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Instructions to authorsAims and ScopePhysics Letters B ensures the rapid publication of letter-type communications in the fields of Nuclear Physics, Particle Physicsand Astrophysics. Articles should influence the physics community significantly.

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Theoretical High Energy Physics (General Theory) preferably from southern EuropeJ.-P. Blaizot,Service de Physique Théorique, Orme des Merisiers, C.E.A.-Saclay, F-91191 Gif-sur-Yvette Cedex, France,E-mail address: [email protected]

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Theoretical High Energy Physics preferably from countries outside EuropeG.F. Giudice,CERN, CH-1211 Geneva 23, Switzerland, E-mail address: [email protected]

Theoretical High Energy Physics preferably from southern EuropeW. Haxton, Institute for Nuclear Theory, Box 351550, University of Washington, Seattle, WA 98195-1550, USA, E-mailaddress: [email protected]

Theoretical Nuclear Physics and Nuclear AstrophysicsP.V. Landshoff, Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Universityof Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK, E-mail address: P.V. [email protected]

Theoretical High Energy Physics preferably from northern EuropeV. Metag, II. Physikalisches Institut, Universität Giessen, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany, E-mail address:[email protected]. UNI-GIESSEN.DE

Experimental Nuclear PhysicsL. Rolandi, EP Division, CERN, CH-1211 Geneva 23, Switzerland, E-mail address: [email protected]

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Experimental High Energy Physics

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vi Instructions to authors

H. Weerts, 3247 Biomedical and Physical Sciences Building, Department of Physics and Astronomy, Michigan StateUniversity, East Lansing, MI 48824-1111, USA, E-mail address: [email protected]

Experimental High Energy PhysicsT. Yanagida, Department of Physics, Faculty of Science, University of Tokyo, Tokyo 113-0033, Japan, E-mail address:[email protected]

Theoretical High Energy Physics preferably from Asia

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Instructions to authors vii

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EDITORS

L. ALVAREZ-GAUMÉ J.-P. BLAIZOT M. CVETI CGENEVA SACLAY PHILADELPHIA, PA

M. DOSER J. FRIEMAN H. GEORGIGENEVA BATAVIA, IL CAMBRIDGE, MA

G.F. GIUDICE W. HAXTON P.V. LANDSHOFFGENEVA SEATTLE, WA CAMBRIDGE

V. METAG L. ROLANDI J.P. SCHIFFERGIESSEN GENEVA ARGONNE, IL

W.-D. SCHLATTER H. WEERTS T. YANAGIDAGENEVA EAST LANSING, MI TOKYO

VOLUME 577, 2003

Amsterdam – Boston – London – New York – Oxford – ParisPhiladelphia – San Diego – Shannon – St Louis – Tokyo

b

data

energyfuture a

ta of thematternst,the DM

Physics Letters B 577 (2003) 1–9

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Superheavy dark matter as UHECR source versus the SUGAR

M. Kachelrießa, D.V. Semikoza,b

a Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München, Germanyb Institute for Nuclear Research of the Academy of Sciences of Russia, 117312 Moscow, Russia

Received 2 July 2003; received in revised form 3 September 2003; accepted 1 October 2003

Editor: G.F. Giudice

Abstract

Decay or annihilation products of superheavy dark matter (SHDM) could be responsible for the end of the ultra-highcosmic ray (UHECR) spectrum. In this case, the south array of the Pierre Auger Observatory should observe in thesignificant anisotropy of UHECR arrival directions towards the galactic center. Here we use the already existing daSUGAR array to test this possibility. If decaying SHDM is distributed according a Navarro–Frenk–White (NFW) darkprofile with core radiusRc = 15 kpc and is responsible only for UHECRs above∼ 6 × 1019 eV, i.e., the AGASA excess, thethe arrival directions measured by the SUGAR array have a probability of∼ 10% to be consistent with this model. By contrathe model of annihilating SHDM is disfavoured at least at 99% C.L. by the SUGAR data, if the smooth component ofdominates the signal. 2003 Elsevier B.V. All rights reserved.

PACS: 98.70.Sa; 14.80.-j

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1. Introduction

Protons accelerated by uniformly distributed extgalactic astrophysical sources would be a perfect mimal explanation of the UHECR data above 1019 eV.However, protons with energyE > 4× 1019 eV loosequickly energy due to pion production on cosmic mcrowave background photons. Thus the proton sptrum should show the so-called Greisen–ZatsepKuzmin (GZK) cutoff [1], which is not observed bthe AGASA experiment [2]. Moreover, if the smascale clusters in the arrival directions of UHECR msured by AGASA [3] are due to point-like sources [4

E-mail address: [email protected] (D.V. Semikoz).

0370-2693/$ – see front matter 2003 Elsevier B.V. All rights reserveddoi:10.1016/j.physletb.2003.10.017

one can estimate their number [5]. This numbeso small that the nearest source should be locatethe distanceRmin ∼ 100 Mpc [6]. This means that thGZK cutoff is exponentially sharp atE ≈ 6× 1019 eVand even the data of the HiRes experiment [7]inconsistent with the expected proton spectrumThis inconsistency becomes even stronger if BL Lawhich show a statistically significant correlations wthe arrival directions of UHECR with energyE ∼(4–6)× 1019 eV [8], are sources of UHECR.

A possible solution to this problem would be texistence of superheavy dark matter (SHDM) [9,1Superheavy particles with massMX ∼ 1013–14 GeVcan be naturally produced during inflation and wobe today the dominant component of dark matter [1Such particles will concentrate in galactic halos a

.


2 M. Kachelrieß, D.V. Semikoz / Physics Letters B 577 (2003) 1–9

ibleeenDM

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the secondaries from their decay could be responsfor the highest energy cosmic rays. It has also bsuggested that not decays but annihilations of SHparticles produce the observed UHECRs [17].

By construction, this model has two clean signtures: the dominance of photons at the highest egies [9] and an anisotropy of the arrival directions wan increased flux from the Galactic center [12,13]. Ufortunately, both signatures are not very clean forpresent experiments. Indeed, at 95% C.L.,∼ 30% ofthe UHECR aboveE > 1019 eV can be photons [14which means that still most of UHECRs withE >

4 × 1019 eV can be photons without any contradtion to the experimental data. Since experiments innorthern hemisphere do not see the Galactic cethey are not very sensitive to a possible anisotroparrival directions of UHECR from SHDM. In contrasthe Galactic center was visible for the old AustraliSUGAR experiment.

The anisotropy of the arrival directions using dafrom the full sky was discussed in Refs. [15,1Ref. [15] compared the flux from the Galactic cento the one from the anti-center and found them tocomparable. Similarly, the full-sky harmonic analyincluding AGASA and SUGAR data from Ref. [16found no significant anisotropy. In this Letter, we ustwo-component energy spectrum of UHECRs consing of protons from uniformly distributed, astrophyscal sources and the fragmentation products of SHcalculated in SUSY-QCD. We compare their expecarrival direction distribution to the data of the SUGAexperiment using a Kolmogorov–Smirnov test. Cotrary to the harmonic analysis, this test allows to qutify directly the (dis-)agreement of the measured dtribution of arrival direction with the expected onethe SHDM model. We consider both decays and anhilations of SHDM.

The Letter is organized as follows: in Sectionwe discuss the status of the SUGAR data. The ctribution of SHDM to the UHECR spectrum is dicussed in Section 3. In Section 4 we perform an hmonic analysis of the arrival directions measuredthe SUGAR experiment. Then we use a KolmogoroSmirnov test in one and two dimensions to chethe consistency of the SUGAR data with the proability distribution of arrival directions expected foSHDM in Section 5. Finally we conclude in Setion 6.

2. Assessment of the SUGAR data

In order to use the SUGAR energy spectrum crectly we compare their data given in Refs. [20,2to the energy spectrum measured by the AGASAand HiRes experiments [7] in Fig. 1. RescalingSUGAR energies calculated with the Hillas prescrtion by 15% downwards,EHillas → EHillas/1.15,makes their data consistent with the ones frAGASA. The same is true for the HiRes spectrumthe energy is rescaled upwards by 25%.1 We have cho-sen arbitrary the AGASA spectrum as reference,changing the overall normalization of the spectrafects our results only weakly. As seen from Fig.the SUGAR spectrum has the ankle at the corplace aroundE ≈ 1019 eV and is consistent with thAGASA spectrum in the whole energy range. In pticular, the SUGAR spectrum also does not showGZK cutoff at the highest energies.

The rescaling of the SUGAR data downwards15% should be compared to the recent reevaluaof the energy conversion formula used in the HavePark experiment [22]. In this reference, the relatbetweenρ(600) and the primary energy has berecalculated using QGSJET [24] and comparedthe original relation suggested by Hillas. The ncalibration results in∼ 30% lower primary energies.

The SUGAR experiment was a very sparse arradetectors and its energy determination of each sinevent was therefore rather unprecise. Thus, we suse as a statistical test later on a method which reonly on the total flux measured by the SUGAR arrbut uses not the energy of each single event. Sincethe rescaling of the energies measured by SUGEHillas → EHillas/1.15, its measured flux is consistewith newer experiments like AGASA and HiRes, wconclude thaton average the energy determination ithe SUGAR experiment was reliable.

The energy conversion formula used in SUGARconnect the measured muon numberNµ with the pri-mary energy assumes that the primary is a hadFor photon primaries, predicted to be dominantthe SHDM model, the muon content of the showis smaller by a factor 5–10 [23]. Thus the energ

1 The aperture of HiRes is energy dependent; the rescalingperform should be seen therefore just as a crude approximation

M. Kachelrieß, D.V. Semikoz / Physics Letters B 577 (2003) 1–9 3

fluence
Fig. 1. UHECR spectrum measured by the AGASA, HiRes and SUGAR experiments. We scale the SUGAR spectrum down byE/1.15 and theHiRes spectrum up by 1.25×E using the AGASA spectrum as reference. The overall normalization of the spectra has only a weak inon our results.
m

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of photon events is expected to beunderestimatedby the SUGAR experiment. The SUGAR spectrushown in Fig. 1 would be unchanged at energiesE 5 × 1019 eV, i.e., at energies where all three expements agree after rescaling.

The angular acceptanceη(δ) as function of decli-nationδ averaged over time of an experiment at ggraphical latitudeb (b = −30.5 for SUGAR) observ-ing showers with maximal zenith angleθmax is

η(δ)∝αmax∫0

dα cos(θ)

(1)

∝ [cos(b)cos(δ)sin(αmax)+ αmaxsin(b)sin(δ)

],

where

(2)ξ = cos(θmax)− sin(b)sin(δ)

cos(b)cos(δ)

and

(3)αmax =arccos(ξ), for −1 ξ 1,π, for ξ <−1,0, for ξ > 1.

We have checked that the zenith angle distributof the SUGAR events agrees with the theoreti

predicted one,dNth ∝ dθ sin(θ)cos(θ), aboveE 4 × 1019 eV. At lower energies, the acceptance ofexperiment becomes energy dependent and deviafrom dNth start to grow.

3. Superheavy dark matter contribution toUHECR spectrum

We fix the contribution of SHDM to the totaUHECR flux following the assumptions of Ref. [18we assume that no galactic astrophysical sourcestribute to the cosmic ray flux above 1019 eV andthat the extragalactic cosmic ray flux can be chacterized by an injection spectra of protons withsingle power law,jex(E) ∝ E−α . For the choice ofα = 2.7, this energy spectra modified by redshe+e− and pion production fits very well the mesured spectra belowE < (6–8) × 1019 eV [18]. Theonly difference with [18] is that we take into acount that total number of sources is small [6],the small scale clusters measured by the AGASAperiment are due to point-like sources. The AGAdata favor as minimal distance to the nearest soDmin ∼ 100 Mpc [6]. Therefore, the contribution o


tons fromic

Fig. 2. UHECR spectrum measured by AGASA experiment. Protons from extragalactic sources contribute below the GZK cutoff, phoSHDM decays mainly above the GZK cutoff; for hard, 1/E2.3 (left panel) and soft, 1/E2.7 (right panel) injection spectrum of extragalactprotons.

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protons from extragalactic sources has a sharpoff. For the calculations of the proton spectrumused the code [28]. We use then the SUSY QCD frmentation functionsD(x,MX) of superheavy particles with massMX calculated in Ref. [19] to modethe fluxjDM(E)∝Dγ (x,MX). The total UHECR fluxis thus

(4)j (E)= (1− ε)jex(E)+ εjDM(E).

We fix the constantε determining the relativecontribution of SHDM to the UHECR flux byfit of j (E) to the AGASA data [2]. In Fig. 2, weshow our fits for the case of a harder 1/E2.3 (left)and a softer 1/E2.7 (right) injection spectrum oextragalactic protons. In the first case, the contribuof SHDM to the UHECR spectrum below the GZcutoff is minimal and starts to dominate onlyhighest energiesE > 6 × 1019 eV. For this choiceof injection spectrum, the contribution of galacsources dominate forE < 1019 eV. In the secondcase, SHDM gives a larger contribution at lowenergiesE < 6 × 1019 than before, and again starto dominate atE > 6 × 1019 eV. Note, that mosUHECRs aboveE > 6×1019 eV should be photons ithis model, but this does not contradict the rather wexisting bound of 30% of photons atE > 1019 eV[14].

In the following, we shall use conservatively thcase of the harder 1/E2.3 injection spectrum if nootherwise stated. Then the contribution of SHDMthe UHECR spectrum is fixed by Eq. (4).

4. Harmonic analysis

In order to compare SUGAR data with an unifodistribution typical for extragalactic sources we haperformed an one-dimensional harmonic analysis.usual we sum

(5)ak = 2

n

n∑a=1

cos(kφ) and bk = 2

n

n∑a=1

sin(kφ)

over then data points.The amplituderk and phaseφk of thekth harmonic

are given by

(6)rk =√a2k + b2

k and φk = arctan(bk/ak)

with chance probability

(7)pch = exp(−nr2

k /4).

