (1)

In addition, electron neutrinos can participate in the charged current (CC) reaction:

H+u, + p + p + e - , (2) 2

and all flavors can undergo the elastic scattering (ES) reaction, with reduced sensitivity to up and u,.:

e- + u, + e- + v,. In the CC and ES reactions, the relativistic electron produces a Cherenkov light cone.

(3)

*On behalf of the SNO Collaboration.

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The SNO experiment is located 6800 feet underground (6010 meters water equivalent) in the INCO Creighton mine near Sudbury, Ontario in Canada. The detector consists of 1000 tonnes of ultra-pure D2O enclosed in an acrylic sphere 12 m in diameter. This is surrounded by a geodesic support structure holding 9456 photomultiplier tubes. All of this is im- mersed in about 7000 tonnes of pure H20, which shields the heavy water from radioactivity originating in the rock walls of the cavity.'

The signature of the NC reaction is a free neutron, so a primary goal in SNO is the detection of free neutrons. This is done with a different detection medium in each of the three phases of the SNO experiment: pure heavy water, salt, and neutral current detectors. In the first phase, the neutron captures on deuterium, producing a 6.25 MeV photon that Compton scatters electrons and makes Cherenkov light. Results from this phase indicate that solar neutrinos undergo flavor change and that the total neutrino flux from the sun agrees quite well with the predictions of the Standard Solar M ~ d e l . ~ ? ~ ? ~ During the second phase, chlorine is added to the heavy water in the form of NaC1. Neutron capture on chlorine produces up to three photons with 8.6 MeV total energy. The neutral current signal is enhanced by the larger neutron capture cross section on chlorine.

2. The Neutral Current Detectors

In the neutral current detector (NCD) phase of the SNO experiment, 3He proportional counters will be deployed into the heavy water to capture neutrons liberated in the NC reaction. The neutron signal is detected and read out in a completely independent manner from the Cherenkov light signal observed with the PMTs, breaking the correlation between the NC and CC signals. This allows the best possible determination of the CC spectrum and a search for spectral distortions. In addition, the systematics in the NCD phase are largely independent from the pure heavy water and salt phases of the SNO experiment. In the NCD phase, the NC and CC signals are distinguished on an event-by-event basis, so time variations can be followed separately in NC and CC.

The NCDs detect neutrons via the 3He(n, P ) ~ H reaction. The proton and triton ionize gas in the NCD proportional counters and the electrons accelerate toward a central anode wire at high voltage. The voltage is sufficient to cause an avalanche as the electron nears the wire, but is low enough that the NCD remains in the proportional regime. The NCDs will be deployed vertically in the SNO detector on a one meter grid. Each NCD

364

is a 2, 2.5, or 3 m long, two-inch diameter nickel tube filled with 3He gas. Three or four NCDs welded together form a string 9 to 11 m in length. There will be 40 such strings deployed into SNO, for a total of 398 m of NCD length.

One of the primary considerations in the NCD design is minimization of radioactive backgrounds introduced into the SNO detector. Because of the stringent radioactivity limits (24 parts per trillion of uranium and 2 parts per trillion of thorium), commercial proportional counters could not be used, so the NCDs were custom designed and built at Los Alamos National Laboratory and the University of Washington. The bodies were made from ultra-pure chemical-vapor-deposited (CVD) nickel 0.36 mm thick. CVD nickel endcaps that contain a fused-silica high-voltage feedthrough tube were welded into each end of the NCD. Each NCD was strung with a 50 pm diameter copper anode wire. It was then filled to 1900 torr with a 85:15 mixture of 3He and CF4 for quenching.

The NCD data acquisition system consists of two primary paths. Both paths go from an NCD string to a current preamplifier through the same cable that provides high voltage. If the pulse passes the digitization threshold, it is sent through a delay to a digital oscilloscope. The other path is to shaper/ADC cards that can acquire integrated current signals proportional to energy at much higher rates than the digitized path. This allows the NCD array to handle the high data rates expected from a supernova burst, where digitization to distinguish backgrounds is not as important due to the short time scale.

3. NCD deployment

The NCDs were built in 2, 2.5, and 3 m long sections, since anything longer would not fit into the mine shaft hoist. These segments must be welded together into longer strings and deployed into the SNO acrylic vessel (AV). All the welding is done with a very clean Nd-YAG pulsed laser that was also used to weld together tube sections and endcaps during construction. One end of each NCD is slightly flared so it can slip over the straight end of another NCD. The laser is directed at the overlap and the NCDs are rotated, creating a series of overlapping craters melted into the nickel that fuse the two NCDs together. Just prior to welding, a small amount of 4He is injected into the space between the two NCDs to be used as a tracer gas when leak checking the weld.

The deployment is being performed in two stages in order to minimize

365

the time that the SNO detector will be offline. During the pre-deployment welding phase, the NCDs were welded together into sections that do not exceed 5.5 m in length. Longer NCD sections cannot be turned vertically over the neck of the AV for deployment, due to limited overhead clearance. Of the 196 required welds, 148 were done during this phase of deployment, greatly reducing the down time for deployment itself. For the NCD deployment the lower half of a string will be lowered into the neck of the AV. The upper half of the string will then be welded on and the string lowered into the AV using a pulley system. A submersible remotely operated vehicle will be used to install the string into its anchor socket.

4. NCD signals

The NCDs are optimized to detect neutrons liberated in the NC reaction in SNO, but are capable of detecting other types of signals as well. Other thermal neutrons can capture on 3He, producing a characteristic back-to- back proton-triton track. In addition, charged particles can ionize the gas and produce a signal. The most important of these are alpha particles that come from radioactive decays in the NCD itself, since an alpha particle from outside the NCD cannot travel through the nickel wall. The primary sources of alpha backgrounds in the NCDs are 238U and 232Th decay chains and 'loPo. The 210Po is a radon daughter that adheres to the surface of the nickel from the air - its decays produce a 5.3 MeV alpha. Uranium and thorium in the NCDs can lead to neutron production in SNO as well. Both 238U and 232Th have gammas in their decay chains energetic enough to photodisintegrate deuterium, mimicking the NC reaction. The alphas from the uranium and thorium decay chains can provide a measurement of the uranium and thorium in the NCDs, and thus the photodisintegration neutron background introduced by the NCDs.

A neutron event in an NCD will deposit up to 764 keV in the gas, the Q-value of the 3He(n, P ) ~ H reaction. If either one of the charged particles hits the wall before losing all its energy to the gas, then less than the full 764 keV will be deposited. An energy histogram of NCD data that consists primarily of neutrons has a distinct peak at 764 keV, as shown in Figure 1. An alpha will generally deposit several MeV in an NCD, so it is often quite easy to distinguish from a neutron event. It is possible, however, for an alpha to deposit only 764 keV in the gas if it is produced deep inside the wall or if it hits a different part of the wall before depositing its full energy. In either of these wall effect situations the alpha will have the same energy

366

as expected for a neutron event and will have to be distinguished by pulse shape analysis techniques using the digitized data.

Figure 1. length. The horizontal axis is in arbitrary units.

Energy spectrum of 60 days of pre-deployment data from 62.5 m of NCD

The purpose of digitizing the NCD data is that pulse shape can be used to separate neutron events from backgrounds, particularly alphas. Neu- tron events can be distinguished from alpha events by their longer track length. If the tracks are perpendicular to the anode wire, then the longer track length corresponds directly to longer pulse duration. If the tracks are parallel to the wire, then, lateral straggling aside, all the ionization arrives simultaneously and no information about track length is recorded in the digitized pulse. Thus there are inherent limitations to the separation of neutron events from alphas in the NCDs and it is not possible to identify all events with complete certainty. A simple technique for separat- ing neutrons from alphas involves producing two-dimensional phase space plots of the pulse duration and energy. In these scatter plots, about 45% of neutron events fall into a background-free region with no alphas or other backgrounds.

A digitized pulse from a neutron event will sometimes show a double

367

peak structure from the Bragg peak of the proton and the triton ionization reaching the anode wire at different times. This structure will not be visible, however, if the proton-triton track is oriented parallel to the wire, as in this case all the ionization will arrive at the wire at essentially the same time. These two neutron event topologies are shown in Figure 2.

Figure 2. allel (right) to the anode wire.

Neutron events where the proton-triton track is perpendicular (left) and par-

Deployment of the SNO neutral current detectors is expected to occur in the fall of 2003, and production data-taking in the NCD phase should commence in 2004.

References

1. The SNO Collaboration, Nucl. Instr. and Meth. A449, 172 (2000). 2. Q. R. Ahmad et al., Phys. Rev. Lett. 87, 071301 (2001). 3. Q. R. Ahmad et al., Phys. Rev. Lett. 89, 011301 (2002). 4. Q. R. Ahmad et al., Phys. Rev. Lett. 89, 011302 (2002). 5. M. C. Browne, Ph.D. Thesis, University of Washington (1999).

ENERGY AND PARTICLE FLOW MEASUREMENTS AT HERA

KATSUO TOKUSHUKU (ON BEHALF OF THE H1 AND ZEUS COLLABORATIONS)

KEK, 1-1 Oho, Tsukuba

Ibaraki 305-0801, Japan E-mail: katsuo. tokushukuOkek.jp

Recent results related to particle and energy flow in the hadronic final state in e p deep inelastic scattering are presented, and compared with the expectations of Monte Carlo models with different types of QCD evolution, models with a resolved photon contribution and a model which simulates QCD instanton induced interactions.

1. Introduction

Deep-Inelastic lepton-proton scattering (DIS) experiments have played a very important role in establishing Quantum-Chromodynamics (QCD) as the theory of strong interactions.

As presented in another talk,' the strong coupling constant has been extracted from various hadronic final state measurements. It has also been demonstrated that jet cross sections are successfully described by next-to- leading order (NLO) QCD calculations.2 In the region where the Bjorken scaling variable z becomes very small (< however, there are still large uncertainties in some of the measurements of the hadronic final state as well as in the theoretical predictions. When the hadronic mass (W) is very high, a parton in the proton can emit many other partons before it finally interacts with the virtual photon. Fixed order perturbative calculations, such as, those at O(a;) , that are currently available, are not sufficient to describe the data in certain phase space regions.

In perturbative QCD, different types of evolution are proposed to describe the parton emissions to fill the gap in the fixed order calculation: DGLAP evolution at large Q 2 , BFKL evolution at the small z as well as the CCFM evolution equation, which forms a bridge between DGLAP and

368

369

H1 Forward Jet Data

A 41251 ’

0 ’ o i o i 0.d02 0.603 a X

I04

Figure 1. 5GeV, with the predictions from the CDM, RG and CASCADE Monte Carlos.

The cross section for forward jet production as a function of 2 for det >

BFKL. In DGLAP evolution, the transverse energy of the emitted partons is strongly ordered, whereas BFKL evolution results in partons with strongly decreasing longitudinal momenta but “random” transverse momenta.