The direction to the signal isφ = kφk.Results of a harmonic analysis in right ascensioα

depending onEmin andθmax are given in Table 1. Theresults for all harmonics show generally good agrment with an isotropic distribution for any cutoff eergy we have used. Only the third harmonics shosome anisotropy, in particular at the highest energE > 8 × 1019 eV; however its phase does not pointowards the galactic center (lying atα = 266). Gen-erally, all harmonics point instead towardsα ∼ 130.Ref. [25] derived the probability distribution (pdf) tha data set with phaseφ1 and amplituder1 is drawnfrom an arbitrary pdf. However, we are not aware


uts
Table 1Directionφ to the signal in right ascension and chance probability of thekth harmonics to arise from an isotropic distribution; for different cin energyE and zenith angleθ < 55
k φ (deg) pch (%) k φ (deg) pch (%) k φ (deg) pch (%)

1 111 91 1 157 80 1 124 522 130 32 2 117 13 2 140 163 131 17 3 124 16 3 119 34 151 58 4 133 27 4 136 33

Emin = 4.0× 1019 eV Emin = 6.0× 1019 eV Emin = 8.0× 1019 eV

θmax= 55 θmax= 55 θmax= 55

tic-n-usehen of

c

Asis

ted

lavenlueed.

ted

v–

nn

are

f

ofn-alted

nts-

of

a generalization to higher harmonics and, in parular, of a method to combine the information cotent of several harmonics. In the next section, wetherefore a Kolmogorov–Smirnov test to quantify t(dis-)agreement between the expected distributioarrival direction and the SUGAR data.

5. Kolmogorov–Smirnov tests

The pdf to detect an event with energyE andarrival directionα, δ is a combination of the isotropiextragalactic and the SHDM flux,

p(E,α, δ)

(8)

∝ η(δ)

[jex(E)+ jDM(E)

smax∫0

ds nDM(r(α, δ)

)],

where smax = RE cosθ +√R2h −R2

E sin2 θ is givenby the extensionRh = 100 kpc of the DM halo andθ is the angle relative to the direction to the GC.explained, the relative size of the two contributionsfixed by the fit to Eq. (4).

For the two-dimensional test, we have integraEq. (8) over energy,

(9)P2d (α, δ)=Emax∫

Emin

dE p(E,α, δ),

whereEmin andEmax are the minimal and maximaenergy considered in the UHECR spectrum. We husedEmax = 1021–22 eV, but the results do depend overy weakly on the exact value. By contrast, the vaof Emin has a strong influence on the results obtain

For the one-dimensional test, we have integraEq. (9) over the declination,

(10)PCR(α)=π/2∫

−π/2

dδ cosδP2d(α, δ).

In the standard one-dimensional KolmogoroSmirnov (KS) test, the maximal differenceD be-tween the cumulative probability distribution functioP(x) = ∫

dx ′p(x ′) and the cumulative distributiofunction of the data,

(11)S(x)= 1

n

∑i

θ(xi − x),

is used as estimator for the belief that the datadrawn from the distributionp. A variant of this testwhich is equally sensitive on differences for allx andis especially well suited for data onS1 uses instead oD the symmetric estimator

V =D+ +D−(12)= max

[S(x)− P(x)

] + max[P(x)− S(x)

].

The significance of a certain value ofV is calculatedwith the formula given in [26]. Since the exposurea ground-array experiment is uniform in right ascesion α, we useα as variable in the one-dimensionKS test. More exactly, we use as pdf Eq. (8) integraoverdE anddδ cosδ.

As simplest test, we assume that all SUGAR eveaboveEmin are produced by SHDM. Thus we compareS(α) with P(α) = ∫ α

0 dα′ PCR(α′). The result is

shown forE > 8 × 1019 eV in Fig. 3(a) for two dif-ferent values of the maximal zenith angle,θmax= 45andθmax = 55. While for θmax = 45 SHDM is dis-favoured at the two sigma level for realistic values


Fig. 3. (a) Consistency level of the SUGAR data with SHDM distributed according a NFW profile as function of the core radiusRc ; SHDM isassumed to be the source of all UHECRs aboveEmin = 8× 1019 eV. (b) Comparison ofS(α) andP (α) for Rs = 15 kpc,Emin = 8× 1019 eVandθmax= 45.

–e

u-

ted

si-y-ni-es.

gyse

testcesen--M

sing

es

tic

ob-

rd-tionc--

d-n-in-Ratahthe

heis

ar-a,anws

p-

thee

the core radius,Rc ∼ 20 kpc, of a Navarro–FrenkWhite profile [27], the SUGAR data have for thchoice ofθmax= 55 a rather large probabilityp to beconsistent with the SHDM hypothesis,p ∼ 20%. InFig. 3(b), we compare the two commutative distribtionsS(α) andP(α) forRs = 15 kpc,Emin = 8×1019

eV and θmax = 45. InspectingS(α) makes it clearthat the data in this case are not uniformly distribubut clustered aroundα ∼ 130 andα ∼ 350. Sincenone of these two directions coincide with the potion of the GC, this data set disfavours the SHDM hpothesis more strongly than one would expect for uformly distributed events from extragalactic sourcHowever, one should use a rather low value ofEminto minimize the uncertainties in the SUGAR enerdetermination and we will therefore not rely on theresults.

We consider therefore next as more realisticthe case that both SHDM and extragalactic sourcontribute to the UHECR spectrum. Then the depdence ofp on Emin should be diminished. More exactly, one would expect in the case that the SHDhypothesis is disfavoured by the data that decreaEmin first decreasesp. This decrease ofp should con-tinue down untilE ∼ (3–4) × 1019 eV, i.e., until apoint where the signal-to-background ratio becomconsiderably smaller than one. DecreasingEmin evenfurther should result in a increase ofp becausenow practically all new events are from extragalacsources.

In Fig. 4(a), we show the dependence of the prability on the energy cutoff forRc = 15 kpc andθmax = 55. The two thick solid lines showp for acombination of SHDM and uniform sources accoing Eq. (4); the upper one corresponds to an injecspectrum 1/E2.3, the lower one to an injection spetrum 1/E2.7. The behaviour ofp suggest that the minimum forEmin ∼ 7×1019 eV is a fluctuation similar tothe maximum aroundEmin ∼ 5×1019 eV. In the rangeEmin ∼ (3–4)×1019 eV, the fluctuations adding an aditional event are relatively small. Therefore, we cosider the probability in this range as more reliabledicator for the consistency of SHDM with the SUGAarrival directions; we conclude that the SUGAR dhave the probabilityp = 5–20% to be consistent witthe SHDM depending on the injection spectrum ofextragalactic protons.

The thin solid line shows how consistent tSUGAR data are with an isotropic distribution. Thdistribution has also a minimum aroundEmin ∼ 7 ×1019 eV where the events cluster around tworival directions. After including more low-energy datthe SUGAR arrival directions are consistent withisotropic distribution. Finally, the dashed line shothe consistency of the SUGAR data with the assumtion that all UHECR events aboveEmin are fromSHDM. It is clear that only values ofEmin aboveEmin ∼ 4 × 1019 eV are compatible with the SUGARdata. Similar, the spectral shape of the flux inSHDM model allows a dominance of SHDM in th


est give
Fig. 4. (a) Dependence of the probability on the energy cutoff in the SUGAR data for decaying SHDM. (b) Two-dimensional KS tresults similar to one-dimensional test.
Fig. 5. Dependence of the probability on the energy cutoff in the SUGAR data for annihilations of SHDM. (a) For core radiusRc = 15 kpc anddifferent ε determining the SHDM contribution. (b) For several core radiiRc ; assumes that all events aboveE are from SHDM.

o-

re-

ysheofhethee.perntthe

icalis

t a0].thatntses

ive

M.weing

UHECR spectrum only aboveE > 6 × 1019 eV [19].In Fig. 4(b) we compare results from one- and twdimensional KS tests (ofα andδ) as function of theenergy cutoff and find that they give rather similarsults.

Finally, we consider the model where not decabut annihilations of SHDM particles produce tobserved UHECRs [17]. In the original versionthis model it was suggested that the flux of tclumpy component dominates over the one fromsmooth SHDM profile by 3 orders of magnitudOn the other side, it was shown in a recent pa[29] that the contribution of the clumpy componecan be just a factor few larger than the one of

smooth component. Moreover, the newest numercalculations show that the contribution of clumpseven subdominant and that it is very unlikely thanearby clump will outshine the Galactic center [3Because of the arguments above, we assumethe clumpy part of the SHDM gives a subdominacontribution to the UHECR flux. In the opposite caour results for the SHDM model with annihilationwill be less significant, depending on the relatcontribution of the two components.

Since the flux is now∝ n2DM, the anisotropy in

this model is much stronger than for decaying SHDThis can be clearly seen in Fig. 5(b) whereshow the dependence of the probability of annihilat


seo

en-

esin-

nc-M4

oftorgy

areiesm inengery

SAstsat

mesirn

stthe

%urAne

utsoDM

sionor

,kyhis

sge-m.

a

tro-

tro-

ro-

d-tro-

aro-

v.

8

ke,

a-

maro-

9

8,

ep-

9)

ep-

SHDM on the core radiusRc assuming that all eventaboveE are from SHDM. Even for core radii as largas 30 kpc, annihilating SHDM is disfavoured by twsigma. Fig. 5(a) shows similar to Fig. 4(a) the depdence of the probability on the energy cutoff forRc =15 kpc andθmax= 55. The two thick solid lines showp for a combination of SHDM and uniform sourcaccording Eq. (4); the upper one corresponds to anjection spectrum 1/E2.3, the lower one to an injectiospectrum 1/E2.7. Depending on the injection spetrum of extragalactic protons, annihilations of SHDare disfavoured by the SUGAR data between 3 andσ .

6. Conclusions

In this Letter we have tested the consistencythe SHDM model with the SUGAR data. In orderuse the SUGAR data, we have compared its enespectrum to the one of AGASA and found that theycompatible after rescaling down the SUGAR energby 15%. We have assumed that the energy spectruthe region 1019<E < 6×1019 eV, i.e., between ankland GZK cutoff, is dominated by protons comifrom uniformly distributed extragalactic sources. Aftfitting the relative contributions of SHDM decaproducts and extragalactic protons to the AGAdata, we have performed Kolmogorov–Smirnov teof the SUGAR data. As result we have found thSUGAR data are able to disfavour strongly extrecase like annihilations of SHDM without clump(5σ ) or decaying SHDM (99% C.L.) assuming thecontribution to the UHECR flux dominates dowto E = 4 × 1019 eV. The phenomenologically mointeresting case, decaying SHDM dominatingUHECR spectrum only aboveE > 6 × 1019 eV,is consistent with the SUGAR date with 5–20probability. Thus the SUGAR data do not disfavostrongly this model but they neither support it.statistically significant test of this model can be doby the Pierre Auger Observatory.

Note added

After completing this work we have learnt aboa preprint of Kim and Tinyakov [31] discussing althe consequences of the SUGAR data for the SH

hypothesis. These authors come to similar concluas ours. We thank H.B. Kim and P. Tinyakov fsending us the preprint before publication.

Acknowledgements

We would like to thank L. Anchordoqui, R. DickJ. Primack, K. Shinozaki, M. Teshima, S. Troitsand S. White for discussions and comments. Twork was supported by the Deutsche Forschungmeinschaft (DFG) within the Emmy Noether progra

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[5] S.L. Dubovsky, P.G. Tinyakov, I.I. Tkachev, Phys. ReLett. 85 (2000) 1154, astro-ph/0001317.

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[7] D. Kieda, et al., in: Proceedings of the 26th ICRC, Salt La1999, see alsohttp://www.physics.utah.edu/Resrch.html;T. Abu-Zayyad, et al., High Resolution Fly’s Eye Collabortion, astro-ph/0208243.

[8] P.G. Tinyakov, I.I. Tkachev, JETP Lett. 74 (2001) 445, Pis’Zh. Eksp. Teor. Fiz. 74 (2001) 499 (in Russian), astph/0102476;See also P. Tinyakov, I. Tkachev, astro-ph/0301336.

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[11] V. Kuzmin, I. Tkachev, Phys. Rev. D 59 (1999) 123006, hph/9809547;D.J. Chung, E.W. Kolb, A. Riotto, Phys. Rev. D 60 (199063504, hep-ph/9809453.

[12] S.L. Dubovsky, P.G. Tinyakov, JETP Lett. 68 (1998) 107, hph/9802382.

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[14] M. Ave, J.A. Hinton, R.A. Vazquez, A.A. Watson, E. Zas, PhRev. Lett. 85 (2000) 2244, astro-ph/0007386;K. Shinozaki, et al., AGASA Collaboration, Astrophys. J. 5(2002) 117.

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[20] M.M. Winn, J. Ulrichs, L.S. Peak, C.B. Mccusker, L. HortoJ. Phys. G 12 (1986) 653;See also the complete catalogue of SUGAR data in: Cataloof Highest Energy Cosmic Rays No. 2, WDC-C2 for CosmRays, 1986.

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astro-ph/0307026.[31] H.B. Kim, P. Tinyakov, astro-ph/0306413.

b

at

e, 2770 mtherrocesses is



Measurement of cosmic-ray proton and antiproton spectramountain altitude

T. Sanukia,∗, M. Fujikawaa, H. Matsunagaa,1, K. Abeb, K. Anrakua,2, H. Fukea,S. Hainoa, M. Imori a, K. Izumia, T. Maenob,3, Y. Makidac, N. Matsuia,H. Matsumotoa, J. Nishimuraa, M. Nozakib, S. Oritoa,4, M. Sasakic,5,Y. Shikazeb, J. Suzukic, K. Tanakac, A. Yamamotoc, Y. Yamamotoa,

K. Yamatob, T. Yoshidac, K. Yoshimurac

a The University of Tokyo, Bunkyo, Tokyo 113-0033, Japanb Kobe University, Kobe, Hyogo 657-8501, Japan

c High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan

Received 27 June 2003; received in revised form 3 October 2003; accepted 8 October 2003

Editor: L. Rolandi

Abstract

Energy spectra of atmospheric secondary cosmic-ray protons and antiprotons were measured at mountain altitudabove sea level. We observed more than 105 protons and 102 antiprotons. Our proton spectrum is generally consistent with oprevious measurements. The observed antiproton spectrum suggests that the energy loss due to non-annihilation pless significant than that assumed in previous model calculations. 2003 Published by Elsevier B.V.

PACS: 13.85.Tp; 95.85.Ry

Keywords: Atmospheric cosmic ray; Cosmic-ray proton; Cosmic-ray antiproton; Superconducting spectrometer

05-

awa

.

stra-.

ererac-ary

pri-ec-mica-Atnts

* Corresponding author.E-mail address: [email protected] (T. Sanuki).