2. Forward Energy Flow

The forward region, which is the region between the current jet and the proton remnant, is a good place to test the evolution of the partonic emissions. DGLAP evolution predicts less jet production in that regions than BFKL evolution does. Figure 1 shows the jet cross section in 7” < ejet < 20” measured from the proton direction in the laboratory frame.3 The prediction from a pure DGLAP-type MC (RG-DIR)4 falls below the data. The colour dipole model (CDIVI),~ which has no p~ ordering, and DGLAP including resolved virtual photons4 give a good description. The CASCADE‘ implementation of the CCFM evolution equation overestimates the data.

Measurements of high-pT r0 cross sections in a similar kinematical range lead to similar conclusion^.^

3. Resolved Photon

It is interesting that the model with the resolved photon contribution could reproduce the forward jet and pion data. A more direct way to see the effect of the resolved photon is to measure z:ss using the two highest p~ jets.

370

.-. Her dirwes, GRV d . 5

Her dirwes, GRV d . 2 Her res, SaSlD

f s : c - 2

g o 2" 03

- 1 y' 05

-- 055

035

0 3

0.15

a1 0.05

0 0 3 0 4 0.6 0.8 1

'4 Y

Figure 2. compared with HERWIG with different virtual photon parton distribution functions

Triple differential dijet cross-section as a function of zyBS , @, and Q2,

Defined as;

zjets ~p~ exp(-@t) xOBS = Y 2EY*

where EFt and qjet are the transverse energy and pseudorapidity of the jets, and EY* is the photon energy, x7Bs is an estimator of the fraction of the photon energy contributing to the hard scattering. If the photon reacts as a whole in the hard reaction (direct process), it is close to 1, while if the photon is a source of partons and one of the partons contributes to the hard scattering (resolved process) its value becomes lower. As Q2 becomes larger, the exchanged photon is more virtual and hence has no time to develop partonic structure so the resolved contribution is expected to decrease.

Figure 2 shows the dijet cross sections' as a function of xyBS, the square of the average transverse energy of the two highest transverse energy jets (@), and Q2. When compared with a leading order MC (HERWIG)g with direct component only, the data show a clear excess at low x $ ' ~for the low Q2 sample. Various parameterisations of the resolved photon component allow better agreement to be achieved. It is, however, worth noting that the resolved photon component is not the only way of achieving good agreement. CASCADE also gives a reasonable result.' (not shown)

37 1

ZEUS

Q2(GeV2)

Figure 3. Measured ratio $(zvBS < 0 . 7 5 ) / 3 ( z q B S > 0.75) as a function of Q2

in different region of g. Also shown are the NLO calculations with (JetVip)'l and without (DISASTER++)12 the resolved photon contributions.

The ratio of the cross section for x7Bs > 0.75 and xyBS < 0.75 was measuredlo and compared with a recent NLO QCD calculation including the effects of resolved photon interactions (Figure 3). It is seen that the resolved component decreases as Q2 increases. Neither NLO QCD calculation with nor without the resolved photon component is able to explain the absolute scale of the measurements, although the shape is reasonably reproduced. This is a recent development and more progress is expected in the calculations including the study of the effects of different parameterisations of the structure of the virtual photon.

4. Instantons

Once the hadronic final state in ep scattering is well understood, searches for "unusual" events become possible, for example those induced by QCD in~tant0ns.l~ QCD is a non-Abelian gauge theory and has a complicated vacuum structure. Tunnelling processes between topologically different types of vacuum state can occur. These are mediated by instantons.

The cross section from instanton induced processes in DIS14 can be 0(10-3) of the total DIS cross section. This is still small, but by using sophisticated final state selection procedures, it is possible to enhance this fraction.

In (anti-)instanton processes, light quarks and anti-quarks are produced

372

i-.- ’ I....

SPh,

Figure 4. Distributions of the sphericity ( S p h s ) in the reconstructed instanton centre- of-mass frame before and after instanton enrichment cuts. Data (filled circles), two QCD model background MCs (solid and dashed line) and the instanton MC (dotted line) are shown. In the left plot, the instanton prediction is scaled up by a factor of 500.

“democratically” and with the same chirality:

?’* -k A (HR -k qR) -k 1299, (1 + 7, R + L) , (1) flavours

with ng N 3. It is very difficult to measure the handedness in the final state, so the signature used in searches is based on the emission of a large number of partons in a limited rapidity range.

An example15 of the difference in the final state is shown in Figure 4. The variable used in the plots is the sphericity of particles in the reconstructed instanton-rest-frame. The left plot is before enhancement cuts. Instanton events are more circular than “normal” DIS events, but the fraction is very small so that in the plot it is rescaled by a factor of 500.

After enhancement cuts using various kinematical variables15, the instanton contribution becomes visible (the right plot). The shape of the distributions of the “normal” DIS Monte Carlo predictions is, however, similar to that arising from the instanton process. Moreover, the difference between the two DIS MCs is comparable to the expected instanton contribution. Given these systematic uncertainties, H1 choose to set a limit on the instanton cross section. The 95% confidence limit for instanton induced events is set to 221pb, which is about a factor of five above the prediction.

5 . Conclusions

A lot of activities directed at understanding the hadronic final state in DIS are ongoing. At low-x, a fixed order pQCD is not sufficient. Various parton

373

evolution schemes have been tested as well as the effects of the inclusion of the resolved photon contributions. The increasing precision of the data provides a continuing challenge to QCD based models of the hadronic final state.

A search for instanton induced processes was performed in DIS. While an excess of events with instanton-like topology is observed, it cannot yet be claimed to be significant given the uncertainty of the standard DIS expectations. Better understanding of the energy flows in the ep hadronic final state, with improved Monte Carlo event generators, will help to further test this and other aspects of QCD.

Acknowledgments

I would like to thank the organizers for a very pleasant conference. I would also like to acknowledge the support of the Japanese Ministry of Educa- tion, Culture, Sports, Science and Technology (MEXT) and its grants for Scientific Research.

References 1. K. Tokushuku, “High PT jet production and as measurements in electron-

proton collisions”, in this conference. 2. J. Breitweg et al. (ZEUS Collaboration), Phys. Lett. B507, 70 (2001). 3. C. Adloff et al. (H1 Collaboration), contributed paper #lo01 to the 31st

International Conference on High Energy Physics, ICHEPO2. 4. H. Jung, RAPGAP version 2.08, Lund University, 2002. 5. L. Lonnblad, Comput. Phys. Commun. 71, 15 (1992). 6. H. Jung, Comput. Phys. ‘Commun. 143, 100 (2002). 7. C. Adloff et al. (H1 Collaboration), contributed paper #lo00 to the 31st

International Conference on High Energy Physics, ICHEPO2. 8. C. Adloff et al. (H1 Collaboration), contributed paper #lo09 to the 31st

International Conference on High Energy Physics, ICHEP02. 9. G. Marchesini et al., Comput. Phys. Commun. 67, 465 (1992). 10. S. Chekanov et al. (ZEUS Collaboration), contributed paper #854 to the

31st International Conference on High Energy Physics, ICHEPO2. 11. B. Potter, Comput. Phys. Commun. 133, 105 (1997). 12. D. Graudenz, hep-ph/97102& (1997). 13. G. ’t Hooft, Phys. Rev. Lett. 37, 8 (1976);

G. ’t Hooft, Phys. Rev. D 14, 3432 (1976); Erratum-ibid. D 18, 2199 (1976); A. A. Belavin et al. Phys. Lett. B 59, 85 (1975).

ibid. B 459, 249 (1999); ibid. B 503, 331 (2001). 14. A. Ringwald and F. Schrempp, Phys. Lett. B 438, 217 (1998);

15. C. Adloff et al. (H1 Collaboration), Euro. Phys. J . C25, 495 (2002).

HIGH PT JET PRODUCTION AND LYS MEASUREMENTS IN ELECTRON-PROTON COLLISIONS

KATSUO TOKUSHUKU (ON BEHALF OF THE H1 AND ZEUS COLLABORATIONS)

KEK, 1-1 Oho, Tsukuba

Ibaraki 305-0801 , Japan E-mail: katsuo.tokushukuQkek.jp

Recent HERA jet cross sections are presented and the resulting as measurements are discussed.

1. Introduction

Jet production in ep deep inelastic scattering (DIS) provides a rich testing ground for perturbative QCD (pQCD). The jet production cross section in DIS can be expressed in the form;

0 = C_ J dxfa (2, P F ; a s ) d e ( x p , Pp ; PR; a s ) (1 + bhad) (1) a=979>9

where, the fa are the parton density functions (PDFs) in the proton, d8 is the partonic cross section and the (1 +dhad) term represents the corrections due to hadronisation. The dependency on the strong coupling constant (a,) of the PDFs allows measurements of a, to be performed from the inclusive DIS cross section measurements.'

Given the improved understanding of the parton distributions in the proton and the theoretical progress in the NLO QCD calculations for jet cross sections,2 measurements of jets have also become important in the determination of a,. At HERA, thanks to the high centre-of-mass energy, jets can be studied in a wide kinematical range in Q2 and/or jet transverse momentum (ECt) . The running of the coupling constant can be seen with a large lever arm. As presented elsewhere in these proceeding^,^ there are kinematical regions where the data and NLO QCD do not agree. Studies of a, are done in the regions which are well described, i.e. at high Q2(2 100GeV') and/or high EPt.

374

375

9 a&) a, from inclusive jet cross section lor CTEQIMI panon densities

inclusive k , alaorithm HI A aS(M3

150 < Qz < 200 GeV2 0.24 as 0.22

0.2 0.16 0.16 0.14 0.12 n i

0.24 1 300 < a2 < 600 GeV2 1 600 c a2 < 5000 GeV2 0.22

0.14 YA-3

10 lo2 10 102 E, lGeV E, I GeV

Figure 1. Determination of as from the inclusive jet cross section. Dots are results for the as values in each Q2 region as a function of jet EFt . The triangles are the values extrapolated to the Z o mass.

2. Measurements of a8 from jets in DIS

A classical way of measuring a, is to study the ratio of one-current-jet to two-current-jet events. By taking the ratio between the two cross sections, many experimental uncertainties cancel. Both the H1 and ZEUS collaborations have invested much effort on improving the kinematical cuts and jet algorithm^.^ The latest measurements from ZEUS with dijet events of Q2 > 470GeV2 give,5

as ( M z ) = 0.1166 f O.O019(~t~t.)?::::Z: (syst . ) +0.0057 -0,0044 (th.).

The running of a, as a function of Q was seen within one experiment, as predicted by QCD.