1 Present address: University of Tsukuba, Tsukuba, Ibaraki 38571, Japan.

2 Present address: Kanagawa University, Yokohama, Kanag221-8686, Japan.

3 Present address: CERN, CH-1211 Geneva 23, Switzerland4 Deceased.5 Present address: National Aeronautics and Space Admini

tion, Goddard Space Flight Center, Greenbelt, MD 20771, USA

0370-2693/$ – see front matter 2003 Published by Elsevier B.V.doi:10.1016/j.physletb.2003.10.021

1. Introduction

Primary cosmic rays hit the Earth’s atmosphand produce baryons and mesons via hadronic intetions. Absolute fluxes of these atmospheric secondcosmic rays at any altitudes can be calculated ifmary cosmic-ray intensity and interaction cross stions are precisely known. Measurement of cosrays at various altitudes will give us useful informtion to verify the accuracy of those calculations.balloon altitude or in space, a number of experime


T. Sanuki et al. / Physics Letters B 577 (2003) 10–17 11

riedd oniodicsay

aryavero-re-

esre--rayki-ese

pro-revi-ure-e ofob-s-r-lei.

u-igh-

torayf thewstru-ld

ing

ck-m-de

fit-es-ityht

.

ep-SS

ero-cash-

ro-elfec-ld

vethisper

ri-heal

tum

Fr”.bym

er.

rvedof

ical

for measuring primary cosmic rays have been carout. Atmospheric muons have also been measurethe ground, as well as under the ground. A long-perobservation at mountain altitude with high statistwill provide a good reference for studying cosmic-rparticles inside the atmosphere.

A few measurements of the atmospheric secondcosmic-ray proton fluxes at mountain altitudes hbeen reported [1–4]. Atmospheric secondary antipton fluxes at mountain altitudes have also beenported [4]. In this latter result, the reported fluxwere substantially higher than model calculationsults. We report here a new observation of cosmicprotons and antiprotons at mountain altitude in anetic energy range between 0.25 and 3.3 GeV. Thcosmic-ray particles must be secondary particlesduced inside the atmosphere. Compared to the pous works, statistically much more accurate measment was performed and thus the spectral shapcosmic-ray antiprotons at mountain altitude wastained for the first time. These data will provide esentially important information about hadronic inteactions between cosmic rays and atmospheric nuc

2. BESS experiment

2.1. Detector

The BESS (Balloon-borne Experiment with a Sperconducting Spectrometer) detector [5–10] is a hresolution spectrometer with a large acceptanceperform highly sensitive searches for rare cosmic-components, as well as precise measurement oabsolute fluxes of various cosmic rays. Fig. 1 shoa schematic cross-sectional view of the BESS insment. In the central region, a uniform magnetic fieof 1 Tesla is provided by using a thin superconductsolenoidal coil. A magnetic-rigidity (R ≡ Pc/Ze) ofan incoming charged particle is measured by a traing system, which consists of a jet-type drift chaber (JET) and two inner-drift-chambers (IDC’s) insithe magnetic field. The deflection (R−1) and its errorare calculated for each event by applying a circularting using up to 28 hit points, each with a spatial rolution of 200 µm. The maximum detectable rigid(MDR) was estimated to be 200 GV. Time-of-flig(TOF) hodoscopes provide the velocity (β) and en-

Fig. 1. Schematic cross-sectional view of the BESS detector

ergy loss (dE/dx) measurement. A 1/β resolution of1.6 % was achieved in this experiment. In order to sarate protons and antiprotons from muons, the BEspectrometer is equipped with a threshold-type agel Cerenkov counter. The refractive index of siliaerogel radiator is 1.022. It corresponds to a threold kinetic energy of 3.6 GeV for protons and antiptons. By requiring no light output from the aerogCerenkov counter, protons and antiprotons were eftively distinguished from muons below the threshoenergy. An acrylicCerenkov counter is installed abothe bottom TOF hodoscope, but was not used inanalysis. Each particle is identified by requiring pro1/β , as well as dE/dx, as a function of the rigidity.

All detector components are arranged in a cylindcal configuration. This simple configuration and tuniform magnetic field result in a large geometricacceptance and uniform performance in momenmeasurement.

A simple coincidence of the top- and bottom-TOhodoscope signals issues the first-level “T0-triggeThe live data-taking time is measured exactlycounting 1 MHz clock pulses with a scaler systegated by a “ready” status that controls the T0-trigg

2.2. Observations

The atmospheric cosmic-ray events were obseat Norikura Observatory, ICRR, the UniversityTokyo, Japan. It is located at 3606′N,13733′E.The altitude is 2770 m above sea level. The vertgeomagnetic cutoff rigidity is 11.2 GV [11].

12 T. Sanuki et al. / Physics Letters B 577 (2003) 10–17

tion.and

ri-99.

andeanera-

sideto

owres-h for

chdethengm-he

ob-out

ionata

ntsllys-Them-tionrti-lim-ar-in-lec-te

mu-rial].84,androrith3%nd

nd

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n a

n

thede-t ofro-ons.ki-hens

pureopt-er

em-

fe

Fig. 2. Atmospheric depth and temperature during the observaThe experiment was performed during two periods of 17th–19th21st–23rd.

The observation was performed during two peods of 17th–19th and 21st–23rd of September 19During the observation, the atmospheric depthtemperature varied as shown in Fig. 2. The m(root-mean-square) atmospheric depth and tempture were 742.4 (2.9) g/cm2 and 10.9 (1.1)C, re-spectively. The BESS detector was operated outthe building and in a nylon plastic sheet tent so asbe less influenced by ambient conditions. A gas flsystem was implemented to keep the purity and psure of the gas inside the chambers stable enougoperation.

The T0-trigger rate was about 50 Hz. It is mulower than that at a usual balloon floating altituof about 37 km. Thus, all events which satisfiedT0-trigger condition were recorded without imposisecond-level trigger nor on-line rejections. This siple trigger condition reduced systematic errors. Tlive-time ratio was as high as 98.8% through theservation. The number of collected events was ab2.0× 107.

3. Data analysis

The procedure of data analysis and flux calculatwas almost the same as that of the balloon-flight d[12–14].

3.1. Data reduction

The first stage of off-line analysis selected evewith a single track, which was required to be fucontained within a fiducial volume of the tracking sytem and to pass through the silica aerogel radiator.two dE/dx measurements inside the top- and bottoTOF hodoscopes were loosely required as a funcof rigidity to ensure that only one singly-charged pacle passed through the detector. These selections einated rare interacting events. The probability that pticles can go through the BESS detector withoutteractions was evaluated by applying the same setion criterion to the Monte Carlo events. The MonCarlo events were generated by GEANT-based silation code [15], which incorporated detailed matedistribution andp +A (nuclei) cross sections [16–22The resultant probability at 0.3, 1 and 3 GeV was88 and 85%, respectively, for protons, and 59, 6768%, respectively, for antiprotons. A systematic erwas studied by comparing the simulation results wthe accelerator beam test data [10]. It was 2 andbelow and above 1 GeV, respectively, for protons, a5, 2 and 5% below 0.3 GeV, from 0.3 to 1 GeV, aabove 1 GeV, respectively, for antiprotons.

The cosmic rays at the mountain altitude are doinated by muons. In order to reduce the muon bagrounds, we imposed theCerenkov veto, in which theCerenkov light output was required to be less thacertain threshold. The threshold was set at 1/12 ofthe mean light output from energetic muons (R >

25 GV, β ∼ 1). This Cerenkov veto reduced muobackgrounds by a factor of 1.5 × 104 while keepinghigh efficiency for protons and antiprotons. SinceCerenkov light output is reasonably assumed topend only on particle’s velocity and be independenparticle species, the efficiency for protons and antiptons was evaluated by using muons as well as protThe obtained efficiency was 93, 85 and 73% at anetic energy of 0.3, 1.0 and 3.0 GeV, respectively. Ttwo efficiencies evaluated from protons and muowere compared between 0.85 and 1.2 GeV, whereproton and muon samples were obtained by ading a tight 1/β-band cut. They agreed with each othwithin 4%. This discrepancy was treated as a systatic error.

Fig. 3 shows 1/β distribution as a function origidity after imposingCerenkov veto. The particl


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Fig. 3. Identification of antiproton events. The solid lines defineantiproton selection band.

identification was performed by requiring proper 1/β

as a function of the momentum. The 1/β distributionwas well described by Gaussian distribution. A hwidth of the 1/β selection band was set at 3σ . Takinginto account a small deviation from pure Gaussdistribution, the efficiency was evaluated to be 99.7±0.2%. It was constant over the whole energy randiscussed here.

In this analysis, the zenith angle(θz) was limitedas cosθz 0.95 for protons. Because of the vesmall flux of antiprotons, the lower limit of cosθz

for antiproton analysis was relaxed to be 0.84as to improve its statistics. With the data reductdescribed above, 128 625 proton candidates andantiproton candidates were selected.

3.2. Contamination estimation

As shown in Fig. 3, the proton and antiproton seltion bands were slightly contaminated with the mubackgrounds in a rigidity range of|R| > 1.7 GV (ki-netic energy of 1 GeV), due to inefficiency of thaerogelCerenkov veto. The number of contamining muons in the proton (antiproton) candidates westimated by dividing the total number of positive(negatively-) charged particles in each energyby the Cerenkov veto rejection factor. As describ

above, theCerenkov veto reduced muon backgrounby a factor of 1.5 × 104. Since the distribution oCerenkov light output from muons was found notchange its shape in a rigidity range of|R| > 1 GVthe rejection factor was assumed to be constant.resultant muon background was negligibly smallthe protons. Inside the antiproton selections bandthe other hand, the muon contamination amounte1% at 1.4 GeV and 24% at 3 GeV. When the threold for Cerenkov light output changed, the rejectifactor changed very rapidly. The variation of resultproton flux was, however, as small as 0.1%. This vation was treated as a systematic error in protonantiproton fluxes.

4. Results and discussion

The observed energy spectra of protons andtiprotons are shown in Figs. 4 and 5, respectivtogether with previous measurements [1–4] and pdictions [23–26]. Tables 1 and 2 summarize thetained spectra. The first and second errors in Tabland 2 represent statistical and systematic errorsspectively. Since the statistics of antiproton measment was very limited, the statistical error was callated as a 68.7% confidence interval based on a “fied approach” [27].

4.1. Protons

There is some disagreement among the profluxes observed by various experiments as showFig. 4. Table 3 summarizes their locations andperimental conditions. The higher geomagnetic curigidity prevents the primary cosmic rays to get inthe earth up to the higher energy. It leads to the lototal primary cosmic-ray flux, which, in turn, resultsthe lower flux of atmospheric secondary cosmic raSince the cutoff rigidity at Mt. Norikura is the highest among those observation sites, our result showlowest flux. The effect of the atmospheric depth diffence was evaluated to be small enough, comparedthe geomagnetic effect. The overall spectral shapereproduced by the model calculations [23,26].

Fig. 6 shows the zenith angle dependence ofobserved proton flux,F(cosθz), in two kinetic energyregions. The dashed lines show the expectation


Table 1Observed spectrum of protons

Kinetic energy Number ofp’s 〈cosθz〉 Proton flux

range mean cosθz 0.95 cosθz → 1(GeV) (GeV)

(m−2 sr−1 s−1 GeV−1)

0.25–0.30 0.28 10528 0.98 10.05± 0.10± 0.46 10.70± 0.10± 0.730.30–0.36 0.33 11472 0.98 8.66± 0.08± 0.40 8.89± 0.08± 0.610.36–0.44 0.40 12048 0.98 7.33± 0.07± 0.34 7.81± 0.07± 0.530.44–0.52 0.48 12219 0.98 6.04± 0.05± 0.28 6.26± 0.06± 0.430.52–0.63 0.58 12014 0.98 4.91± 0.04± 0.23 5.16± 0.05± 0.350.63–0.76 0.69 11487 0.98 3.93± 0.04± 0.18 4.17± 0.04± 0.280.76–0.91 0.83 10711 0.98 3.06± 0.03± 0.14 3.21± 0.03± 0.220.91–1.10 1.00 9664 0.98 2.37± 0.02± 0.12 2.52± 0.03± 0.181.10–1.32 1.20 8889 0.98 1.84± 0.02± 0.09 1.94± 0.02± 0.141.32–1.58 1.44 7803 0.98 1.38± 0.02± 0.07 1.47± 0.02± 0.111.58–1.90 1.73 6877 0.98 1.03± 0.01± 0.05 1.07± 0.01± 0.081.90–2.29 2.09 5947 0.98 0.75± 0.01± 0.04 0.80± 0.01± 0.062.29–2.75 2.50 4940 0.98 0.53± 0.01± 0.03 0.57± 0.01± 0.042.75–3.31 3.01 4026 0.98 0.36± 0.01± 0.02 0.39± 0.01± 0.03

Table 2Observed spectrum of antiprotons

Kinetic energy Number ofp’s Number of BG’s 〈cosθz〉 Antiproton flux

range mean cosθz 0.84(GeV) (GeV)

(m−2 sr−1 s−1 GeV−1)

0.25–0.54 – 0 0.0 – 1.37× 10−4 upper limit

0.54–0.70 0.63 2 0.0 0.97 3.67+4.14+0.17−2.32−0.17 × 10−4

0.70–0.91 0.84 6 0.0 0.97 8.11+4.44+0.38−2.94−0.38 × 10−4

0.91–1.18 1.06 12 0.0 0.94 1.25+0.45+0.08−0.33−0.08 × 10−3

1.18–1.53 1.38 10 0.1 0.96 8.09+3.10+0.53−2.62−0.53 × 10−4

1.53–1.98 1.82 18 1.3 0.96 1.06+0.31+0.07−0.27−0.07 × 10−3

1.98–2.56 2.23 29 5.2 0.96 1.18+0.29+0.08−0.26−0.08 × 10−3

2.56–3.31 2.96 33 7.8 0.94 9.70+2.43+0.63−2.18−0.63 × 10−4

he

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simple one-dimensional approximation, in which tzenith angle dependence can be described as

(1)F(cosθz) = F0 exp

(X

Λ

(1− 1

cosθz

)),

whereX is the atmospheric depth at the observatsite andΛ is the attenuation length of cosmic-raprotons inside the atmosphere. Since the atmosphdepth was 742.4 g/cm2 and the proton attenuatiolength is about 120 g/cm2, X/Λ = 6 was assumedThe expected zenith-angle dependence could no

produce the observed results. The solid lines showsults of the analytic calculation, in which the anguspread of secondary protons was taken into accoThey reproduce the observed data in the whole enrange better than the one-dimensional calculations

As mentioned above, the proton flux shownFig. 4 was obtained by using the events satisfyingzenith angle condition of cosθz 0.95. The averagezenith angle,〈cosθz〉, was 0.98. The vertical fluxF0 ≡F(cosθz → 1) was obtained by fitting the observefluxes using a formula (1), where “X/Λ” was used


ious

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Fig. 4. The observed proton spectrum compared with the prevworks, and with the calculations.