Recently both H1 and ZEUS experiments measured precisely the inclusive jet cross sections in the Breit frame and demonstrated that the NLO QCD calculations give a reasonable description of the data. The extraction of a, from the cross sections was performed directly from Equation 1. Compared with the di-jet cross sections, inclusive cross sections have less theoretical uncertainties related to the selection cuts for the second jet.6

The results of the H1 collaboration are seen in Figure l.7 The running of a, is clearly visible as a function of EFt. The combined result for all data points gives;

a, ( M z ) = 0.1186 f 0 .0030(e~~ . ) t : : : :~~( th . ) f : : : :~~ (pdf).

376

ZEUS h a

V QCD predictions (DISENT) =- 1.8

C-lObdmTeW 1.7

11 G T € W l W W

1.5 maMl I%w.aII"

CTEMA1I-I*a

1A

13

1 2

p 1A

0' 1 1

1

1.1 1

0 9

20 30 40 54 W

ETJst (GeV)

Figure 2. a) The mean subjet multiplicity corrected to the hadron level for inclusive jet production in NC DIS with Q2 > 125GeV2 and -1 < qJet < 2(dots). b) The parton-to-hadron correction, Chad used to correct the QCD predictions. c) The relative uncertainty on the NLO QCD calculation.

With a similar analysis, ZEUS obtained;8 +0.0023 +0.0028 a, ( M z ) = 0.1212 f 0.0017(stat.) -0.0031 (syst.)-0.0027(th.).

3. Measurements of a# from jet structure

A recent comparison shows that pQCD does not only describe distinct high ET jets but also jets with a small ~eparation.~ This indicates there is another way t o measure a,; through the study of the internal structure of jets, or subjets. The mean subjet multiplicity is defined as the number of clusters resolved in a jet by re-applying the jet algorithm at a smaller resolution scale, ycut.

Figure 2 shows the subjet multiplicity as a function of EFt.lo The ycut value is set to 0.01 to ensure that the measurement is performed in a region in which non-perturbative effects are under control. The subjet multiplicity decreases as the jet energy increases. In the figure the NLO prediction for various values of as is also shown. Obviously, the higher the a, the larger the subjet multiplicity observed. The extracted result is;

which is consistent with the results obtained from jet cross sections, with

377

a 1 ' " I " ' I " ' I " '

d - *ZEUS%-00 -

- NLO QCD __... sealing P

I cWn> = 180 GeVl<Wn> = 255 GeV and -2 c qEc 0 . g -

jet energy d e uncertainty Izrm NLOuncertainty

0.51' " ' I " ' I " " " J 0.2 0.3 0.4 0 5

yr

Figure 3. function of XT. The dashed line is the scaling expectation. together with its uncertainty, is also shown.

Measured ratio of scaled jet invariant cross sections for different W,, as a NLO QCD prediction,

slightly larger theoretical errors, which result mainly from the renormalization scale uncertainty.

4. Jet XT scaling in photoproduction and the

Recently the ZEUS collaboration has performed a measurement of high Et inclusive jet cross section in photoproduction." Jet production in the yp reaction can be regarded as a result of the scattering of a parton in the proton off a parton in the photon (or the photon itself). In the simple quark-parton model, when one measures with different centre-of-mass energy (WTP), the cross section scales with a scaling variable ZT, defined as 2EP/WTP. On the other hand, QCD predicts scaling violations due both to the evolution of the parton densities of the incoming particles and to the running of as.

The scaling violation has already been observed in p p collisions12 where NLO gives a good description of the shape of the data but the predicted magnitude is significantly higher than the measurements. It is interesting to study this in -yp reactions.

Photoproduction events in the region 142 < W,, < 293 GeV with at least one jet satisfying ECt > 17GeV and -1 < qjet < 2.5 were selected.

determination of a,

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The jet cross sections were measured as a function of XT for two different W,, regions, with the same qrp cut.

Figure 3 shows the results as a function of XT. The data show a clear deviation from unity. This is the first observation of this scaling violation in -yp reactions. The magnitude of the violation is well described by the NLO calculation.

Since the NLO QCD predictions agree reasonably well with the data, a, was extracted using a similar procedure to that used in the DIS inclusive jet measurement. The results was

+0.0054 h ( M z ) = 0.1224 f 0.0001 stat.)+^:^^^^ (syst . ) -0.0042 (t .). In this case, dominant uncertainty again came from higher order effects, which were estimated by varying the renormalization scale.

5. Conclusions

Recent HERA measurements of a, are summarized in Figure 4. The measurements are of good precision and are consistent both with each other and with the world average, demonstrating the universality of the strong coupling constant.

All results shown here are based on HERA-I data corresponding to an integrated luminosity of - 100pb-l. Statistical uncertainties are already quite small. We expect that the large amount of data to be collected at HERA-I1 will help to reduce the systematic uncertainties. Further developments in the theory, in particular an understanding of the effects of higher orders would make a large impact on the precision with which a, can be measured.

For the first time in y p reactions, the cross section was compared for the different CM energy, in terms of the scaling variable XT. Scaling violations are observed, which, in contrast to the pjj results, agree with the NLO QCD prediction.

Acknowledgments

I would like to thank the organizers for a very pleasant conference. I would also like to acknowledge the support of the Japanese Ministry of Education, Science and Culture (MEXT) and its grants for Scientific Research.

References

1. C. Adloff et al. (H1 Collaboration), Euro. Phys. J. C21, 33 (2001); S. Chekanov et al. (ZEUS Collaboration), Phys. Rev. D67, 012007 (2003).

379

Inclusive jet cross sections in ’Ip (hepex10212064) Subjet multiplicity in DIS (hep-ex10212030) Jet shapes in DIS (Contributed paper to IECHEPOI)

(Phys Rev D 67 (2003) 012007) Inclusive jet cross sections in DIS (Eur Phys J C 19 (2001) 289) Inclusive jet cross sections in DIS (Phys Lett B 547 (2002) 164) Duet cross sections in DIS (Phys Lett B 507 (2001) 70) World average

0.1 0.12 0.14 a&)

Figure 4. Summary of as values measured at HERA. The thick solid error bars show the statistical uncertainty. The thin error bars show the statistical and experimental systematic uncertainties added in quadrature. The dotted lines indicate the theoretical uncertainty.

2. S. Catani and M. H. Seymour, Nucl. Phys. B 485, 291 (1997); Erratum-ibid. B510 503 (1997); E. Mirkes and D. Zeppenfeld, Phys. Lett. B 380, 205 (1996); D. Graudenz, hep-ph/97f 0244.

3. K. Tokushuku, “Energy and Particle Flow measurements at HERA”, in this conference.

4. C. Adloff et al. (H1 Collaboration), Euro. Phys. J . C6, 575 (1999); C. Adloff et al. (H1 Collaboration), Euro. Phys. J. C5, 625 (1998); M. Derrick et al. (ZEUS Collaboration), Phys. Lett. B363, 201 (1995); T. Ahmed et al. (H1 Collaboration), Phys. Lett. B346, 415 (1995).

5. J. Breitweg et al. (ZEUS Collaboration), Phys. Lett. B507, 70 (2001). 6. M. Klassen and G. Kramer, Phys. Lett. B366, 385 (1996);

S. Frixione and G. Ridolfi, Nucl. Phys. B507, 315 (1997); B. Potter, Comput. Phys. Commun. 133, 105 (2000).

7. C. Adloff et al. (H1 Collaboration), Euro. Phys. J . C19, 289 (2001). 8. S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B547, 164 (2002). 9. C. Adloff et al. (H1 Collaboration), Euro. Phys. J . C24, 33 (2002). 10. S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B558, 41 (2003). 11. S. Chekanov et al. (ZEUS Collaboration), DESY-02-228, hep-e~/0212064

submitted to Phys. Lett. B. 12. F. Abe et al. (CDF Collaboration), Phys. Rev. Lett. 70, 1376 (1993);

B. Abbott et al. (DO Collaboration), Phys. Rev. Lett. 86, 2523 (2001).

STUDY OF THE e+e- +. Z e+e- PROCESS AT LEP

R. VASQUEZ Purdue University, Department of Physics

525 Northwestern Avenue, West Lafayette, IN 4 7907-2036 USA, E-mail: [email protected]

The cross section of the process e+e- + Ze+e- is measured with 0.7ft-’ of data collected with the L3 detector at LEP. Decays of the Z boson into quarks and muons are considered at centre-of-mass energies ranging from 183 GeV up to 209 GeV. The measurements are found to agree with Standard Model predictions.

1. Introduction

The study of gauge boson production in e+e- collisions constitutes one of the main subjects of the scientific program carried out at LEP. Above the Z resonance “single” weak gauge bosons can also be produced via t-channel processes lV2. A common feature of this single boson production is the emission of a virtual photon off the incoming electron or positron. This electron or positron remains in turn almost unscattered at very low polar angles and hence not detected. Figure 1 presents two Feynman diagrams for the single

Figure 1. Main diagrams contributing to the “single Z” production.

Z production, followed by the decay of the Z into a quark-antiquark or a muon-antimuon pair. The signal definition applied in this study requires the final state fermions to satisfy the kinematical cuts

mf? > 60 GeV, eunscattered < 12”, 60” < @scattered 168”, Escat tered > 3.0 GeV,

380

38 1

where mfF refers to the invariant mass of the produced quark-antiquark or muon-antimuon pair, ounsca t t e red is the polar angle at which the electron” closest to the beam line is emitted, Oscattered and E s c a t t e r e d are respectively the polar angle with respect to its incoming direction and the energy of the electron scattered at the largest polar angle.

2. Data and Monte Carlo samples

This analysis is based on 675.5pb-l of integrated luminosity collected at fi = 182.7 - 209.0 GeV with the L3 detector ’. For the investigation of the e+e- + Ze+e- + qpe+e- channel, this sample is divided into eight different energy bins whose corresponding average fi values and integrated luminosities are reported in Table 1. The signal process is mod-

Table 1. luminosities of the data sample used in this study.

The average centre-of-mass energies and the corresponding integrated

I I I

&[[GeV] I 182.7 188.6 191.6 195.5 199.5 201.7 204.9 206.6 L[pb-’] I 55.1 176.0 29.4 83.0 80.8 36.7 76.6 137.9

elled with the WPHACT Monte Carlo program ‘. Events are generated in a phase space broader than the one defined by the criteria (1). Those events who do not satisfy these criteria are considered as background. The GRC4F event generator is used for systematic checks. The e+e- + qq(y), e+e- + p+p-(y) and e+e- + T-T+(Y) processes are simulated with the KK2f Monte Carlo generator, the e+e- + ZZ process with PYTHIA 7,

and the e+e- + W+W- process, with the exception of the qq‘eu final state, with KORALW *. EXCALIBUR is used to simulate the qq’eu and other four-fermion final states. Hadron and lepton production in two-photon interactions are modelled with PHOJET lo and DIAG36 11, respectively. The generated events are passed through the L3 detector simulation program 12.