Fig. 5. The observed antiproton spectrum compared withprevious works, and with the calculations. The dashed linereproduced by interpolating between two spectra at 700 g/cm2 and900 g/cm2 using a power law.

as a fitting parameter. TheF0 obtained by fitting thedata in cosθz 0.95 is summarized in the last columof Table 1. The systematic error due to this fitti

Fig. 6. The zenith angle dependence of proton flux. The dolines show the expected dependence in simple one-dimenscalculations. The solid lines were calculated by taking accounangular spread of secondary particles.

Table 3Summary of the observation sites at mountain altitude

This work Refs. [1,2] Refs. [3,4]

Site Mt. Norikura Mt. Aragats Mt. LemmonAltitude 2770 m 3200 m 2750 mAtmospheric depth 742 g/cm2 710 g/cm2 747 g/cm2

Cutoff rigidity 11.2 GV 7.6 GV 5.6 GV

procedure was estimated to be around 5% by checvariations ofF0 in changing the fitting regions.

4.2. Antiprotons

Fig. 5 shows that the observed antiproton spectabove 1 GeV is generally consistent with predictioobtained through transport equation calculationsBowen and Moats [23] and Stephens [24], as welthrough a three-dimensional Monte Carlo simulatby Huang et al. [25]. In the lower energy region, hoever, the transport equation calculations show sigicant disagreement with our results. Those threeculations predict similar antiproton spectrum abo0.3 GeV at a thin residual atmosphere of 5 g/cm2.At mountain altitude, however, their predictionsnot agree so well with each other. It suggests that


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production spectra of antiprotons are very similareach other, and that the difference at mountain atude would be mainly due to the different treatmeof the propagation inside the atmosphere. The prodtion spectrum of antiprotons has a sharp peak aro2 GeV [24]. The flux at 0.5 GeV is as small as 1/10of the peak flux. Therefore most antiprotons obserbelow 1 GeV must be tertiary antiprotons, those whhave been produced inside the atmosphere andlost their energy during the propagation inside themosphere. In this case, interaction processes ofp + A

have to be precisely treated for an accurate evation of antiproton spectrum at mountain altitude.the calculation of Refs. [23,24], the probability than antiproton with initial energy ofE0 possesses energy E after a collision was assumed to be unifofrom E = 0 to E = 0.90E0 [23] or 0.95E0 [24]. Onthis assumption, the average energy after a collisis about a half of the initial energy. In the calcutions of Ref. [25], on the other hand, only annihilatichannels were taken into account in the inelasticteractions. Non-annihilating inelastic processes wnot included as a process of antiproton energy loOur result suggests the small probability of tertiarytiproton production in an energy range below 1 GIn this low energy region, the non-annihilation proceshould not make significant contribution to the ineltic interactions of antiprotons during their propagatinside the atmosphere.

The antiproton flux measured by Sembroski et[4] is much higher than our measurements in spof the similar observational conditions in altitud(Table 3). In that experiment, a particle trajectowas measured with six chambers outside the magnfield. No information about the particle trajectory wobtained inside the magnetic field. It might leadsome difficulty in strict identification of antiprotons.

5. Summary

We have measured the spectra of secondary proand antiprotons produced inside the atmospherekinetic energy range of 0.25–3.3 GeV at Mt. Noriku2 770 m above sea level, in Japan. The verticalomagnetic cutoff rigidity is 11.2 GeV. The meaatmospheric depth during the measurement742.4 g/cm2.

The measured proton spectrum is consistent wthe previous results by other authors, in taking theferent geomagnetic cutoff rigidities at their obsertion sites into account. The zenith angle dependeof the proton flux was observed. It shows importanof the angular spread in secondary baryon productespecially in the low energy region.

The measured antiproton flux generally agrees wthe model calculations above 1 GeV, irrespective oftreatment of non-annihilating inelastic interactions.the lower energy region, however, the observed sptrum shows much better agreement with the calction performed only with annihilation channels takinto account in the inelastic interactions. The obserantiproton spectrum suggests the small probabilitytertiary antiproton production in an energy rangelow 1 GeV. In this low energy region, the enerloss of antiprotons due to non-annihilation processhould be less significant than that assumed in prous model calculations [23,24].

Acknowledgements

This study was supported by a Joint ReseaProgram of ICRR, the University of Tokyo. We woulike to thank all staffs at the Norikura Observatofor their cooperation and helpful suggestions.are indebted to Professor M. Buénerd and ProfeL. Derome of Laboratoire de Physique Subatomiqet de Cosmologie, IN2P3/CNRS and Dr. C.Y. Huaof Max-Planck-Institut für Kernphysik for helpfudiscussions on this issue. We would like to thaKEK and ICEPP, the University of Tokyo for thecontinuous support and encouragement duringstudy. This experiment was supported by Granin-Aid, KAKENHI(11694104, 11440085, 09304033from Ministry of Education, Culture, Sports, Scienand Technology, MEXT, and Japan Society forPromotion of Science, JSPS, in Japan.

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b

es



Measurement of heavy quark forward–backward asymmetriand average B mixing using leptons in hadronic Z decays

OPAL Collaboration

G. Abbiendib, C. Ainsleye, P.F. Åkessonc, G. Alexanderu, J. Allisono, P. Amaralh,G. Anagnostoua, K.J. Andersonh, S. Arcellib, S. Asaiv, D. Axenz, G. Azuelosq,1,I. Baileyy, E. Barberiog,15, R.J. Barlowo, R.J. Batleye, P. Bechtlex, T. Behnkex,

K.W. Bell s, P.J. Bella, G. Bellau, A. Bellerivef, G. Benellid, S. Bethkeae, O. Biebelad,O. Boeriui, P. Bockj, M. Boutemeurad, S. Braibantg, L. Brigliadori b, R.M. Browns,

K. Buesserx, H.J. Burckhartg, S. Campanad, R.K. Carnegief, B. Caronaa, A.A. Carterl,J.R. Cartere, C.Y. Changp, D.G. Charltona, A. Csillingab, M. Cuffianib, S. Dadot,

A. De Roeckg, E.A. De Wolfg,18, K. Deschx, B. Dienesac, M. Donkersf, J. Dubbertad,E. Duchovniw, G. Duckeckad, I.P. Duerdotho, E. Etzionu, F. Fabbrib, L. Feldi,P. Ferrarig, F. Fiedlerad, I. Flecki, M. Forde, A. Freyg, A. Fürtjesg, P. Gagnonk,J.W. Garyd, G. Gayckenx, C. Geich-Gimbelc, G. Giacomellib, P. Giacomellib,

M. Giuntad, J. Goldbergt, E. Grossw, J. Grunhausu, M. Gruwég, P.O. Güntherc,A. Guptah, C. Hajduab, M. Hamannx, G.G. Hansond, K. Harderx, A. Harelt,

M. Harin-Diracd, M. Hauschildg, C.M. Hawkesa, R. Hawkingsg, R.J. Hemingwayf,C. Henselx, G. Herteni, R.D. Heuerx, J.C. Hille, K. Hoffmanh, D. Horváthab,2,

P. Igo-Kemenesj, K. Ishii v, H. Jeremieq, P. Jovanovica, T.R. Junkf, N. Kanayay,J. Kanzakiv,20, G. Karapetianq, D. Karleny, K. Kawagoev, T. Kawamotov,

R.K. Keelery, R.G. Kelloggp, B.W. Kennedys, D.H. Kim r, K. Klein j,19, A. Klier w,S. Kluthae, T. Kobayashiv, M. Kobelc, S. Komamiyav, L. Kormosy, T. Krämerx,P. Kriegerf,11, J. von Kroghj, K. Krugerg, T. Kuhl x, M. Kupperw, G.D. Laffertyo,H. Landsmant, D. Lanskem, J.G. Layterd, A. Leinsad, D. Lellouchw, J. Letts14,L. Levinsonw, J. Lillich i, S.L. Lloydl, F.K. Loebingero, J. Luz,22, J. Ludwigi,

A. Macphersonaa,8, W. Maderc, S. Marcellinib, A.J. Martinl, G. Masettib,T. Mashimov, P. Mättig12, W.J. McDonaldaa, J. McKennaz, T.J. McMahona,

R.A. McPhersony, F. Meijersg, W. Mengesx, F.S. Merritth, H. Mesf,1, A. Michelini b,S. Miharav, G. Mikenbergw, D.J. Millern, S. Moedt, W. Mohri, T. Mori v, A. Mutteri,

K. Nagail, I. Nakamurav,21, H. Nanjov, H.A. Nealaf, R. Nisiusae, S.W. O’Nealea,A. Ohg, A. Okparaj, M.J. Oregliah, S. Oritov,23, C. Pahlae, G. Pásztord,6, J.R. Patero,



OPAL Collaboration / Physics Letters B 577 (2003) 18–36 19

G.N. Patricks, J.E. Pilcherh, J. Pinfoldaa, D.E. Planeg, B. Polib, J. Polokg, O. Poothm,M. Przybycieng,13, A. Quadtc, K. Rabbertzg,17, C. Rembserg, P. Renkelw, J.M. Roneyy,

S. Rosatic, Y. Rozent, K. Rungei, K. Sachsf, T. Saekiv, E.K.G. Sarkisyang,9,A.D. Schailead, O. Schailead, P. Scharff-Hanseng, J. Schieckae, T. Schörner-Sadeniusg,

M. Schröderg, M. Schumacherc, C. Schwickg, W.G. Scotts, R. Seusterm,5,T.G. Shearsg,7, B.C. Shend, P. Sherwoodn, G. Sirolib, A. Skujap, A.M. Smithg,

R. Sobiey, S. Söldner-Remboldo,3, F. Spanoh, A. Stahlc, K. Stephenso, D. Stromr,R. Ströhmerad, S. Taremt, M. Tasevskyg, R.J. Taylorn, R. Teuscherh, M.A. Thomsone,

E. Torrencer, D. Toyav, P. Trand, I. Triggerg, Z. Trócsányiac,4, E. Tsuru,M.F. Turner-Watsona, I. Uedav, B. Ujvári ac,4, C.F. Vollmerad, P. Vanneremi,

R. Vértesiac, M. Verzocchip, H. Vossg,16, J. Vossebeldg,7, D. Wallerf, C.P. Warde,D.R. Warde, P.M. Watkinsa, A.T. Watsona, N.K. Watsona, P.S. Wellsg, T. Wenglerg,N. Wermesc, D. Wetterlingj, G.W. Wilsono,10, J.A. Wilsona, G. Wolfw, T.R. Wyatto,

S. Yamashitav, D. Zer-Ziond, L. Zivkovic w

a School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UKb Dipartimento di Fisica dell’Università di Bologna and INFN, I-40126 Bologna, Italy

c Physikalisches Institut, Universität Bonn, D-53115 Bonn, Germanyd Department of Physics, University of California, Riverside, CA 92521, USA

e Cavendish Laboratory, Cambridge CB3 0HE, UKf Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada

g CERN, European Organisation for Nuclear Research, CH-1211 Geneva 23, Switzerlandh Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637, USA

i Fakultät für Physik, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germanyj Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany

k Indiana University, Department of Physics, Bloomington, IN 47405, USAl Queen Mary and Westfield College, University of London, London E1 4NS, UK

m Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germanyn University College London, London WC1E 6BT, UK

o Department of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UKp Department of Physics, University of Maryland, College Park, MD 20742, USA

q Laboratoire de Physique Nucléaire, Université de Montréal, Montréal, Québec H3C 3J7, Canadar University of Oregon, Department of Physics, Eugene, OR 97403, USA

s CLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UKt Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israelu Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

v International Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113-0033,and Kobe University, Kobe 657-8501, Japan

w Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israelx Universität Hamburg/DESY, Institut für Experimentalphysik, Notkestrasse 85, D-22607 Hamburg, Germany

y University of Victoria, Department of Physics, PO Box 3055, Victoria BC V8W 3P6, Canadaz University of British Columbia, Department of Physics, Vancouver BC V6T 1Z1, Canada

aaUniversity of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canadaab Research Institute for Particle and Nuclear Physics, H-1525 PO Box 49, Budapest, Hungary

ac Institute of Nuclear Research, PO Box 51, H-4001 Debrecen, Hungaryad Ludwig-Maximilians-Universität München, Sektion Physik, Am Coulombwall 1, D-85748 Garching, Germany

aeMax-Planck-Institute für Physik, Föhringer Ring 6, D-80805 München, Germanyaf Department of Physics, Yale University, New Haven, CT 06520, USA

Received 11 July 2003; received in revised form 1 October 2003; accepted 8 October 2003

Editor: L. Rolandi

20 OPAL Collaboration / Physics Letters B 577 (2003) 18–36

nssigned tontifiedg

metries

with otherctroweak

Abstract

A measurement of the forward–backward asymmetries of e+e− → bb and e+e− → cc events using electrons and muoproduced in semileptonic decays of bottom and charm hadrons is presented. The outputs of two neural networks deidentify b→ − and c→ + decays are used in a maximum likelihood fit to a sample of events containing one or two ideleptons. The b and c quark forward–backward asymmetries at three centre-of-mass energies

√s and the average B mixin

parameterχ are determined simultaneously in the fit. Using all data collected by OPAL near the Z resonance, the asymare measured to be:

AbbFB = (4.7± 1.8± 0.1)%, Acc

FB = (−6.8± 2.5± 0.9)% at〈√s 〉 = 89.51 GeV,

AbbFB = (9.72± 0.42± 0.15)%, Acc

FB = (5.68± 0.54± 0.39)% at〈√s 〉 = 91.25 GeV,

AbbFB = (10.3± 1.5± 0.2)%, Acc

FB = (14.6± 2.0± 0.8)% at〈√s 〉 = 92.95 GeV.

For the average B mixing parameter, a value of:

χ = (13.12± 0.49± 0.42)%

is obtained. In each case the first uncertainty is statistical and the second systematic. These results are combinedOPAL measurements of the b and c forward–backward asymmetries, and used to derive a value for the effective elemixing angle for leptons sin2 θeff of 0.23238± 0.00052. 2003 Published by Elsevier B.V.

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1 And at TRIUMF, Vancouver, Canada V6T 2A3.2 And Institute of Nuclear Research, Debrecen, Hungary.3 And Heisenberg Fellow.4 And Department of Experimental Physics, Lajos Koss

University, Debrecen, Hungary.5 And MPI München.6 And Research Institute for Particle and Nuclear Phys

Budapest, Hungary.7 Now at University of Liverpool, Department of Physic

Liverpool L69 3BX, UK.8 And CERN, EP Division, 1211 Geneva 23.9 And Manchester University.

10 Now at University of Kansas, Department of Physics aAstronomy, Lawrence, KS 66045, USA.

11 Now at University of Toronto, Department of Physics, ToronCanada.

12 Current address: Bergische Universität, Wuppertal, Germa13 Now at University of Mining and Metallurgy, Cracow, Polan14 Now at University of California, San Diego, CA, USA.15 Now at Physics Department, Southern Methodist Univers

Dallas, TX 75275, USA.16 Now at IPHE Université de Lausanne, CH-1015 Lausan

Switzerland.17 Now at IEKP Universität Karlsruhe, Germany.18 Now at Universitaire Instelling Antwerpen, Physics Depa

ment, B-2610 Antwerpen, Belgium.19 Now at RWTH Aachen, Germany.20 And High Energy Accelerator Research Organisation (KE

Tsukuba, Ibaraki, Japan.

1. Introduction

The measurement of the forward–backward asmetries of heavy quarks,Aqq

FB (q = b,c), in e+e− →qq events provides an important test of the StandModel. The bb forward–backward asymmetry prvides one of the most precise determinations ofeffective electroweak mixing angle for leptons sin2 θeff(assuming lepton universality). This is of particularterest at the present time in view of the nearly thstandard deviation difference between the averageues of sin2 θeff derived from quark forward–backwaasymmetries at LEP on the one hand and from lepforward–backward asymmetries at LEP and the lright asymmetry at SLD on the other [1].

The forward–backward asymmetry arises fromcosθ term in the differential cross-section for e+e− →qq,

(1)dσ

d cosθ∝ 1+ cos2 θ + 8

3A

qqFB cosθ,

21 Now at University of Pennsylvania, Philadelphia, PA, USA.22 Now at TRIUMF, Vancouver, Canada.23 Deceased.


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uon

where θ denotes the angle between the outgoquark and the incoming electron flight directions, awhere initial and final state radiation, quark maeffects and higher order terms have been neglecThe asymmetryAqq

FB is related to the vector,gV, andaxial-vector,gA, couplings of the Z to the electronand quark q. At the peak of the Z resonance afor the s-channel Z exchange process only, the pasymmetry is given by

A0,qFB ≡ 3

4AeAq

(2)= 3

4

2gVe/gAe

1+ (gVe/gAe)2

2gVq/gAq

1+ (gVq/gAq)2.

In the Standard Model the couplings for any fermif are related to the fermion chargeQf and its effectiveelectroweak mixing angle sin2 θ f

eff as follows:

(3)gVf

gAf= 1− 4|Qf |sin2 θ f

eff.

The values of sin2 θ feff are all close to 0.25, so th

value of the asymmetry parameter for electrons,Ae,is small, and varies rapidly with sin2 θeff, but the valueof Ab is large, approximately 0.94, and varies onslowly with sin2 θb

eff. This results in a relatively largforward–backward asymmetry for bb events, which isthen very sensitive to sin2 θeff via Ae.

This analysis uses hadronic Z decays observedthe OPAL detector at LEP to measureAbb

FB andAccFB.

The event thrust axis is used to estimate the primquark direction. Leptons produced in semileptodecays of b and c hadrons, usually referred toprompt leptons, are used to identify heavy flavoevents, and their charge is used to distinguish betwdecaying quarks and antiquarks. The asymmetrybb events is diluted by the effect of neutral B mesmixing [2]. This is quantified by the average mixinparameter,χ , which is the probability that a produceb hadron decays as its antiparticle. The paramχ can be measured from the fraction of like-silepton pairs in events with an identified lepton in eahemisphere of the event. The b and c asymmetries,the mixing parameterχ , are therefore measured insimultaneous fit to events with one or two identifileptons. The contributions of bb and cc events to thelepton samples are separated from each otherfrom background by using several kinematic variab

describing the lepton and its associated jet, combusing neural network flavour separation algorithms

This Letter supersedes our previous publicationCompared to the previous paper, this analysis befits from the inclusion of data recorded after 199and from a reprocessing of the full OPAL datawith final tracking algorithms and detector calibrtions, which have improved in particular the perfomance of the electron identification and flavour saration algorithms. The systematic uncertainties hbeen reduced due to better knowledge of heavy flavproduction and decay, and several details of the fit halso been improved. Similar analyses have beenlished by the other LEP experiments [4–6]. Analysidentifying b quark events via the resolvable declength of b hadrons [7–10] also give precise measments of the b quark forward–backward asymmeIn addition, the charm asymmetry has been measusing reconstructed charm hadrons [11–13].

2. Data sample and event simulation

The OPAL detector is described in detail elsewh[14–16]. The central tracking system is located insa solenoid which provides a uniform axial magnefield of 0.435 T along the beam axis. The beam acoincides with thez-axis of the detector, with the polaangleθ measured with respect to the direction of telectron beam. The azimuthal angleφ is measuredaround thez-axis, and the radiusr is the distancefrom the z-axis. The innermost part of the trackinsystem is a two-layer silicon micro-vertex detectThe silicon detector is surrounded by a vertex dchamber, a large volume jet chamber with 159 layof axial anode wires and a set ofz chambers measurinthe track coordinates along the beam direction. Thechamber also provides a measurement of the ratenergy deposition along the track, dE/dx.

Outside the magnet coil, the tracking systemsurrounded by a lead-glass electromagnetic caloriter. The barrel region covers the polar angle ra|cosθ |< 0.82, and full acceptance to|cosθ |< 0.98 isprovided by the endcaps. The iron return yoke and ppieces of the magnet are instrumented with streatubes and thin multiwire chambers to act as a hadrocalorimeter. The calorimeters are surrounded by mchambers.


e numbers ofb-purity

events

Table 1The number of events selected below, on and above the Z peak. The average centre-of-mass energies of the selected Z events, thZ events, and the numbers of events with identified leptons are shown. Note that dilepton events are only selected in a region of high

Mean energy of Z events Selected Z decays Single lepton events Dilepton

Electrons Muons

peak− 2 〈√s 〉 = 89.51 GeV 194 211 11 567 19 809 321peak 〈√s 〉 = 91.25 GeV 4079 047 239 505 410 877 6014peak+ 2 〈√s 〉 = 92.95 GeV 278 257 16 977 30 066 394

ysisndex91,

rom

untifttiontor

ardate Z, to-ali-un-ec-andd to

um-le,rgieoff-tre-

omrgyeserd–ints

sing9].asrks.

1]Ken-atedatedgh

ing-

ave

urali-gtumry.andndi-ther

islec-is

the

chtorsuonvedtsrity

bd

Some flavour separation aspects of this analexploit the long lifetimes of b and c hadrons, atherefore rely in particular on the silicon microvertdetector. This detector was first operational in 19providing measurements in ther–φ plane only. In1993 it was upgraded to measure tracks in bothr–φandr–z planes [15], and in 1996 the cosθ coverage forat least one silicon measurement was extended f|cosθ | < 0.83 to |cosθ | < 0.93 [16]. The changingdetector performance with time was taken into accoin the analysis. The resolution of the vertex drchamber is sufficient to ensure some flavour separaeven in data taken without silicon microvertex detecinformation.

Hadronic Z decays were selected using standcriteria, as in [17]. All the LEP1 data collectedcentre-of-mass energies close to the peak of thresonance between 1990 and 1995 were includedgether with Z-peak data recorded for detector cbration purposes during the higher energy LEP2 rning between 1996 and 2000. The thrust axis dirtion was calculated using charged particle trackselectromagnetic calorimeter clusters not associateany track. The polar angle of the thrust axisθT wasrequired to satisfy|cosθT| < 0.95. Over four mil-lion hadronic events were selected. The exact nbers are listed in Table 1. As indicated in the tabsome events were recorded at centre-of-mass eneabove and below the Z peak. The bulk of thesepeak data were recorded in 1993 and 1995 at cenof-mass energies approximately 1.8 GeV away frthe peak. The other off-peak centre-of-mass enesamples from 1990 and 1991 are combined with thmain samples, yielding measurements of the forwabackward asymmetries at three separate energy po

Monte Carlo simulated events were generated uJETSET 7.4 [18] with parameters tuned by OPAL [1The fragmentation function of Peterson et al. [20] wused to describe the fragmentation of b and c qua

s

.

The semileptonic decay model of Altarelli et al. [2with parameters fixed by CLEO, DELCO and MARIII data [22–24] was used to predict the lepton momtum in the rest frame of b and c hadrons. The generevents were passed through a program that simulthe response of the OPAL detector [25] and throuthe same reconstruction algorithms as the data.

3. Lepton identification and flavour separation

Leptons were identified in hadronic events uswell established algorithms [17]. All tracks with momentum greater than 2 GeV and|cosθ | < 0.96 wereconsidered as lepton candidates.

Electron candidate tracks were required to hat least 20 measurements of dE/dx from jet cham-ber hits. Electrons were then identified using a nenetwork algorithm. The identification relies on ionsation energy loss (dE/dx) measured in the trackinchamber, together with spatial and energy–momen(E/p) matching between tracking and calorimetThe neural network output was in the range 0 to 1,was required to be greater than 0.9 for electron cadates. Photon conversions were rejected using anoneural network algorithm [17]. The efficiency of thselection for genuine electrons, not considering etrons from photon conversions, is 66%. The purity73%, where photon conversions are included inbackground.

Muons were identified by requiring a spatial matbetween a track reconstructed in the tracking detecand a track segment reconstructed in the external mchambers. Further rejection of kaons was achiewith loose dE/dx cuts [17]. These requiremenselected muons with an efficiency of 74% and a puof 53%.

In this analysis, only leptons from the decay of aor c hadron in a primary bb or cc event are considere


ndd asheghtnyonnd

thegi-onsareesnd

a cde-

atethis

,es

aveaysesecay-the

in

ctosi-

ksratee

ies,nedali-fercks

r.

erea

rgy

n-ingde-areea-

n-s.

n-

so-

ofslec-ely,net-e

herb

ruir-

in-d-s,orkfol-es,d

entthe

thectedgo-hethearye

as signal. Any other genuine electron or muon, aany hadron misidentified as a lepton, is considerebackground. With this definition, about 11% of telectron background is from genuine electrons in liquark events, 49% from misidentified hadrons in aprimary quark flavour event, and 40% from photconversions. About 68% of the muon backgrouoriginates from pions, and 28% from kaons.

The relationship between the lepton charge andprimary quark or antiquark from whose decay it orinated is vital for the asymmetry measurement. Leptcoming directly from the weak decay of b hadronsdenoted b→ −. A negatively-charged lepton comfrom the decay of a hadron containing a b quark, aa positive lepton from a b antiquark.24 Electrons andmuons from leptonicτ decays where theτ leptoncomes from a direct b decay, b→ τ− → −, have thesame sign correlation as the b→ − events. Both lep-ton charges are possible if a b hadron decays tohadron, which then decays semileptonically. Thesecays are written as b→ c → + and b→ c → −,according to the charm content of the intermedimeson, and are both called cascade decays. Inanalysis, any identified leptons from cc mesons, e.g.J/ψ → +− decays, are included with the cascadof the appropriate sign. A neutral B meson may hmixed before decay, so that a primary b quark decas a b antiquark, or vice versa. Leptons from thmixed mesons are classified according to the deing b quark, and contribute to the asymmetry withwrong sign for their category, causing a reductionthe observed bb asymmetry by a factor of(1 − 2χ).Leptons from the decay of c hadrons produced incevents, c→ +, have the opposite sign correlationdirect b→ − decays; a primary c quark gives a potive lepton.

As in the previous analysis [3], two neural networ[26] denoted NETb and NETc were used to sepab → − and c→ + decays from each other, from thcascade decays, b→ c→ + and b→ c → − whichdilute the observed forward–backward asymmetrand from backgrounds. The networks were retraito take full advantage of the improved detector cbrations. Several of the network input variables reto the jet containing the lepton track. The same tra

24 Charge conjugate decays are implied throughout this Lette

and clusters used to define the event thrust axis wcombined into jets using a cone algorithm [27] withcone half-angle of 0.55 rad and a minimum jet eneof 5.0 GeV. The transverse momentum,pt , of eachtrack was defined relative to the axis of the jet cotaining it, where the jet axis was calculated excludthe momentum of the track. A lepton sub-jet wasfined as in [3]. The sub-jet includes particles thatnearer to the lepton than to the jet axis, and is a msure of the lepton isolation.

The first network, NETb, was trained to distiguish between b→ − events and all other categorieThe input variables were the momentump and trans-verse momentumpt of the lepton candidate, the eergy of the lepton sub-jet,Esub-jet, the total visible en-ergy of the jet (calculated using all tracks and unasciated calorimeter clusters comprising the jet),Evis

jet ,and the scalar sum of the transverse momentumall tracks within the jet,(

∑pt )jet. Separate network

were trained for electrons and for muons. For the etron nets, two extra variables were included, namthe outputs of the electron and conversion neuralworks. The distributions of the NETb output in thOPAL data are shown in Fig. 1(a) and (b), togetwith the predictions from Monte Carlo; at high NETvalues, the separation of b→ − events from all othelepton sources is clearly visible. For example, reqing NETb> 0.7 gives a sample 89% pure in b→ −decays, with 3% b→ c → + and 4% c→ +, whilstretaining 45% of all b→ − decays with an identifiedlepton (averaged over electrons and muons).

The second network, NETc, was trained to distguish c→ + events from all other categories, incluing b→ −. The network used all the NETb variableincluding the electron and conversion neutral netwoutputs for electron candidates, together with thelowing three quantities: the decay length significanc(L/σL)1,2, of the jet containing the lepton (jet 1) anof the most energetic of the other jets in the ev(jet 2), and the impact parameter significance oflepton with respect to the primary vertex,d/σd . Thedecay length significance is the distance betweenprimary vertex and a secondary vertex, reconstrufrom a subset of the tracks in the jet using the alrithms described in [17], divided by the error on tdecay length. The impact parameter significance isdistance of closest approach of a track to the primvertex, divided by its error. The distributions of th


he
Fig. 1. Outputs of the neural networks designed to select (a) b→ e, (b) b→ µ, (c) c→ e and (d) c→ µ decays. The data are shown by tpoints with error bars, and the expected contributions from different lepton sources by the hatched histograms.
(c)te

thble

dis-

edtonkedon

ateston

wasingleton

m-

ntsnt

NETc output in the OPAL data are shown in Fig. 1and (d), together with the predictions from MonCarlo; again the separation of c→ + events fromother leptons is clearly visible. Requiring NETc> 0.7gives a sample 59% pure in c→ + decays, with 12%b → − and 6% b→ c→ +, whilst retaining 19% ofall c → + decays with an identified lepton. For boNETb and NETc, the Monte Carlo gives a reasonadescription of the data, and the effects of the smallcrepancies visible are discussed in Section 5.4.