3. Event selection

3.1. e+e- -+ Ze+e- + qqe+e- channel

The selection of events in the e+e- + Ze+e- + qqe+e- channel proceeds from high multiplicity events with at least one electron identified in the BGO electromagnetic calorimeter and in the central tracker with an energy

aThe word “electron” is used for both electrons and positrons.

382

above 3 GeV. The signal topology is enforced requiring events with a reconstructed invariant mass of the hadronic system, stemming from a Z boson, between 50 and 130 GeV, a visible energy of at least 0.40fi and a missing momentum, due to the undetected electron, of at least 0.24fi. Due to the particular signature of an electron undetected at low angles and the other scattered in the detector, two powerful kinematic variables can be considered: the product of the charge, q, of the detected electron and the cosine of its polar angle measured with respect to the direction of the incoming electron, cos 8, and the product of q and the polar angle of the direction of the missing momentum, cos I. Two selection criteria are applied:

q x cose > -0.5 and q x cosy > 0.94,

Distributions of these variables are presented in Fig. 2.

+ Data L3 0 Background 0 e+e-+ze+e-+qqe+e-

-1 -0.5 0 0.5

10

10

In s 9 $10 E al ii

1

L3 .1 b, + Data

0 Background 0 e+e-+ze+e-+qqe+e- R

q x cose

Figure 2. Distributions for data, signal and background Monte Carlo of the product of the charge of the detected electron and a) the cosine of its polar angle and b) the cosine of the polar angle of the missing momentum. The arrows show the position of the applied cuts. All other selection criteria but those on these two variables are applied. Signal events around -1 correspond to charge confusion in the central tracker. The sharp edge of the signal distribution in a) at -0.5 follows from the signal definition criterion es&tered > 60'; moreover, the depletion around f0.7 in data and Monte Carlo is due to the absence of the BGO calorimeter in this angular region.

3.2. e+e- + Ze+e- + p+p-e+e- channel

Candidates for the e+e- -+ Ze+e- -+ p+p-e+e- process are selected by first requiring low multiplicity events with three tracks in the cen-

383

tral tracker, corresponding to one electron with energy above 3 GeV and two muons, reconstructed in the muon spectrometer with momenta above 18 GeV. A kinematic fit is then applied which requires momentum conservation in the plane transverse to the beam axis. The reconstructed invariant mass of the two muons should lie between 55 and 145 GeV. Finally, three additional selection criteria are applied:

-0.50 < q x cose < 0.93, q x C O S ~ > 0.50 and q x cos& < 0.40,

where cosdz is the polar angle of the Z boson as reconstructed from the two muons. These criteria select 9 data events and 6.6 f 0.1 expected events from signal Monte Carlo with an efficiency of 22%. Background expectations amount to 1.5 f 0.1 events, coming in equal parts from muon- pair production in two-photon interactions, the e+e- -+ p+p-(y) process, and e+e- -+ p+p-e+e- events generated with WPHACT that do not pass the signal definition criteria.

4. Results

Figure 3a presents the distribution of the invariant mass of the hadronic system after applying all selection criteria of the e+e- -+ Ze+e- + qqe+e- channel. A large signal peaking around the mass of the Z boson is observed. The single Z cross section at each value of fi is determined from a maximum-likelihood fit to the distribution of this variable. Results are given in Fig. 4 and show a good agreement with the WPHACT Monte Carlo. This agreement is quantified by extracting the ratio R between the measured cross sections aMeasured and the WPHACT predictions aExpected:

aMeasured

= gExpected = 0.88 f 0.08 f 0.06,

where the first uncertainty is statistical and the second systematic. The invariant mass of muon pairs from the e+e- -+ Ze+e- -+

p+p-e+e- selected events is shown in Fig. 3b. The cross section of this process is determined with a fit to the invariant mass distribution, over the full data sample, as:

a(e+e- -+ Ze+e- -+ p+p-e+e-) = 0.043'::::; f 0.003 pb,

where the first uncertainty is statistical and the second systematic. This measurement agrees with the Standard Model prediction of 0.044 pb calculated with the WPHACT program as the luminosity weighted average cross section over the different centre-of-mass energies.

384

a) + Data

2 30 (3 s z Y 20 E

w 10

50 70 90 110 130 Hadron reconstructed mass (GeV)

b 4

Muon reconstructed mass (GeV)

Figure 3. b) the muon system for data, signal, and background Monte Carlo events.

Distribution of the reconstructed invariant mass of a) the hadron system and

L3 DATA WPHACT GRC4F ..........

I + ' t

e+e--+ze+e-+qije+e. Olrrl)' " " 190 ' " " 200 " " 2

Center of Mass Energy (GeV) 0

Figure 4. Measurements of the cross section of the e+e- + Ze+e- -+ qqe+e- process as a function of the centre-of-mass energy. The WPHACT predictions are assigned an uncertainty of 5%. As reference, a line indicates the GRC4F expectations.

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Several possible sources of systematic uncertainty and their effects on the measured cross sections are considered l . Uncertainties related to the energy scales of the calorimeters have the largest impact on the measurements: 2.3% and 6.3% on the qtje+e- and p'p-e+e- cross sections, re- s p ect ively.

In conclusion, the process e+e- -+ Ze+e- has been observed at LEP for decays of the Z boson into both hadrons and muons. The measured cross sections have been compared with the Standard Model predictions, and were found in agreement with an experimental accuracy of about 10% for decays of the Z boson into hadrons.

References 1. L3 Collab., M. Acciarri et al., preprint hep-ex/0303041, and references therein 2. DELPHI Collab., P. Abreu et al., Phys. Lett.B 515 (2001) 238; OPAL Collab.,

G. Abbiendi it et al.,Phys. Lett. B 438 (1998) 391; OPAL Collab., G. Abbiendi it et al.,Eur. Phys. J. C 24 (2002) 1.

3. L3 Collab., B. Adeva et al.,Nucl. Instr. Meth. A 289 (1990) 35; 0. Adriani et al.,Phys. Reports 236 (1993) 1; M. Chemarin et al.,Nucl. Instr. Meth.A 349 (1994) 345; M. Acciarri et al.,Nucl. Instr. A4eth.A 351 (1994) 300; G. Basti et al., Nucl. Instr. Meth.A 374 (1996) 293; I.C. Brock et al.,Nucl. Instr. Meth.A 381 (1996) 236; A. Adam et al., Nucl. Instr. Meth.A 383 (1996) 342.

4. WPHACT version 2.1; E. Accomando and A. Ballestrero,Comp. Phys. Comm. 99 (1997) 270; E. Accomando, A. Ballestrero and E. Maina, preprint hep-ph/0204052

5. GRC4F version 2.1; J. Fujimoto it et al. ,Comp. Phys. Comm. 100 (1997) 128. 6. KK2f version 4.13; S. Jadach, B.F.L. Ward and 2. Wqs,Comp. Phys. Comm. 130

(2000) 260. 7. PHYTHIA version 5.772 and JETSET version 7.4; T. Sjostrand, Preprint CERN-

TH/7112/93 (1993), revised 1995; T. Sjostrand,Comp. Phys. Comm. 82 (1994) 74. 8. KORALW version 1.33; M. Skrzypek it et al.,Comp. Phys. Comm. 94 (1996) 216;

M. Skrzypek it et al.,Phys. Lett. B 372 (1996) 289. 9. F.A. Berends, R. Pittau and R. Kleiss,Comp. Phys. Comm. 85 (1995) 437. 10. PHOJET version 1.05; R. Enge1,Z. Phys. C66 (1995) 203; R. Engel, J. Ranft and

S. Roesler,Phys. Rev. D52 (1995) 1459. 11. F.A. Berends, P.H. Daverfeldt and R. Kleiss, Nucl. Phys. B 253 (1985) 441. 12. The L3 detector simulation is based on GEANT 3.21, see R. Brun et al., CERN

report CERN DD/EE/84-1 (1984), revised 1987, and uses GHEISHA to simulate hadronic interactions, see H. Fesefeldt, RWTH Aachen report PITHA 85/02 (1985).

(2002).

INVESTIGATION OF HIGGS BOSONS IN THE LOW MASS REGION WITH ATLAS

M. WIELERS ON BEHALF OF THE ATLAS COLLABORATION Laboratoire de Physique Subatomique et de Cosmologie

53, rue des Martyrs, 38026 Grenoble cedex, France

E-mail: Monilca. WielersOcern.ch

The present constraints from, electro-weak radiative corrections suggest that the low mass region will be particularly interesting for future Higgs boson searches. In this paper the discovery potential of the Standard Model Higgs boson search in the mass range between 110 and 190 GeV by the ATLAS experiment at the LHC is presented as a function of collected luminosity. In addition, the sensitivity to the lightest Higgs boson of the MSSM (h) in various benchmark scenarios is presented. The prospects for precise measurements of the Higgs boson parameters are demonstrated.

1. Introduction

The Higgs boson is the last missing particle within the Standard Model (SM) and is as well predicted in certain extensions of the SM such as the supersymmetric Models. The SM Higgs is excluded by a direct search at LEP up to 114.1 GeV '. The theoretical upper limit is 1 TeV. However, fits to electro-weak data favour a low-mass Higgs, which is less than 193 GeV (C.L.= 95%). The Higgs search will be one of the mayor physics goals at the Large Hadron Collider (LHC). At the LHC, protons will be collided at a centre of mass energy of 14 TeV. In the first years LHC will run with a luminosity of 2 . 1033~m-2s-1. First collisions are expected in spring 2007. The first goal will be to collect an integrated luminosity of J L = 10 fb-'. After having collected J L = 30 fb-', LHC will switch to design luminosity, which is 1034~m-2s-1. The integrated luminosity per year is expected to be 100 fb-' with the final aim of collecting 300 fb-' per experiment. Two general purpose experiments are foreseen: ATLAS The most demanding signal channels have been evaluated in detail with the full simulation. For the backgrounds studies have been done with the fast simulation program in ATLAS, which uses a parametrised detector

and CMS 3.

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387

response. In the cross-section calculations, no k factors are used, because higher order corrections are not yet known for all signal and background processes.

2. Standard Model Higgs Boson Production Mechanism

At the LHC the main production mechanism for a SM Higgs will be the direct production via gluon-gluon-fusion as can be seen in figure 1. The

100 200 300 400 500 600 Higgs Mass (GeV)

Figure 1. function of the Higgs mass, M H .