The values of NETb and NETc were evaluatfor all lepton candidates. When more than one lepwas identified in an event, the candidates were ranaccording to the value of NETb. If the best two leptcandidates in an event satisfied NETb> 0.6, and were

in opposite thrust hemispheres, then both candidwere retained, and this was classified as a dilepevent. Otherwise, only the best lepton candidateconsidered, and the event was classified as a slepton event. The numbers of single and dilepevents selected are given in Table 1.

4. Fit method and results

The values of the asymmetries andχ were deter-mined using a simultaneous fit to the observed nubers of single lepton events as a function of cosθT,NETb and NETc, and the numbers of dilepton eveas a function of cosθT. The thrust axis of each eve


arysark

ct:

re

ith–of

sary

(1)op-y oftor

e-

ent

i-

teas

gleTa-sts

inesen

uble

4

o

cfa inrylly

llndsrall

was used to estimate the direction of the primquark, and the chargeQ of the identified leptons waused to distinguish between the quark and antiqudirection.

The total likelihood to be maximized is the produ

(4)L = Lsingle e×Lsingleµ ×Ldouble.

The single and double lepton likelihood terms adiscussed in more detail below.

4.1. Single lepton likelihood

For single lepton events, the observabley = −Q ×cosθT was used to classify events as forward, wy > 0, or backward, withy < 0. The observed forwardbackward asymmetry was then examined in binsNETb, NETc and|y|. The fit considers four classeof leptons according to the lepton charge and primquark flavour:

(1) b→ −, b→ τ− → − and b→ c→ −;(2) b→ c→ +;(3) c→ +;(4) background.

Direct b→ − decays and the other decays in classcontribute to the observed asymmetry with theposite sign to classes (2) and (3). The asymmetrevents coming from b decays is scaled by a fac(1 − 2χ) for category (1) decays, and(1 − 2η χ ) forcategory (2), to account for the effects of neutral B mson mixing. The additional correction factorη takesinto account that the two samples include differfractions of different species of b hadron: B0, B+,B0

s, b-baryons, etc., due mainly to the different semleptonic branching ratios of D0 and D+ mesons. Thevalue of η is set to 1.083, evaluated from the MonCarlo simulation. No equivalent correction factor wused for the small fraction of b→ c → − events in-cluded in category (1). The fractions of each sinlepton category in the full data sample are given inble 2. Note that these are fitted fractions. The fit adjuthe overall rate of background in the sample.

Table 2The composition of the single lepton samples. The first three lare combined into category (1) in the fit. The fractions givcorrespond to the fractionsf ′

i after the fit

Electrons Muons

(1) b→ − 35.6% 24.6%b→ c→ − 2.8% 2.3%b→ τ− → − 1.1% 0.7%

(2) b→ c→ + 12.6% 9.7%(3) c→ + 19.3% 14.9%(4) Background 28.6% 47.8%

Table 3Fractions of events in the most important categories in the dolepton sample, together with the total number of ee,µµ and eµevents

ee µµ eµ

(1)(1) 86.9% 86.3% 86.4%(1)(2) 10.3% 8.5% 9.6%(2)(2) 0.3% 0.2% 0.3%(3)(3) 0.4% 0.4% 0.5%(1)(4) 1.8% 4.0% 2.8%Others 0.3% 0.6% 0.4%

Total number 1 308 2 067 3 35

The likelihood for single-lepton events has twterms:

Lsingle =∏

NETb,NETc

∏|y|

(nF + nB)!nF!nB!

(1+AFB

2

)nF

×(

1−AFB

2

)nB

(5)

×∏

NETb,NETc

1√2πσm

exp

(− (nT −m)2

2σ 2m

).

The first term is a product over bins of NETb, NETand |y| of binomial probabilities for the number oforward and backward events observed in the dateach bin,nF and nB, depending on the asymmetAFB expected in the bin. The fit used 10 equaspaced bins in each of NETb, NETc and|y|. Thesecond term constrains the total number of eventsnTin a given NETb–NETc bin (with no binning in|y|)to the expected number,m, and allowed the overanormalisations of the electron and muon backgrouto be determined from the data, reducing the oveuncertainty.


is–

ins

eo

of

nte

as a

ncehe

are],

s inf thehea-

cta-c-eic-

try

ursthe

arkich

to

heon-ontry.

-hetionhetheheec-

d,

on

in

The probability for an event to be forward(1+AFB)/2 where AFB is the expected forwardbackward asymmetry in the bin considered:

AFB(NETb,NETc, |y|)

(6)=4∑

i=1

f ′i ρi

(NETb,NETc, |y|)Ai

FB8

3

|y|1+ y2 .

In this expression,f ′i denotes the fraction of leptons

classi, andρi the normalised distribution of leptonfrom this class in bins of NETb, NETc and|y|,which is taken from Monte Carlo simulation. Thsource fractionsf ′

i are derived from the Monte Carlfractionsfi . However, the fraction of backgroundf ′

4is a free parameter in the fit, and the fractionsprompt sources withi = 1,2,3 are given byf ′

i =(1 − f ′

4)fi/(f1 + f2 + f3). In this way, the relativerates of the prompt leptons are fixed by the MoCarlo simulation, and the fractions satisfy

∑i f

′i = 1.

The nominal asymmetriesAiFB for each class are:

A1FB = (1− 2χ)Abb

FB,

A2FB = −(1− 2ηχ )Abb

FB,

A3FB = −Acc

FB,

(7)A4FB =A

BackgroundFB .

The background asymmetryABackgroundFB also depends

on the primary quark asymmetries. It is expressedsum over quark flavours:

(8)ABackgroundFB =

∑q

fqqbackc

qqdiluteA

qqFB.

This introduces a very weak additional dependeon the fitted values of the b and c asymmetries. Tcentral values of the light quark asymmetriestaken from the predictions of ZFITTER 6.36 [28and are listed in Table 4. The quoted uncertaintiethese asymmetries are taken from measurements ostrange quark asymmetry by DELPHI [29] and of tlight quark asymmetries by OPAL [30]. These mesurements are consistent with the ZFITTER expetions, with relatively large statistical errors. The frations f qq

back of each quark flavour contributing to thbackground are taken from the Monte Carlo predtion, as are the dilution factorscqq

dilute which take intoaccount the fraction of the primary quark asymme

Table 4The values of the forward–backward asymmetries for light flavotaken from ZFITTER, and the variations used for calculatingbackground asymmetry

AFB (%) (ZFITTER prediction)

〈√s 〉 (GeV) 89.51 91.25 92.95

ss 5.95± 5.0 9.64± 1.3 11.89± 5.0uu −3.08± 20.0 6.32± 7.3 12.07± 20.0dd 5.96± 10.0 9.64± 3.7 11.89± 10.0

Table 5The fractions of background coming from each primary quflavour for electrons and muons, and the dilution factors by whthe primary quark forward–backward asymmetry are scaledevaluate the background asymmetry

Electrons Muons

fqqback c

qqdilute f

qqback c

qqdilute

bb 0.139 0.028 0.192 0.093cc 0.146 −0.104 0.178 −0.043ss 0.214 0.025 0.243 0.103uu 0.220 −0.114 0.169 −0.123dd 0.218 0.107 0.218 0.083

that is seen in background events of this flavour. Tfractions and dilutions are listed in Table 5. Some ctributions to the background, for example, for photconversions, have zero forward–backward asymmeOthers, in particular kaons in ss events, inherit a significant fraction of the primary quark asymmetry. Tbackground asymmetry actually varies as a funcof NETb and NETc, but this effect is neglected in tfit, and the small resulting bias is treated as part ofoverall bias correction described in Section 4.3. Tuncertainty from this procedure is discussed in Stion 5.3.

In the second term in the single lepton likelihoothe number of events,m, expected in a bin of NETband NETc is calculated by:

(9)m(NETb,NETc)=NData

4∑i=1

f ′i ρi (NETb,NETc),

whereNData denotes the total number of single lept

events in the data (= e,µ), andρi is the normaliseddistribution in bins of NETb and NETc for leptonsclassi. The observed number of events in a bin,nT, isassumed to be Gaussian distributed with meanm andstandard deviationσm computed asσ 2

m =m+ (δMCm )2,


erlo

nse

nee

frved

ardn.orard

nts

ndnd

theonnceingofesion

rses

3es

eible

therac-loofm-he

at-

binsym-ts,

whereδMCm is the uncertainty on the expected numb

m of events in this bin due to the limited Monte Carstatistics.

4.2. Double lepton likelihood

The double lepton likelihood is a product in biof |y| of multinomial probabilities for the event to bforward, pF, backward,pB, or same-sign,pS. Bothleptons have NETb> 0.6, and no further subdivisioin NETb or NETc is made. The composition of thdouble lepton sample is given in Table 3. The ee,µ

andµµ events are all considered together:

(10)

Ldouble=∏|y|

(nF + nB + nS)!nF!nB!nS! (pF)

nF(pB)nB(pS)

nS.

In this case,nF, nB and nS are the number oforward, backward and same-sign events obsein the data in this|y| bin. A dilepton event withopposite charge leptons is called forward or backwaccording to the direction of the negative leptoThe probability of such an event being forwardbackward usually depends on the forward–backwasymmetry of the dilepton category,ij , where thetwo indices refer to the categoriesi = 1–4 of thetwo leptons. The fraction of same-sign dilepton evedepends only on the mixing parameterχ , and not onthe asymmetries. Note that the fraction of forward abackward events with one lepton from category 1 athe other from category 2 is also independent offorward–backward asymmetry, and only dependsthe mixing parameter. This is because in the abseof mixing these events would all be same sign, losthe information about the asymmetry. If they areopposite sign, without knowing which lepton comfrom the mixed meson, the asymmetry informatcannot be recovered.

Only certain categoriesij are possible. Any flavouevent can give a background lepton, but lepton clas1 and 2 can only come from bb events, and classonly from cc events. The possible dilepton classare therefore:ij = 11,12,22,33,14,24,34,44. Theoverall probabilities for forward, backward or samsign events are given by a sum over the possclassesij :

(11)pX =∑ij

fij (|y|)pijX(|y|).

Since the contribution of background leptons todouble-lepton sample is small (see Table 3), the ftions fij are taken directly from the Monte Carsimulation, without being corrected for the ratesbackground leptons fitted in the single lepton saple. Similarly, the small residual asymmetries of tbackground leptons are neglected. WritingY = 8|y|/3(1 + y2), the probabilitiespijF,B,S for an event to beforward, backward or same-sign for each dilepton cegory are given by (taking the upper signs forpF andthe lower signs forpB):

p11F,B = 1

2

(1− 2χ + 2χ2 ± (1− 2χ)Abb

FBY),

p11S = 2χ(1− χ),

p12F,B = 1

2η χ (1− χ)+ 1

2χ(1− ηχ ),

p12S = (1− χ)(1− ηχ )+ ηχ2,

p22F,B = 1

2

(1− 2ηχ + 2(ηχ)2 ∓ (1− 2ηχ )Abb

FBY),

p22S = 2ηχ (1− ηχ ),

p33F,B = 1

2

(1∓Acc

FBY),

p33S = 0,

p14F,B = 1

4(1− χ)

(1±Abb

FBY) + 1

4χ

(1∓Abb

FBY),

p14S = 1

2,

p24F,B = 1

4(1− ηχ )

(1∓Abb

FBY) + 1

4ηχ

(1±Abb

FBY),

p24S = 1

2,

p34F,B = 1

4

(1∓Acc

FBY),

p34S = 1

2,

p44F,B = 1

4,

(12)p44S = 1

2.

4.3. Results

The data are divided into three separate energywhose mean energies are shown in Table 1. The asmetries were fitted simultaneously at all energy poin


onetry

ely

li-as

n to

ar-er-ntsk-the

isneinatang

ishe

o

m-ononllyac-m-ra-undme-tedef-ec-

toomedts)tionfit-to

val-n.ronrloingby

esultond

(a)

(b)

Fig. 2. An illustration of the fit results for (a) a b-enriched regiand (b) a c-enriched region of NETb–NETc space. The asymmobserved in the data in each bin of|y| is compared with theexpectation calculated from the full fit. The errors are purstatistical.

the overall likelihood being the product of the likehood in Eq. (4) for each point. Therefore, the fit hnine free parameters: the asymmetriesAbb

FB andAccFB

at three energy points, together with values commoall three energy points for the mixing parameterχ , andthe electron and muon background fractions,f ′

4. Datafrom all years were fitted simultaneously, with the vious fractions and (NETb, NETc) distributions detmined from an appropriate mix of Monte Carlo evewith different simulated detector configurations, taing into account the changes in the performance ofOPAL detector over time.

The result of the fit is illustrated in Fig. 2. For thplot, two regions of NETb–NETc were selected, o93% pure in b→ − events and the other 59% purec → + events. The asymmetry observed in the din bins of |y| and the predicted asymmetry accordito Eq. (6) are shown. The predicted asymmetrycalculated with the fitted results. The sign of t

observed asymmetry is clearly different in the twregions.

A small bias correction is applied to the fitted asymetries to correct for the effects of gluon radiatifrom the primary quark pair and the approximatiof the original quark direction by the experimentameasured thrust axis [31]. This correction alsocounts for any residual biases in the fit, for exaple, from the lepton identification and flavour sepation procedures, and the treatment of the backgroasymmetry. It is evaluated by comparing the asymtries fitted on a large sample of Monte Carlo simulaevents with the true quark level asymmetries. Thefects of gluon radiation have been calculated to sond order inαs using the parton level thrust axisdefine the asymmetry [32], and the translation frthe parton level to the hadron level thrust axis (definusing all final state particles without detector effechas been determined using Monte Carlo hadronisamodels [31]. However, the detector acceptance andting method reduce the sensitivity of the analysisthese QCD corrections, which must therefore be euated from full detector-level Monte Carlo simulatioIn calculating the overall bias correction, the hadlevel thrust axis QCD corrections in the Monte Caare scaled to the theoretical values [33]. Combinall effects, the raw fitted asymmetries were scaledfactors of 1.0050± 0.0063± 0.0050 for b quarks and1.0117± 0.0063± 0.0062 for c quarks to determinthe quark level results, where the first errors refrom theoretical uncertainties [31,33] and the secfrom limited Monte Carlo statistics.

After correcting for all biases, the results are:

AbbFB = (4.7± 1.8± 0.1)%,

AccFB = (−6.8± 2.5± 0.9)%,

at 〈√s 〉 = 89.51 GeV,

AbbFB = (9.72± 0.42± 0.15)%,

AccFB = (5.68± 0.54± 0.39)%,

at 〈√s 〉 = 91.25 GeV,

AbbFB = (10.3± 1.5± 0.2)%,

AccFB = (14.6± 2.0± 0.8)%,

at 〈√s 〉 = 92.95 GeV.


singtted

andem-hen innd

rlonly.ain-

ofro-ts,theos-ngnly

ple,et-

peak

n ases 7s ofsult

fest

Table 6Statistical correlation matrices at each centre-of-mass energy uthe entire (1990–2000) data sample. The correlations with the fibackground fractions are negligibly small (< 0.01) and are not givenhere

AbbFB Acc

FB χ

peak

AbbFB 1.00 0.17 0.30

AccFB 1.00 0.01

χ 1.00

peak− 2

AbbFB 1.00 0.18 0.03

AccFB 1.00 0.00

χ 1.00

peak+ 2

AbbFB 1.00 0.17 0.10

AccFB 1.00 0.00

χ 1.00


χ = (13.12± 0.49± 0.42)%

is obtained. In each case the first error is statisticalthe second systematic. The evaluation of the systatic errors is described in the following section. Tstatistical correlations between the results are giveTable 6. The background levels in the electron amuon samples were fitted to be(89.4 ± 0.6)% and(94.4±0.3)% of the rates estimated from Monte Casimulation, where the quoted errors are statistical oThese values are consistent with the known uncertties in modelling the lepton background levels [17].

5. Systematic uncertainties

Systematic uncertainties result from a numbersources, including modelling of b and c hadron pduction and decay, external branching ratio inpubackground uncertainties and the performance ofOPAL detector. For the first two sources, the propals of the LEP Heavy Flavour Electroweak WorkiGroup have been adopted [33]. Where errors are oassessed by a variation in one direction, for examto an alternative model, or when slightly asymm

Table 7Results and breakdown of systematic uncertainties for the on-forward–backward asymmetries and the mixing parameterχ

AbbFB (%) Acc

FB (%) χ (%)

Fitted value 9.716 5.683 13.121Statistical error ±0.418 ±0.542 ±0.485Systematic error ±0.150 ±0.386 ±0.421

Sources of systematic errors

b→ − semileptonic decay model ±0.011 ∓0.101 ±0.175c→ + semileptonic decay model ±0.064 ∓0.036 ∓0.286〈xbE

〉 ± 0.008 ∓0.012 ∓0.008 ∓0.074〈xcE

〉 ± 0.008 ±0.054 ∓0.024 ±0.010Total models 0.085 0.110 0.344

BR(b→ −) (10.65± 0.23)% ∓0.020 ±0.104 ±0.120BR(b→ c → +) (8.08± 0.18)% ∓0.006 ∓0.050 ∓0.105BR(b→ c → −) (1.62± 0.44)% ±0.011 ±0.174 ±0.014BR(b→ τ− → −) (0.419± 0.05)% ∓0.001 ±0.028 ±0.007BR(c→ +) (9.77± 0.32)% ±0.028 ∓0.151 ±0.008Rb (21.647± 0.072)% ∓0.003 ±0.009 0.000Rc (16.83± 0.47)% ±0.019 ∓0.099 ±0.002Total branching ratios 0.041 0.277 0.161

e ID efficiency±4.1% ∓0.005 ∓0.007 ±0.004µ ID efficiency±3.0% ∓0.002 ∓0.021 ±0.022Conversions±15% ±0.001 ±0.012 ∓0.007Muon background (K)±30% ±0.011 ±0.023 ∓0.034Muon background (π ) ±5% ±0.004 ±0.026 ∓0.015Muon background (other)±100% ±0.009 ±0.017 ∓0.058Background asymmetry u, d, s events±0.002 ±0.102 ±0.002Background flavour separation ±0.020 ±0.020 0.000Total background effects 0.026 0.114 0.073

Correction ofχ for b→ c→ + −0.008 −0.069 −0.068cosθT dependence (fractions) −0.018 +0.001 +0.000Tracking resolution −0.025 −0.046 −0.016Flavour separation variables ±0.067 ±0.163 ±0.099Time-dependent mixing +0.032 +0.098 −0.091Monte Carlo statistics ±0.050 ±0.041 ±0.070Charge reconstruction ±0.015 ±0.004 0.000LEP centre-of-mass energy ±0.010 ±0.027 0.000QCD correction ±0.061 ±0.036 0.000Total other systematics 0.114 0.216 0.167

ric errors are assessed, the larger deviation is take1σ . The systematic errors are summarised in Tabland 8 and discussed in more detail below. The signthe errors indicate the direction of change in the rewhen the corresponding quantity is varied.

5.1. Modelling of b and c production and decay

Semileptonic decay models. A correct description othe lepton momentum spectra in the r


Table 8Results and breakdown of systematic uncertainties for the off-peak forward–backward asymmetries

Peak− 2 Peak+ 2

AbbFB (%) Acc

FB (%) AbbFB (%) Acc

FB (%)

Fitted value 4.70 −6.83 10.31 14.59Statistical error ±1.80 ±2.52 ±1.50 ±2.04Systematic error ±0.098 ±0.928 ±0.224 ±0.837

Sources of systematic errors

b→ − semileptonic decay model ±0.031 ∓0.036 ∓0.020 ∓0.101c → + semileptonic decay model ∓0.019 ±0.070 ±0.106 ∓0.108〈xbE

〉 ± 0.008 ∓0.008 ∓0.037 ∓0.019 ∓0.034〈xcE 〉 ± 0.008 ∓0.013 ±0.009 ±0.090 ∓0.051

Total models 0.039 0.088 0.142 0.160

BR(b→ −) (10.65± 0.23)% ∓0.001 ∓0.034 ∓0.012 ±0.198BR(b→ c→ +) (8.08± 0.18)% ∓0.003 ∓0.047 ∓0.024 ∓0.036BR(b→ c→ −) (1.62± 0.44)% ∓0.023 ±0.024 ±0.055 ±0.250BR(b→ τ− → −) (0.419± 0.05)% ∓0.003 ∓0.002 ∓0.002 ±0.044BR(c→ +) (9.77± 0.32)% ±0.009 ±0.161 ±0.033 ∓0.381Rb (21.647± 0.072)% ∓0.001 ∓0.010 ∓0.004 ±0.023Rc (16.83± 0.47)% ±0.006 ±0.106 ±0.023 ∓0.250Total branching ratios 0.026 0.203 0.074 0.560

e ID efficiency±4.1% ∓0.001 ±0.005 ∓0.007 ∓0.019µ ID efficiency±3.0% ∓0.002 ±0.030 ∓0.002 ∓0.049Conversions±15% ±0.003 ∓0.002 ±0.003 ±0.025Muon background (K)±30% ±0.003 ∓0.032 ±0.010 ±0.073Muon background (π ) ±5% ±0.003 ∓0.036 ±0.005 ±0.056Muon background (other)±100% ±0.002 ∓0.044 ±0.009 ±0.062Background asymmetry u, d, s events ±0.018 ±0.832 ±0.006 ±0.302Background flavour separation ±0.020 ±0.025 ±0.010 ±0.065Total background effects 0.028 0.836 0.021 0.333

Correction ofχ for b→ c→ + −0.000 −0.033 −0.027 −0.079cosθT dependence (fractions) +0.005 −0.024 −0.030 +0.001Tracking resolution −0.011 +0.261 −0.002 −0.215Flavour separation variables ±0.029 ±0.172 ±0.097 ±0.403Time dependent mixing −0.037 +0.036 +0.069 +0.112Monte Carlo statistics ±0.058 ±0.102 ±0.064 ±0.118Charge reconstruction ±0.007 ±0.005 ±0.016 ±0.010LEP centre-of-mass energy ±0.007 ±0.018 ±0.003 ±0.007QCD correction ±0.030 ±0.043 ±0.062 ±0.092Total other systematics 0.082 0.337 0.155 0.500

ialicby

-s

s of

-ed-

],

restthei--

frame of decaying b and c hadrons is crucfor the flavour separation. The semileptondecays of heavy hadrons were describedthe free-quark model of Altarelli et al. (ACCMM) [21], with its two free parameterfixed by fits to CLEO data [22] for b→ −decays and the combined measurementDELCO [23] and MARK III [24] for c→ +decays [33]. For cascade decays b→ c→ +

and b→ c → −, the D momentum spectrum measured by CLEO [35] was combinwith the c→ + model to generate the lepton momentum distribution. Following [33the systematic uncertainties for b→ − de-cays were assessed by reweighting theframe momentum spectrum according toform-factor model of Isgur et al. [34], with ether 11% or 32% of b→ − decays produc


theorfob-

.

ns

releds

-l-]the

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ion

k-

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ing a D∗∗ meson. Uncertainties in the c→ +decay model were assessed by varyingfree parameters of the ACCMM model. Fboth b→ − and c→ + decays, the sign othe error assigned indicates the variationserved with the harder alternative spectrum

Heavy quark fragmentation. The lepton momentumspectra depend on the energy distributioof the heavy hadrons produced in bb andcc events. The Monte Carlo events wereweighted so as to vary the average scaenergy〈xE〉 of weakly decaying b hadronin the range〈xE〉 = 0.702± 0.008 and of chadrons in the range〈xE〉 = 0.484± 0.008[33]. The fragmentation functions of Peterson et al., Collins and Spiller, Kartveishvili et al. and the Lund group [20,36were each used as models to determineevent weights, and the largest observed vations were assigned as the systematicrors. For b fragmentation, the largest shiwere observed with the function of Collinand Spiller, and for c fragmentation with thfunction of Peterson et al.

5.2. Branching ratios and partial widths

Semileptonic branching ratios. The values and uncetainties used for the branching ratios of semleptonic b and c hadron decays are listedTables 7 and 8 [2,33].

Partial widths of the Z. The fractions of hadronic Zdecays to bb and cc were varied accordinto the uncertainties in the LEP average vues [2]:Rb = 0.21647± 0.00072 andRc =0.1683± 0.0047. In each case, the fractioof Z hadronic decays to light quarks was ajusted to compensate the variation.

5.3. Background uncertainties

Lepton identification. The analysis is only weaklsensitive to the lepton identification efficiency, since this mainly affects the ratioprompt to background leptons, which is efectively determined from the data via theof the background level. However, a smcomponent of the background is composed

genuine leptons, so the lepton identificatiefficiencies were varied by±4.1% for elec-trons and±3.0% for muons [17].

Background composition. The overall backgrounfraction is a fitted parameter. However, tbackground shape as a function of NETNETc and|y| may be different for differencontributions to the background. The rateuntagged photon conversions was varied±15% [17]. In addition, the|y| distributionof conversions was varied according to tdifference in the rate of identified conversioobserved between data and Monte Carlo sulation. The contributions to the muon bacground fromπ , K and other sources were vaied in turn by 5%, 30% and 100%. These ucertainties were evaluated using control saples of K0

s → π+π−, three-prong tau decayand tracks with an enhanced kaon fractselected using dE/dx cuts [37]. The varia-tion of the source fractions, including bacgrounds, as a function of cosθT is discussedin Section 5.4 below.

Background asymmetries. The uncertainties in thbackground asymmetry were evaluatedvarying the light primary quark forwardbackward asymmetries by the uncertaintlisted in Table 4. Note that the up and dowasymmetries measured by OPAL are+91%correlated [30]. They were therefore variat the same time, and the resulting unctainty combined in quadrature with the unctainty in the strange asymmetry. The bb andcc asymmetries are treated self-consistenin the fit, and the uncertainty in these quatities is therefore automatically reflected invery small contribution to the statistical ucertainty.

Background flavour separation. The dependence othe background asymmetry on NETb aNETc is neglected in the fit (see Eq. (8)) bany residual bias is removed by the bias crection procedure described in Section 4provided the Monte Carlo gives an adequdescription of the variations. To quantify thsize of any mismodelling, an additionalwas performed using a binned backgrouasymmetry without changing the bias corre


ndsys-

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un-

on

ofheloforrd-en-ght-tohetingm-theac-he

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i-the

i-c-

he

ins

rlo

iser-

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ra-r-in

ue

%n-e

ectof

-fer-r--

tion, and half the difference between this athe standard fit result was assigned as atematic error.

5.4. Other uncertainties

Correction factor for mixing in cascade decays. Thedifference between using the standard vaof η = 1.083 and setting it equal to 1.000 wasassigned as a conservative estimate of thecertainty.

Dependence of source fractions on cosθT. The des-cription of the source fractions as a functiof cosθT was checked by selecting b→ −,c → + and background enriched regionsthe NETb–NETc plane, and comparing tcosθT distributions of data and Monte Carsimulation. No systematic trend was seenthe c→ + enriched sample. The ratio fobackground varied by up to 10% in the encap region, with smaller deviations for thb → − enriched sample. A systematic ucertainty was therefore assessed by reweiing the Monte Carlo background accordingthe data/Monte Carlo ratio observed for tbackground enriched sample, and repeathe fit. The change in the background saple was compensated by an increase inprompt leptons, so this procedure alsocounted for any possible discrepancy in tb → − sample.

Tracking resolution. A global 10% degradation inthe tracking resolution was applied to tMonte Carlo sample, separately in ther–φandr–z planes, as discussed in [10,17]. Tfit was repeated with each of these modifisamples, and the sum in quadrature of theshifts in the results was taken as a systemuncertainty.

Flavour separation variables. Possible uncertaintiedue to mismodelling of the neural netwoinput variables were taken into accountreweighting the Monte Carlo events by tratio between the data and Monte Carlo dtributions of each variable in turn, and rpeating the fit. The sum in quadrature of tshifts in the results was assigned as a systatic uncertainty, dominated by the result

reweighting the leptonp andpt distributionsfor the asymmetries, and the input paramesignificance forχ . The neural network output distributions were also reweighted, to acount for the discrepancies between dataMonte Carlo visible in Fig. 1, but the resuling changes in the results were much smathan those seen when reweighting the inpand no additional systematic error wassigned.