Higgs production cross section at the LHC and Higgs branching ratios as a

second largest cross-section arises from vector-boson fusion (VBF) for which the cross-section is M 20% of the direct production for mH < 2 . mZ. In this process the initial state quarks will radiate Z or W-bosons, which subsequently will produce the Higgs. The signature for this process are two jets in the forward region from the scattered incoming quarks and low hadronic activity in the central region due to a lack of colour exchange between the quarks. This helps in reducing the backgrounds and thus the VBF processes offer a good discovery potential for Higgs masses below 150 GeV. Another mechanism to produce Higgs bosons at the LHC is its associated production together with a W, Z, tt, or bb. The cross-section of this process is of the order of 1-10 % of the direct production and is sizable for a Higgs mass below 200 GeV. These four different production mechanisms will be the key to measure the Higgs boson parameters. The Higgs branching ratio as a function of its mass is shown in figure 1. The main decay mode for mH < 2 . mz is the decay into a bb pair. However, due to the overwhelming bb production cross-section there is no hope to trigger or extract fully the hadronic final states for these events.

388

3. Standard Model Higgs Searches

The SM Higgs boson will be searched for at the LHC in various decay channels. The choice on the decay channel depends on the signal rates and the signal-to-background ratios in the various mass regions. Three different mass regions can be distinguished, which will be discussed below.

3.1. Low mass region, mH < 130 GeV

The most clean decay channel is the rare decay mode H+ yy with a branching ratio of w The signal needs to be observed above a huge background. A powerful particle identification, and an excellent energy and angular resolution are required from the electro-magnetic calorimeter system. A complimentary channel is the tEH channel, with H+ bb, leading to two W-bosons and four b-jets in the final state. For trigger purposes one of the W’s needs to decay to leptons. A good tagging of the b-jets is required in this mode. Another promising channel, which has been studied recently, is the VBF process qqH-+ q q n . For this channel the decay modes TT + l~uul*uu and TT + l f u u had u are considered. The Z+jet production followed by the Z - + TT decay constitutes the principal background.

3.2. Intermediate mass region, 13QGeV < mH < 2 - mZ

The H+ ZZ(*) + 41 channel provides a rather clean signature. In addition to the irreducible background from ZZ* and Zy* continuum production, there are large reducible backgrounds from ti and ZbL production. The decay mode H+ ZZ(*) is suppressed for 150 < mH < 180 GeV because of the opening of the H+ WW(*) channel. Therefore, the H+ WW(*) -i Zulu channel will help to increase the significance in this mass region, where direct or VBF production gives accessible rates. Due to the decay in U’S no mass peak can be reconstructed and the Higgs boson has to be observed from an excess of events above the backgrounds in the transverse mass spectrum. Analyses which explore the VBF topology lead to a better signal- to-background ratio but is much more demanding for the understanding of the detector performance (forward tagging jets, central jet veto).

3.3. High mass region, mH > 2 - mZ

The H+ ZZ + 41 is the most reliable channel for a discovery of the SM Higgs at the LHC. It can be exploited up to a Higgs mass of around 700 GeV. Above this value the production cross section becomes too small.

389

The expected background which is dominated by the continuum production of Z-boson pairs is smaller than the signal. For a very heavy Higgs (mH > 500 GeV), the H-+ ZZ + 22vv and H+ WW + 2vjj can be exploited. Around 25-30% of the production cross-section comes from the VBF channel.

3.4. SM Higgs Discovery Potential

The ATLAS Higgs boson discovery potential in the mass region between the LEP limit and 200 GeV is shown in figure 2 for j” L = 10 fb-’ and 30 fb-I respectively. Already with j” L = 10 fb-’ a SM Higgs can be discovered

L

Iw $20 140 1W 180 ZW

rn. (GeV/c’)

Figure 2. ATLAS sensitivity for the discovery of a SM Higgs boson for J”LlOft-’ and 30 fb-l. The signal significance are plotted for individual channels as well as the combination of all channels. A systematic uncertainty of &lo% on the background has been included for the VBF processes.

with a 5u significance in the mass range 120 < m(H) < 190 GeV. For L = 30 fb-’ a significance exceeding 50 is expected for several individual

channels. Several complimentary channels will be available. A systematic uncertainty of 10% on the background is assumed in these results.

4. MSSM Higgs Searches

In supersymmetric theories, the Higgs sector is extended to contain at least two doublets of scalar fields. In the minimal version, the so-called MSSM model, there are five physical Higgs particles: h, H , A, H*. In these models there is a large variety of observation modes. They can either be SM like, such as h 3 yy, h + b8, H + 42 or MSSM like AIH + rr, pp, tt, H + hh.

390

Figure 3 shows the 5u discovery potential in the m A - t anp plane for the

m, (GeV) mA (GeV)

Figure 3. ATLAS sensitivity for the discovery of a MSSM Higgs boson for an integrated luminosity of 30 ft-' and 300 fb-' in the mA - t a n p plane. The signal significance are plotted for individual channels on the left-hand side, whereas on the right-hand side plot the multiplicity of observable Higgs bosons is shown in the different regions of the mA - tan f l plane. The combined results for ATLAS and CMS are shown for the case of maximal mixing.

various Higgs bosons and their decay channels. The figures show the results combined for ATLAS and CMS. For an integrated luminosity of L = 3Ofb-1 the TTZA - tan@ plane is fully covered. The VBF production of the lightest Higgs boson (not yet included in this plot) will enhance the coverage of the m A - t anp parameter space. At the end of the LHC program which corresponds to L = 300 fb-', more than one MSSM Higgs bosons can be observed in most of the parameter space. This will allow to disentangle a SM from a MSSM Higgs.

5. Measurement of the Higgs Boson Parameters

Assuming the Higgs boson has been discovered its parameters such as mass, width, production rate and branching ratios can be measured. Such measurements will give further insight into the process of the electroweak symmetry-breaking and the way the Higgs couples to fermions and bosons. As an example figure 4 shows the precision of the measurement of the Higgs mass for an integrated luminosity of L = 300 fb-l. The Higgs mass can be measured with a precision of 0.1% up to masses of around 400 GeV. The precision on the boson-boson and fermion-boson couplings are 10-30% for mH < 190 GeV. The results for the later couplings are shown on the

39 1

0 H+U-t41 * H-tWW-Mv 0 WH (H-rWW-tlvlv) A all channels

ATLAS + CMS !L df= 300 fb'

10 lo2

mu (Ge\

3 100 120 140 160 180

m, (GeV)

Figure 4. Relative precision AmH/mH on the measured Higgs mass and the relative precision to measure the boson-fermion couplings for an integrated luminosity of 3Oft-l. For the mass mesurement the precision is shown assuming an overall uncertainty of 0.1% and the expected uncertainty of 0.02% on the absolute energy scale of the electromagnetic calorimeter.

right-hand side of figure 4.

6. Conclusions

Already after one year of data taking with an integrated luminosity of 10 fb-' the Standard Model Higgs could be discovered over the full mass range up to 1 TeV with ATLAS. To do so, a variety of channels in the different mass ranges can be exploited. Especially with the help of the VBF processes the sensitivity for a Higgs discovery can be enhanced in the mass region below 2.m(Z). Already with the rather modest luminosity of 10 fb-I it will be possible to explore most of the mA - t anp plane to discover possible MSSM Higgses. For a complete coverage J L = 30 fb-' are needed. Once the Higgs boson has been discovered and an adequate statistics is available its parameters can be measured.

References

1. LEP Collaborations, CERN-EP/2001-055 (2001), hep-ex/0107029. 2. ATLAS Collaboration, Detector and Physics Performance Technical Design

Report, CERN/LHCC/99-14 (1999). 3. CMS Collaboration, CMS Technical Proposal, CERN/LHCC 94-38, CERN

(1994). 4. E. Richter-Was, D. Froidevaux, L. Poggioli, ATLFAST 2.0, a fast simulation

package for ATLAS, ATLAS internal note ATL-PHYS-98-131 (1998).

UNIFIED APPROACH FOR MODELLING NEUTRINO AND ELECTRON NUCLEON SCATTERING CROSS SECTIONS

FROM HIGH ENERGY TO VERY LOW ENERGY

ARIE BODEK Department of Physics and Astronomy, University of Rochester, Rochester, New

York 14618, USA

UN-KI YANG Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

We use a new scaling variable t,,,, and add low Q2 modifications to GRV98 leading order parton distribution functions such that they can be used to model electron, muon and neutrino inelastic scattering cross sections (and also photoproduction) at both very low and high energies.

In a previous communication we used a modified scaling variable xw and fit for modifications to the GRV94 leading order PDFs such that the PDFs describe both high energy low energy e/p data. In order to describe low energy data down to the photoproduction limit (Q2 = 0), and account for both target mass and higher twist effects, the following modifications of the GRV94 LO PDFs are need:

(1) We increased the d /u ratio at high x as described in our previous analysis '.

(2) Instead of the scaling variable x we used the scaling variable x , = (Q2 +B)/(2Mv+A) (or =x(Q2 + B ) / ( Q 2 +Ax) ) . This modification was used in early fits to SLAG data '. The parameter A provides for an approximate way to include both target mass and higher twist effects at high x , and the parameter B allows the fit to be used all the way down to the photoproduction limit (Q2=O).

(3) In addition as was done in earlier non-QCD based fits lo to low energy data, we multiplied all PDFs by a factor K=Q2 / (Q2 +C). This was done in order for the fits to describe low Q2 data in the photoproduction limit, where F2 is related to the photoproduction

392

393

, . . . , . . . ....., , 3.0

2.5

3 2.0 q

u + 1.5 0 PJ

h c

1.0 'p +.. v

0.5

0.0

Figure 1. Electron and muon F2 data (SLAC, BCDMS, NMC, H1 94) used in our GRV98 tW fit compared to the predictions of the unmodified GRV98 PDFs (LO, dashed line) and the modified GRV98 PDFs fits (LO+HT, solid line); [a] for FZ proton, [b] for FZ deuteron, and [c] for the H1 and NMC proton data at low 5.

cross section according to

47r2CYEM 0.112mb GeV2 F 2

Q 2 ~ ( Y P ) = 7 F 2 = Q

(4) Finally, we froze the evolution of the GRV94 PDFs at a value of Q2 = 0.24 (for Q2 < 0.24), because GRV94 PDFs are only valid down to Q 2 = 0.23 GeV2.

In our analyses, the measured structure functions were corrected for the BCDMS systematic error shift and for the relative normalizations between the SLAC, BCDMS and NMC data ' s 3 . The deuterium data were corrected for nuclear binding effects 2 9 3 .

394

o.80 o.85 o,so o~050.s.50 0.076 O.SOO OBZb 0.060 0.8,b 1.000 0.0 0.2 0.4 0.8 0.8 nW 0.8 0.4 0.8 0.8

[ Q Z = l 5 ] [Q2=25l Y [ P I [CIY C U l

Figure 2. Comparisons to data not included in the fit. (a) Comparison of SLAC and JLab (electron) FzP data the resonance region (or fits to these data) and the predictions of the GRV98 PDFs with (LO+HT, solid) and without (LO, dashed) our modifications. (b) Comparison of photoproduction data on protons to predictions using our modified GRV98 PDFs. (c) Comparison of representative CCFR vp and Fp on iron at 55 GeV and the predictions of the GRV98 PDFs with (LO+HT, solid) and without (LO, dashed) our modifications.

In this publication we update our previous studies, which were done with a new improved scaling variable &,,, and fit for modifications to the more modern GRV98 LO PDFs such that the PDFs describe both high energy and low energy electron/muon data. We now also include NMC and H1 94 data at lower 2. Here we freeze the evolution of the GRV98 PDFs at a value of Q2 = 0.8 (for Q2 < 0.8), because GRV98 PDFs are only valid down to Q2 = 0.8 GeV2. In addition, we use different photoproduction limit multiplicative factors for valence and sea. Our proposed new scaling variable is based on the following derivation. Using energy momentum conservation, it can be shown that the fractional momentum 5 = (pz + p0)/(Pz +.PO) carried by a quark of 4-mometum p in a proton target of mass M and 4-momentum P is given by [ = XQ’~/[O.~Q~(~+[~+

395

where 2Qt2 = [Q2 + Mf2 - Mi2] + [(Q2 + Mf2 - Mi2)2 + 4Q2(Mi2 + P;)]’l2. Here Mi is the initial quark mass with average initial transverse mo-

mentum PT and Mf is the mass of the quark in the final state. The above expression for 5 was previously derived for the case of PT = 0. Assuming Mi = 0 we use instead:

5, = x(Q2 + B + Mf2)/(0.5Q2(1 + [l + ( ~ M Z ) ’ / Q ~ ] ~ / ~ ) + Ax) Here Mf=O, except for charm-production processes in neutrino scatter-

ing for which Mf=1.5 GeV. For <, the parameter A is expected to be much smaller than for x, since now it only accounts for the higher order (dynamic higher twist) QCD terms in the form of an enhanced target mass term (the effects of the proton target mass are already taken into account using the exact form in the denominator of 5, ). The parameter B accounts for the initial state quark transverse momentum and final state quark ef fect ive AMf2 (originating from multi-gluon emission by quarks).

Using closure considerations l1 (e.g. the Gottfried sum rule) it can be shown that, at low Q2, the scaling prediction for the valence quark part of F2 should be multiplied by the factor K=[1-G&(Q2)][1+M(Q2)] where GD = l/(l+Q2/0.71)2 is the proton elastic form factor, and M(Q2) is related to the magnetic elastic form factors of the proton and neutron. At low Q2, [l- G&(Q2)] is approximately Q2/(Q2 +C) with C = 0.71/4 = 0.178. In order to satisfy the Adler Sum rule l2 we add the function M(Q2) to account for terms from the magnetic and axial elastic form factors of the nucleon). Therefore, we try a more general form Kua1e,,e=[l-G&(Q2)][Q2+C2u]/[Q2 +C1,], and KSea=Q2/(Q2+Csea). Using this form with the GRV98 PDFs (and now also including the very low x NMC and H1 94 data in the fit) we find A=0.419, B=0.223, and clu=0.544, C2,=0.431, and Csea=0.380 (all in GeV2, x2 = 1235/1200 DOF). With these modifications, the GRV98 PDFs must also be multiplied by N=1.011 to normalize to the SLAC F2p data. The fit (Figure 1) yields the following normalizations relative to the SLAC F2p data (sLAC~=0.986, BCDMSp=0.964, BCDMs~=0.984, NMCp=1.00, NMC~=0.993, Hlp=0.977, and BCDMS systematic error shift of 1.7). (Note, since the GRV98 PDFs do not include the charm sea, for Q2 > 0.8 GeV2 we also include charm production using the photon- gluon fusion model in order to fit the very high v HERA data. This is not needed for any of the low energy comparisons but is only needed to describe the highest Y HERA electro and photoproduction data).

Comparisons of predictions using these modified GRV98 PDFs to other data which were not included in the fit is shown in Figures 2 and 3. From

396

0.3, . . . , . I " ' I " ,

- - 0.2 0.4 0.6

0.0 t 0.0

x O . S C . . . , . . . , . . , 4

0.1

0.0 0.3

E-4 .0 GeV theta=30 l . 6 c Q a C Z . 7

. 0.4 0.5 0.6 0.7 0.8 0.9

x

E-4 .0 GeV theta=30 l . 6 c Q a C Z . 7

. 0.4 0.5 0.6 0.7 0.8 0.9

Deuteron CRV98L.O VB - __

0.2 0.5 1.0 2.0 5.0 10.0 20.0 Pbeam (GeV) [b]

0.3

E = 3 . Z GeV theta=27

0.1

0.4 0.6 0.8 0.0

0.2 x

0 . 2 0 1 . . . I . . . . , . . I

0.05

0.00 0.4

E = 4 . 0 GeV

. . 0.5 0.6 0.7 0.8 0.9

1.02

Shadowing effect

o.e+ , , , , , , 1 0.2 0.5 1.0 2.0 5.0 10.0 20.0

Pbeam (GeV) [ C ]

Figure 3. Comparisons to data on deuterium which were not included in our GRV98 t,,, fit. (a) Comparison of SLAC and JLab (electron) F2d data in the resonance region and the predictions of the GRV98 PDFs with (LO+HT, solid) and without (LO, dashed) our modifications. (b) Comparison of photoproduction data on deuterium to predictions using our modified GRV98 PDFs (including shadowing corrections). (c) The shadowing corrections t.hat were applied to the PDFs for predicting the photoproduction cross section on deuterium.

duality l4 considerations, with the Cw scaling variable, the modified GRV98 PDFs should also provide a reasonable description of the average value of FZ in the resonance region. Figures 2(a) and 3(a) show a comparison between resonance data (from SLAC and Jefferson Lab, or parametrizations of these data 15) on protons and deuterons versus the predictions with the standard GRV98 PDFs (LO) and with our modified GRV98 PDFs (LO+HT). The modified GRVB98 PDFs are in good agreement with SLAC and JLab resonance data down to Q2 = 0.07 (although resonance data were not included in our fits). There is also very good agreement of the predictions of our modified GRV98 in the Q2 = 0 limit with photoproduction data on protons and deuterons as shown in Figure 2(b) and 3(b). In predicting the photoproduction cross sections on deuterium, we have applied shadowing corrections l6 as shown in Figure 3(c). We also compare the predictions with our modified GRV98 PDFs (LO+HT) to a few representative high

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energy CCFR vp and V p charged-current differential cross sections 4J3 on iron (neutrino data were not included in our fit). In this comparison we use the PDFs to obtain F2 and xF3 and correct for nuclear effects in iron The structure function 2xF1 is obtained by using the Rvrorld fit from reference '. There is very good agreement of our predictions with these neutrino data on iron at 55 GeV (assuming that vector and axial structure functions are the same). We are currently working on further corrections to account for the fact that at low energies, the vector and axial structure functions are different.

References

1. A. Bodek and U. K. Yang, (hep-ex/0203009) Nucl.Phys.Proc.Suppl.l12:70- 76,2002

2. U. K. Yang and A. Bodek, Phys. Rev. Lett. 82, 2467 (1999). 3. U. K. Yang and A. Bodek, Eur. Phys. J. C13, 241 (2000). 4. U. K. Yang, Ph.D. thesis, Univ. of Rochester, UR-1583 (2001). 5. L. W. Whitlow et al. (SLAC-MIT) , Phys. Lett. B282, 433 (1995); A. C.

Benvenuti et al. (BCDMS) , Phys. Lett. B237, 592 (1990); M. Arneodo et al. (NMC), Nucl. Phys. B483, 3 (1997).

6. H. Georgi and H. D. Politzer, Phys. Rev. D14, 1829 (1976); R. Barbieri et al., Phys. Lett. B64, 171 (1976), and Nucl. Phys. B117, 50 (1976); J. Pestieau and J. Urias, Phys. Rev. D8, 1552 (1973).

7. A.L. Kataev et al., Phys. Lett. B417,374 (1998), and also hep-ph/0106221; J. Bluemlein and A. Tkabladze, Nucl. Phys. B553, 427 (1999).

8. A. Bodek, U. K. Yang, hep-ex/0210024 , J. Phys. G. Nucl. Part. Phys. 29, 1 (2003); A. Bodek and U. K. Yang, To be published in Proceeding of NUINTO2 2nd Workshop on Neutrino - Nucleus Interactions in the Few GeV Region (NuIntOl), Irvine CA, 2002; A. Bodek and U. K. Yang, hep- ex/0301036.

10. A. Donnachie and P. V. Landshoff, Z. Phys. C 61,139 (1994); B. T. Fleming et al. (CCFR), Phys. Rev. Lett. 86, 5430 (2001).

11. S. Stein et al., Phys. Rev. D12, 1884 (1975); K. Gottfried, Phys. Rev. Lett. 18, 1174 (1967).

12. S. Adler, Phys. Rev. 143, 1144 (1966); F. Gillman, Phys. Rev. 167, 1365 (1968).

13. U. K. Yang et al. (CCFR), Phys. Rev. Lett. 87, 251802 (2001). 14. E. D. Bloom and F. J. Gilman, Phys. Rev. Lett. 25, 1140 (1970). 15. C. Keppel, Proc. of the Workshop on Exclusive Processes at High PT,

Newport News, VA, May (2002). 16. Badelek and Kwiecinski, Nucl. Phys. B370, 278 (1992).

9. A. Bodek et al., Phys. Rev. D20, 1471 (1979).

CHARMONIUM AND B-QUARK PRODUCTION AT HERA-B

T.ZEUNER University of Saegen, 0-57068 Saegen, Germany

E-mail: zeunerOelfil .physik. uni-siegen. de

FOR THE HERA-B COLLABORATION

Results from the HERA-B experiment based on data collected in 2000 are presented in this paper. During the shutdown of the HERA accelerator in 2000/01 the HERA- B detector and trigger were improved. HERA-B data taking restarted in October 2002 and ended at begin of March 2003 for a HERA shutdown. A first look at the statistics gathered in 2002/03 will be presented.

1. Introduction

HERA-B is a fixed target experiment at the HERA 920 GeV/c proton storage ring at DESY. The pN (N=p,n) c.m.s. energy is fi = 41.6 GeV. During detector comissioning in 2000 HERA-B recorded a dedicated data sample based on a dilepton J /+ trigger for studies of b-quark and Charmo- nium production. Measurements of the bb production cross section a(bb) on a nucleus of atomic number A and of the ratio of xc and J / $ production cross sections a(x,)/a(J/+) were performed.

After a shutdown of the HERA accelerator for a luminosity upgrade in 2000/01 HERA-B collected a new data sample from October 2002 till the beginning of March 2003.

2. Detector, Trigger and Data sample

The HERA-B detector 394 is a magnetic forward spectrometer. The main components of the detector are a silicon micro-strip vertex detector (VDS), a gaseous mircostrip detector with gas electron multipliers (ITR) , honey- comb drift chambers (OTR), and a large acceptance 2.13 T.m magnet. The particle identification is performed by a ring imaging Cherenkov ho- doscope (RICH), an electromagnetic calorimeter (ECAL), and a muon system (MUON). The target assembly consists of two wire stations, each con-

398

399

taining 4 independently moveable target wires of different materials. The analysis results presented are based on data samples collected in 2000, part of the data was taken with a carbon wire; the other part with two wires (carbon and tungsten) operated simultaneously. In the two wire runs the wires were separated by 3.3 cm along the beam direction. The resolution of the reconstructed dilepton vertices of 0.6 mm along the beam direction allows a clear association of the interaction to a specific target wire. The data were collected by triggering on dimuon and dielectron signatures. A multilevel trigger chain reduces the initial interaction rate of 5 MHz to the final output rate of 20 Hz. A total of x 450,000 dimuon and x 900,000 dielectron candidates were recorded under these conditions in the data taking of 2000. The ITR and the inner part of the MUON system were not included in the trigger. Thus the trigger acceptance for J / $ was limited to the XF range -0.25 5 XF 5 0.15, XF being the Feynman-x variable. Dur- ing the luminosity upgrade shutdown of the HERA accelerator in 2000101 major efforts were undertaken to improve the detector and trigger performance of the HERA-B experiment. As a result of the upgrade work the rate of J / $ per hour data taking could be increased from about 35 J / $ per hour to a value of 1200 - 1400 J / $ per hour. In total HERA-B recorded in 2002103 x 150 . lo6 dilepton triggered events, resulting in about 350,000 reconstructed J / $ -i (e+e-/p+p-) decays.

3. Measurement of bb cross-section

The bb production cross section (a;) on a nucleus of atomic number A is obtained from the inclusive reaction

p A -i bbX with bb -i J /$Y -i (e+e-/p+p-)Y. (1)

The b-hadron decays into J / $ are distinguished from the large prompt J / $ background by exploiting the b lifetime in a detached vertex analysis'. In order to minimize the systematic errors related to detector and trigger efficiencies and to remove the dependence on the absolute luminosity determination, the measurement is performed relative to the known prompt J / $ production cross section (a;). Our measurement covers the J / $ Feynman- x range -0.25 5 XF 5 0.15. Within our acceptance, the b to prompt cross section ratio can be expressed as:

400

where A a i and Aa$ are the b + J /$ and prompt J/$ cross sections limited to the mentioned XF range, NB and N p are the observed number of detached b + J / $ and prompt J/$ decays. ER is the relative detection efficiency of b + J / $ with respect to prompt J/$, including contributions from the trigger, the dilepton vertex and the J/$ reconstruction and E$% is the efficiency of the detached vertex selection (ERE$" = 0.41 f O.O1(pfp- channel); 0.44 f 0.02(e+e- channel)). The branching ratio Br(bb + J / $ Y ) in hadroproduction is assumed to be the same as that measured in Z decays, with the value 2 . (1.16 f 0.10)%13. The prompt J / $ production cross section per nucleon, a(pN + J / $ X ) = a$/Aa, was previously measured by two fixed target experimentsgJO. After correcting for the most recent measurement of the atomic number dependence (a = 0.955 f 0.005)'l and rescaling12 to the HERA-B c.m.s. energy, we obtain a reference prompt J / $ cross section of a(pN + J / $ X ) = (357 f 8(stat) f 27(sys)) nb/nucleon. Since no nuclear suppression has been observed in D-meson production and a similar behavior is expected in the b channel, we assume a = 1.0 for the bb production cross section results presented here; i.e. a; = a(pN + bb) . A. The individual measurements of A a i in the muon and electron channels are combined in a likelihood maximization on the detached candidates. The fit provides the final result of the bb production cross section, to compare the result with theoretical predicitions the measurement has been extrapolated to the full XF range. The final result for the total bb production cross section is:

a(bb) = 32 (stat) ?: (sys) nb/nucleon. (3) The main systematic errors which are not related to the final bz statistics are due to the prompt J / $ reference (ll%), the branching ratio Br(bb + J / $ Y ) (9%), the trigger and detector simulation (5%) and the MC models for prompt J / $ (3.5%) and bb (5%) production. Uncertainties in the J / $ invariant mass fits are dominated by the low statistics of the observed detached events (?;!% for muons and 13% for electrons). Figure 1 shows the HERA-B result compared with the latest QCD calculations beyond next-to-leading order (NLO)'3, and compared to previous experimental results of E78g7 and E771' obtained at 800 GeV proton interactions on Au and Si, respectively.

4. Charmonium production

At present, several theoretical models exist to describe the production of heavy flavours in hadronic collisions (e.g. Colour Singlet Model (CSM),

40 1

h

E771 ...... .......

' R. Bonciani et al. -1

lo 4od ' ' 5o0 ' ' 6o0 ' ' ioo ' ' so0 ' . 900 ' id,, Proton energy (GeV)

Figure 1. and with theoretical predictions.

The comparison of the HERA-B (2000) o(b6) value with other experiments

Non-Relativistic QCD factorisation approach (NRQCD), Colour Evapora- tion Model (CEM)). The dependence of the ratio of production cross sections for different states, e.g. the ratio of xc and J / $ production cross sections g ( x c ) / o ( J / $ ) on fi or the projectile allows one to distinguish among different models. For HERA-B the specific decay xc -+ J / $ y is advantageous since the decay signature J /$ + -!+-!- (-! = p, e) is the standard dilepton trigger. Furthermore, several systematic errors cancel in the ratio, and the only significant difference in the detection of the xc and the J / $ is the photon reconstruction. Due to the small branching ratio of xCo + J /$y , (6.6 f 1.8) . 10-3Ref.14, the xCo contribution to the reconstructed xc signal can be neglected. In most experiments the energy resolution is insufficient to resolve the xcl and x c 2 states, so that one usually quotes the ratio

Here, u( J / $ ) is the sum of production cross sections for direct J / $ and J / $ produced in decays of xc and $(2s). The measurement of R,, in interactions of 920 GeV protons with carbon and titanium nuclei was performed 2 .

The xc is observed in the decay xc + J / $ y + -!?y (-! = p, e) using the mass difference A M = M(-!+-!-y) - Ad(-!+-!-) between the invariant mass of the (-!+-!-y) system and the invariant mass of the lepton pair. An excess of events with respect to the combinatorial background determines the number of xc candidates Nxc , from which the value R,, can be calculated

402

as follows:

where NJ/+ is the total number of reconstructed J /+ + f?+l- decays used for the xc search. The factor E~ M 30% is the photon detection efficiency. The value pE represents the ratio of trigger and reconstruction efficiencies for J /+ and J / $ from xc decays and for all J/+. Since the kinematics, triggering and reconstruction of direct J / + and J / + from xc decays are very similar, pE is close to unity. The final result obtained from the 2000 data sample is:

R,, = 0.32 f 0.06 (stat) f 0.04 (sys) (6) The result has been obtained by averaging over the samples obtained in the electron and muon channel on titanium and carbon wire. Figure 2 shows

'I pA (HERA-B) 0.8

Figure 2. Comparison of HERA-B measurement of R,, with other pp, pA and xp, xA experiments. Also shown are predictions for pN and xN interactions obtained from Monte Carlo based on the NRQCD(solid), CSM(dashed). The CEM predicts a constant value. The dot-dashed line is the average of all measurements.

the HERA-B result in comparison to previous data and predictions from the different models. The result agrees with most previous proton and pion beam measurements, neglecting any possible energy dependence. It agrees also with the predictions of the NRQCD factorisation approach, whereas it falls significantly below the predictions of the Color Singlet Model.

5. Outlook to 2002/03 data sample

During the physics run in 2002103 the data sample of 2000 was increased by about a factor 35. In total about 150. lo6 dilepton triggered events have

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been recorded which yield 350,000 reconstructed J/$ in the electron and muon channel together. The Feynman-x acceptance covered is -0.35 5 x 5 0.15. The data has been recorded with carbon and tungsten wires, a large fraction using both wires simultaneously. This sample will yield the most precise value of the bb production cross section at fixed target energies. The determination of R,, will be possible with a significantly improved statistical accuracy. One of the main goals is the investigation of nuclear A-dependence effects in Charmonium production. In addition to the dilepton triggered data HERA-B recorded about 250. lo6 minimum bias events for QCD studies.

6. Conclusion

With the limited statistics aquired in a short physics run during the HERA- B commisioning in 2000 HERA-B provided first physics results on the bb production cross section and a measurement of the fraction of J / $ produced via radiative xe decays. The HERA accelerator shutdown in 2000101 was used to improve the HERA-B detector and trigger. With the improved detector HERA-B recorded during a physics run in 2002103 about 150 . lo6 dilepton candidates leading to about 350,000 reconstructed J/$. The increased statistics will be used to improve the measurements done with the 2000 data sample and to investigate nuclear A-dependence effects in Charmonium production.

References 1. HERA-B Collaboration, I. Abt et al., l3ur.Phys.J. C26, 345 (2003). 2. HERA-B Collaboration, I. Abt et al., Phys. Lett. B561, 61 (2003). 3. HERA-B Collaboration, E. Hartouni et al., HERA-B Design report, DESY-

4. HERA-B Collaboration, HERA-B Status report, DESY-PRC-00-04, (2000). 5. R. Bonciani et al., Nucl. Phys. B529, 424 (1998). 6. N. Kidonakis et al., Phys. Rev. D64, 114001 (2001) 7. D. M. Jansen et al., Phys. Rev. Lett. 74, 3118 (1995) 8. T. Alexopoulos et al., Phys. Rev. Lett. 82, 41 (1999). 9. M. H. Schub et al., Phys. Rev. D52, 1307 (1995). 10. T. Alexopoulos et al., Phys. Rev. D55, 3927 (1997). 11. M. J. Leitch et al., Phys. Rev. Lett. 84, 3256 (2000). 12. T. Alexopoulos et al., Phys. Rev. B374, 271 (1996). 13. D. E. Groom et al., Eur. Phys. J . C15, 1 (2000). 14. C. Caso et al., Review of Particle Physics, Eur. Phys. Jour. C15, 1 (2000)

PRC-95-01, (1995).

AMSOl RESULTS

P. ZUCCON* INFN - Sezione di Perugia

via Pascoli I-06123 Perugia, ITALY

E-mail: Paolo. Zuccon@pg. infn. i t

AMSOl is a magnetic spectrometer that flew on board the Space Shuttle Discovery in the June 1998 during the STS91 mission. During this precursor flight AMSOl made an accurate measurement of the cosmic rays fluxes in the rigidity range 0.1-200 GV over the whole area enclosed between f51° of latitude. These measurements allowed to put a limit of 1.1 . 10W6 on the presence of anti-He in the cosmic rays fluxes and allowed an accurate determination of the primary H and He fluxes. Furthermore for the first time the subcutoff, or secondary, spectra have been measured with high precision and with an extensive geographical coverage.

1. Introduction

The disappearance of the antimatter 1,2,3 and the presence at all scales in our universe of a non luminous components of matter (dark matter) 4*5 are two of the most intriguing mysteries in our current understanding of the structure of the Universe. To study these problems, a high energy physics experiment, the Alpha Magnetic Spectrometer (AMS)' , is scheduled for installation on the International Space Station in 2005. Goal of AMS is to perform a three year long measurement, with the highest accuracy, of the composition of Cosmic Rays in the rigidity range 0, l GV to several TV. In preparation for this long duration mission AMS a ten days precursor mission on board of the space shuttle Discovery mission STS-91 in June 1998. This high statistics measurement of CR in space, enabled, for the first time, the systematic study the behavior of primary CR near Earth in the rigidity interval from 0.1 to 200 GV , at all longitudes and latitudes up to f51.7'. In this paper we present some relevant results obtained by AMS during the precursor mission.

*on behalf of AMS collaboration

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405

Figure 1. AMS 01 on the Discovery STS-91 precursor flight.

2.

Search of antimatter requires the capability to identify with the highest degree of confidence, the mass of particle traversing the experiment together with the absolute value and the sign of its electric charge. The AMS configuration in 1998 on the Shuttle Discovery (Fig.1) includes a permanent Magnet, Anticounter (ACC) and Time of Flight (ToF) scintillator systems, a large area, high accuracy Silicon Tracker and an Areogel Threshold Cherenkov counter. The magnet is based on recent advancements in permanent magnetic material and technology which make it possible to use very high grade N d - F e - B to build a permanent magnet with BL2 = 0.15Tm2 weighting less than 2 tons.

A charged particle traversing the spectrometer triggers the experiment through the ToF system, which measures the particle velocity with a resolution of - 120ps over a distance of - 1.4m ll. The pattern recognition and tracking is performed using the large area (- 7m2 ), high accuracy Silicon T r a ~ k e r ~ ? ~ , which, for the Space Station mission, will be covered with 2300, high purity, double sided, 300 pm thick silicon wafers, following the technology developed in Italy by INFN for the Alephlo and L3* vertex detectors at LEP.

The momentum resolution for AMS on the precursor mission was about (% - 7%) at 10 GV, reaching (9 N 100%) at about 500 GV.

Four ToF scintillators layers and up to eight Silicon Tracker layers measure z , allowing a multiple determination of the absolute value of the

The AMSOl experiment and the STS-91 mission

406

80 60

g 40

0 -20 -40 -60 -80

3

Y 20

0 50 I 0 0 150 -150 -100 -50 Longitude

Figure 2. to different CR rates, lower at the equator and larger close to the poles.

Shuttle orbits during the STS-91 mission: the different intensities correspond

particle charge. Using the various measurement it is possible to identify the type of particle traversing the magnet with a background rejection which for anti-matter searches is expected to reach one part in 10'. During the period June Znd to June 12th 1998 the Shuttle Discovery has performed 154 orbits at an inclination 51.7" and at an altitude varying between 390 to 350 Icm. During the mission AMS collected a total of about 100 Million triggers(Fig.2), almost all results published so far 12y13714,15316~17 were obtained with data collected during well defined attitude periods with AMS pointing at 0", 20" and 45O with respect to zenith (deep space).

These data are the first high quality CR data collected with a magnetic spectrometer located outside the atmosphere. These data allow a direct and accurate measurement of the CR composition and spectra, as well as a systematic study of the effects of the geomagnetic field.

The measurement of the proton as a function of the geomagnetic latitude (Fig. 3 a - 3 ~ ) ~ shows that, in addition to the primary CR spectrum visible above the geomagnetic cutoff, there is a substantial second spectrum, extending to much lower energy and exhibiting some significant latitude dependence close to the equator. These particles cannot come from the deep space, they are on forbidden orbits, but are produced in the interaction of the primary CR with the top layers of the atmosphere. A characteristic of the second spectrum is that it is up-down symmetric (Fig. 3d-3f).

Second spectra with similar geomagnetic latitude dependence have been detected by AMS in the low energy region of the spectra of ef14, D17118 and, although with weaker intensity, 3He . Fig. 4 show the measured fluxes for electrons and positrons.

A thoughtful study of the features and the origin of this second spectrum

407

Kinetic Energy (GeV)

Figure 3. Proton spectra measured by AMS for different geomagnetic latitude intervals.

10.' 1 10 10" 1 10 E (GeV)

Figure 4. latitude intervals.

Electrons and positrons spectra measured by AMS for different geomagnetic

has been carried 0n19921~20722. Adding all data collected above the geomagnetic cutoff it is possible to

obtain a precise estimate of the primary CR differential flux. It is interesting to compare the AMS measurement of the primary with previous results obtained with stratospheric balloons23~24~25~26~27. Fig.5-left shows the comparison for the proton spectrum, multiplied by E2.5 . The improved statistical significance and the wider energy interval covered by AMS data is evident: thanks to the improved accuracy obtained with only few days in space, it is possible to clarify the situation resulting from the data pub-

408

Figure 5. Left panels: Primary proton(a) and Helium(b) fluxes measured by AMS compared with existing balloons measurements; the lines are parameterizations used in atm. v fluxes calculation: dashed line HKKM 28, dot-dashed Bartol Right panel: Antimatter limits30.

lished over the last 15 years by the various Collaborations using different implementations of the NASA New-Mexico and by the BESS C~l l abora t ion~~ . Similar consideration apply for the comparison of the measurement of Helium primary (Fig.5-left). Both for protons as well as for Helium, AMS shows a nice agreement with the measurement of the BESS C~l l abora t ion~~ . Using the large He sample collected by AMS a search for anti-He candidates has also been performed. Within 2.3 Millions He events no anti-He candidates have been found, up to a rigidity of 140 GV. Assuming identical He and anti-He spectra we obtain a model independent upper limit of 1.1 . lop6 over the rigidity interval 1 to 140 GV, which can be compared to previous results (Figbright)

3. Conclusions

The first mission of the Alpha Magnetic Spectrometer, although lasting only ten days, has been scientifically very rewarding, allowing for the first time a very detailed measurement of high energy cosmic rays outside the atmosphere. In addition to the most accurate measurements obtained so far for the primary spectra over most of the earth surface, these results have shown the existence of a substantial second spectrum of high energy particles trapped within low altitude belts. AMS is currently being refurbished(AMS02) to be ready for a three years mission in 2005. A stronger magnetic field from a superconducting magnet, B = 0.7T , a fully

spectrometer

group

409

equipped Silicon Tracker, a Transition Radiation Detector, a Ring Imaging Cherenkov (RICH) detector and an Electromagnetic Calorimeter, will allow precise particle id up to O(TeV ). For a discussion of the AMSO2 physical capabilities see the contribution of R. Henning in these proceedings.

This work has been partially supported by the Italian Space Agency (ASI) under contract ASI I/R/211/00.

References

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21. P. Zuccon et al. to appear in Astropart. Phys. 22. E. Fiandrini et al., J. Geophys. Res., 107A6, (2002). 23. BESS98, T. Sanuki et al., Astrophys. J . , 545, 1135 (2000). 24. CAPRICE94, M. Boezio et al., ApJ., 518, 457 (1999). 25. IMAX92, W. Menn et al., The Astroph. J., 533, 281 (2000). 26. MASS91, R. Bellotti et al., Phys. Rev., D60, 52002 (1999). 27. LEAP87, E. S. Seo et al., ApJ 378, 763 (1991). 28. HKKM, M. Honda et al., Phys. Rev. 52, 4985 (1995). 29. BARTOL, P. Lipari and T. Stanev, Talk at Now 2000 Conference, (2000). 30. G. Badhwar et al., Nature 274, 137 (1978); A. Buffington et al., ApJ, 248,

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LIST OF PARTICIPANTS

P. Amaral K. Anikeev I. Bailey M. Baker F. Beaudette A. Beloborodov A. Buckley B. Campbell N. F. Castro G.-P. Chen D. Costanzo J. D’Hondt G. Dubois-Felsmann J. Ellis A. Frolov D. Futyan C. Gagliardi A. Geiser T. Gershon K. Graham H.-A. Gustafsson S. Haug R. Henning A. Hicheur M. Hohlfeld L. C. Howlett G. Iacobucci E. Jankowski S. Jolly R. Keeler F. Khanna S. P. Kim J. May

University of Chicago Massachusetts Institute of Technology / FERMILAB University of Victoria Brookhaven National Laboratory Laboratoire de l’Acce1erateur Lineaire CITA / University of Toronto PPARC / University of Cambridge University of Alberta LIP - Lisbon CMU Group / Carnegie Mellon University Lawrence Berkeley Laboratory Vrije Universiteit Brussel Caltech CERN CITA / University of Toronto CERN Texas A & M University DESY Hamburg JSPS / KEK Queens University Lund University University of Oslo Massachusetts Institute of Technology LAPP Institut Fuer Physik - ETAP University of Sheffeld INFN Bologna / DESY Hamburg University of Alberta Imperial College University of Victoria University of Alberta Kunsan National University Lawrence Berkeley Laboratory

41 7

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M. Klute R. Kowalewski M Kupper T. Lastovicka D. Leahy S. H. Lee E. Lipeles W. Lockman D. Machin N. Malden D. Matrasulov D. Maybury G. Medin S. Mine B. Morgan D. Nitz R. Ofierzynski C. Plager D. Pogosyan T. Sakaguchi H. Schatz K. Scholberg S. Sengupta R. Sobie L Stonehill A. Squires K. Tokushuku K. Trabelsi R. Vasquez M. Vincter M. Wielers B. Winer U.-K. Yang T. Zeuner P. Zuccon

FERMILAB / Bonn University University of Victoria Weizmann Institute of Science DESY Zeuthen University of Calgary Seoul National University Caltech Santa Cruz Institute for Particle Physics University of Bristol Manchester University University of Alberta University of Alberta Humboldt University / DESY Zeuthen University of California, Irvine University of Sheffield Michigan Technological University CERN University of Illinois University of Alberta University of Tokyo Michigan State University Massachusetts Institute of Technology University of Alberta IPP / University of Victoria University of Washington Mount Allison University KEK / INPS University of Hawaii Purdue University University of Alberta ISN Grenoble Ohio State University Enrico Fermi Institute DESY Hamburg / University of Siegen INFN Sezione di Perugia

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