Time-dependent mixing. The mixing parameterχ re-flects the fraction of mixed events in an unbased sample of all b hadrons. However,time dependent oscillations for B0 mesonsare sufficiently slow that the lifetime varables used in NETc might change the effetive value of χ as a function of NETc. Toevaluate the impact of such an effect, tvalue of χ was evaluated for all bb MonteCarlo events with a lepton candidate, in bof NETc, and for the entire bb sample. Thefitted value ofχ in the likelihood functionwas then scaled by the ratio of Monte Cavalues ofχ in the NETc bin andχ in all bbevents. The shift in the fit results with threscaling was taken as a systematic unctainty.

Monte Carlo statistics. The fit to the data was repeated 1000 times, with the Monte Carreference distributions being randomly vaied according to the statistical uncertaintyeach bin of NETb, NETc and|y|. The RMSvariation in the results was added in quadture with the Monte Carlo statistical uncetainty on the bias corrections discussedSection 4.3 to give the total uncertainty dto limited Monte Carlo statistics.

Lepton charge reconstruction and asymmetry. MonteCarlo simulation predicts that about 0.03of electrons and 0.3% of muons are recostructed in the tracking chamber with thwrong charge (electron tracks are subjto tighter quality requirements becausethe stronger dE/dx cuts). This effect is accounted for in the fit, and the full size othe correction is taken as a systematicror. Studies in [38] show a possible diffeence of around 10−3 between the lepton iden


a-ll

edes,of

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-nd

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icals are

ceedni-

me-

osednshosethe

large

tification efficiencies for positive and negtive tracks. When combined with the smadifference (2%) in numbers of reconstructleptons in positive and negative hemispherthis leads to negligible asymmetry biasesaround 2× 10−5.

LEP centre-of-mass energy. The LEP centre of masenergy is known to a precision varying btween 3.5 and 20 MeV depending on the eergy point and year [39]. Taking year-to-yecorrelations into account, and assumingStandard Model dependencies of the asymetries on

√s, this leads to the uncertaintie

given in Tables 7 and 8 on the asymmetriesthe quoted values of

√s.

QCD and thrust axis correction. The corrections applied to the raw fitted asymmetries are knowto precisions of 0.80% for b quarks an0.89% for c quarks, as discussed in Stion 4. The theoretical part of this uncertainis assigned as the error on the QCD corrtion, whilst the Monte Carlo statistical uncertainty is accounted for separately as dcussed above.

5.5. Consistency checks

The analysis was performed separately for dfrom 1990 and 1991, for each year separately fr1992 to 1995, and for data from 1996 to 2000. Tresults were consistent among themselves andthe standard result from fitting all data simultanously. Taking into account statistical errors only, tχ2/d.o.f. value for the sixAbb

FB measurements to bconsistent with the same value was 5.9/5. The equiv-alentχ2/d.o.f. values forAcc

FB andχ were 2.4/5 and5.3/5. Separate fits for electron and muon events walso made and showed similar consistency. The nber of bins iny, NETb and NETc were varied, anagain consistent results were obtained. To verifycorrectness of the fit method itself, it was testedlarge samples of test Monte Carlo samples generwith various b and c asymmetries and with source frtions and input NETb and NETc distributions genated to correspond to those in the full simulation.these tests, the fit was found to be unbiased and toturn correct statistical errors on the fitted paramete

6. Conclusions

The forward–backward asymmetries of e+e− →bb and e+e− → cc events have been measured at thenergy points around the Z peak, using electronsmuons produced in semileptonic decays of bottomcharm hadrons. The results, corrected to the primquark level, are:

AbbFB = (4.7± 1.8± 0.1)%,

AccFB = (−6.8± 2.5± 0.9)%,

at 〈√s 〉 = 89.51 GeV,

AbbFB = (9.72± 0.42± 0.15)%,

AccFB = (5.68± 0.54± 0.39)%,

at 〈√s 〉 = 91.25 GeV,

AbbFB = (10.3± 1.5± 0.2)%,

AccFB = (14.6± 2.0± 0.8)%,

at 〈√s 〉 = 92.95 GeV.


χ = (13.12± 0.49± 0.42)%

is obtained. In each case the first error is statistand the second systematic. The asymmetry resultshown as a function of

√s in Fig. 3.

Using the ZFITTER prediction for the dependenof Abb

FB andAccFB on

√s, the measurements are shift

to mZ (91.19GeV), averaged and corrected for itial state radiation,γ exchange,γ –Z interference andquark mass effects. The results for the pole asymtries are:

A0,bFB = (9.81± 0.40± 0.15)%,

A0,cFB = (6.29± 0.52± 0.38)%.

These results are consistent with those ofAbbFB derived

from inclusive jet charge measurements [10] and thof Abb

FB and AccFB derived from fully reconstructe

charm hadrons [13]. Whilst the statistical correlatiobetween the asymmetries measured here and tfrom reconstructed charm hadrons are negligible,jet charges of some of the events involving b→− decays are also used to measureAbb

FB in [10].This results in a statistical correlation of 0.11± 0.12between the two measurements, evaluated using


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othunt,ndina

finalies

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Fig. 3. The measured b and c quark asymmetries as a functiocentre-of-mass energy, for the lepton, inclusive (b only) [10] aD meson (c only) [13] analyses. The measurement of the b qasymmetry from D mesons is of low precision and is not shown.measurements from different analyses are slightly displaced ohorizontal axis for clarity. The combination of the lepton analyand the other analyses is also shown, together with the StanModel expectation for Higgs masses between 114 and 1000calculated using ZFITTER [28].

samples of Monte Carlo simulated events. Taking bstatistical and systematic correlations into accoand making very small corrections to the inclusive acharm meson asymmetries to use the same nomcentre-of-mass energies as in this analysis, theOPAL results for the b and c quark asymmetraround the Z resonance are:

AbbFB = (5.3± 1.2± 0.1)%,

AccFB = (−4.8± 2.2± 0.7)%,

at 〈√s 〉 = 89.51 GeV,

AbbFB = (9.69± 0.29± 0.13)%,

AccFB = (5.83± 0.49± 0.32)%,

at 〈√s 〉 = 91.25 GeV,

l

AbbFB = (11.4± 1.0± 0.2)%,

AccFB = (14.7± 1.8± 0.7)%,

at 〈√s 〉 = 92.95 GeV,

and the pole asymmetries are measured to be:

A0,bFB = (9.89± 0.27± 0.13)%,

A0,cFB = (6.57± 0.47± 0.32)%.

In all cases, the first error is statistical andsecond systematic. Theχ2/d.o.f. of the fit to allOPAL asymmetry measurements to give the two pasymmetries is 11.2/13. (There are six asymmetmeasurements from the lepton tag analysis, three fthe inclusive analysis, and six from the charm meanalysis, which consists of a simultaneous fit tob and c quark asymmetries.) Taking into accostatistical and systematic uncertainties, these avepole asymmetries have+15% correlation. Within theframework of the Standard Model, the measuremeof A0,b

FB andA0,cFB taken together can be interpreted

a measurement of the effective weak mixing angleleptons of

sin2 θeff = 0.23238± 0.00052.

As can be seen from Fig. 3, this result favours lavalues of the Higgs mass, in agreement with otmeasurements of heavy flavour asymmetries ancontrast to measurements of the leptonic forwabackward and left-right asymmetries [1].

Acknowledgements

We particularly wish to thank the SL Divisiofor the efficient operation of the LEP acceleratorall energies and for their close cooperation with oexperimental group. In addition to the support stafour own institutions we are pleased to acknowledthe

– Department of Energy, USA,– National Science Foundation, USA,– Particle Physics and Astronomy Research Co

cil, UK,– Natural Sciences and Engineering Research C

cil, Canada,


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– Israel Science Foundation, administered byIsrael Academy of Science and Humanities,

– Benoziyo Center for High Energy Physics,– Japanese Ministry of Education, Culture, Spo

Science and Technology (MEXT) and a graunder the MEXT International Science ReseaProgram,

– Japanese Society for the Promotion of Scie(JSPS),

– German–Israeli Bi-national Science Foundat(GIF),

– Bundesministerium für Bildung und ForschunGermany,

– National Research Council of Canada,– Hungarian Foundation for Scientific Resear

OTKA T-038240, and T-042864,– The NWO/NATO Fund for Scientific Researc

The Netherlands.

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http://pdg.lbl.gov/2003/contents_listings.html



http://www.cern.ch/LEPEWWG/heavy/


23.7)

on0”,

P. Collins, T. Spiller, J. Phys. G 11 (1985) 1289.[37] OPAL Collaboration, P. Acton, et al., Z. Phys. C 58 (1993) 5[38] OPAL Collaboration, K. Ackerstaff, et al., Z. Phys. C 76 (199

401.[39] L. Arnaudon, et al., Phys. Lett. B 307 (1993) 187;

R. Assmann, et al., Eur. Phys. J. C 6 (1999) 187;LEP Energy Working Group, R. Assmann, et al., “Evaluatiof the LEP centre-of-mass energy for data taken in 200LEPEWG 01/01,http://lepecal.web.cern.ch/LEPECAL/.

http://lepecal.web.cern.ch/LEPECAL/

b



Quark fragmentation toπ±, π0, K±, pandp in the nuclear environment

HERMES Collaboration

A. Airapetianad, N. Akopovad, Z. Akopovad, M. Amarianf,ad, V.V. Ammosovv,A. Andruso, E.C. Aschenauerf, W. Augustyniakac, R. Avakianad, A. Avetissianad,

E. Avetissianj, P. Baileyo, V. Baturinu, C. Baumgartens, M. Beckmanne,S. Belostotskiu, S. Bernreutherh, N. Bianchij, H.P. Blokt,ab, H. Böttcherf,

A. Borissovq, A. Borysenkoj, M. Bouwhuiso, J. Brackd, A. Brüll p, V. Bryzgalovv,G.P. Capitanij, H.C. Chiango, G. Ciulloi, M. Contalbrigoi, P.F. Dalpiazi, R. De Leoc,L. De Nardoa, E. De Sanctisj, E. Devitsinr, P. Di Nezzaj, M. Dürenm, M. Ehrenfriedh,

A. Elalaoui-Moulayb, G. Elbakianad, F. Ellinghausf, U. Elschenbroichl, J. Elyd,R. Fabbrii, A. Fantonij, A. Fechtchenkog, L. Felawkaz, B. Foxd, J. Franzk,

S. Frullanix, G. Gapienkov, V. Gapienkov, F. Garibaldix, K. Garrowa,y, E. Garuttit,D. Gaskelld, G. Gavrilove,z, V. Gharibyanad, G. Graws, O. Grebeniouku,

L.G. Greeniausa,z, I.M. Gregorf, K. Hafidi b, M. Hartigz, D. Haschj, D. Heesbeent,M. Henochh, R. Hertenbergers, W.H.A. Hesselinkt,ab, A. Hillenbrandh, M. Hoekm,

Y. Holler e, B. Hommezl, G. Iaryging, A. Ivanilovv, A. Izotovu, H.E. Jacksonb,A. Jgounu, R. Kaisern, E. Kinneyd, A. Kisselevu, K. Königsmannk, M. Kopytin f,

V. Korotkovf, V. Kozlov r, B. Kraussh, V.G. Krivokhijineg, L. Lagambac, L. Lapikást,A. Lazievt,ab, P. Lenisai, P. Liebingf, T. Lindemanne, K. Lipka f, W. Lorenzonq, J. Luz,B. Maiheul, N.C.R. Makinso, B. Marianskiac, H. Marukyanad, F. Masolii , V. Mexnert,

N. Meynerse, O. Mikloukhou, C.A. Miller a,z, Y. Miyachi aa, V. Mucciforaj,A. Nagaitsevg, E. Nappic, Y. Naryshkinu, A. Nassh, M. Negodaevf, W.-D. Nowakf,

K. Oganessyane,j , H. Ohsugaaa, N. Pickerth, S. Potashovr, D.H. Potterveldb,M. Raithelh, D. Reggianii, P.E. Reimerb, A. Reischlt, A.R. Reolonj, C. Riedlh,

K. Rith h, G. Rosnern, A. Rostomyanad, L. Rubacekm, D. Ryckboschl,∗, Y. Salomatinv,I. Sanjievb,u, I. Saving, C. Scarlettq, A. Schäferw, C. Schillk, G. Schnellf,

K.P. Schülere, A. Schwindf, J. Seeleo, R. Seidlh, B. Seitzm, R. Shanidzeh, C. Shearern,T.-A. Shibataaa, V. Shutovg, M.C. Simanit,ab, K. Sinrame, M. Stancarii, M. Staterai,


.


38 HERMES Collaboration / Physics Letters B 577 (2003) 37–46

ent attargets.vari-

e

E. Steffensh, J.J.M. Steijgert, H. Stenzelm, J. Stewartf, U. Stössleind, P. Taith,H. Tanakaaa, S. Taroianad, B. Tchuikov, A. Terkulovr, A. Tkabladzel, A. Trzcinskiac,

M. Tytgatl, A. Vandenbrouckel, P. van der Natt,ab, G. van der Steenhovent,M.C. Vetterliy,z, V. Vikhrov u, M.G. Vinctera, C. Vogelh, M. Vogth, J. Volmerf,

C. Weiskopfh, J. Wendlandy,z, J. Wilberth, G. Ybeles Smitab, S. Yenz, B. Zihlmannt,ab,H. Zohrabianad, P. Zupranskiac

a Department of Physics, University of Alberta, Edmonton, Alberta T6G 2J1, Canadab Physics Division, Argonne National Laboratory, Argonne, IL 60439-4843, USA

c Istituto Nazionale di Fisica Nucleare, Sezione di Bari, 70124 Bari, Italyd Nuclear Physics Laboratory, University of Colorado, Boulder, CO 80309-0446, USA

e DESY, Deutsches Elektronen-Synchrotron, 22603 Hamburg, Germanyf DESY Zeuthen, 15738 Zeuthen, Germany

g Joint Institute for Nuclear Research, 141980 Dubna, Russiah Physikalisches Institut, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany

i Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara and Dipartimento di Fisica, Università di Ferrara, 44100 Ferrara, Italyj Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, 00044 Frascati, Italy

k Fakultät für Physik, Universität Freiburg, 79104 Freiburg, Germanyl Department of Subatomic and Radiation Physics, University of Gent, 9000 Gent, Belgium

m Physikalisches Institut, Universität Gießen, 35392 Gießen, Germanyn Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK

o Department of Physics, University of Illinois, Urbana, IL 61801-3080, USAp Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

q Randall Laboratory of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USAr Lebedev Physical Institute, 117924 Moscow, Russia

s Sektion Physik, Universität München, 85748 Garching, Germanyt Nationaal Instituut voor Kernfysica en Hoge-Energiefysica (NIKHEF), 1009 Amsterdam DB, The Netherlands

u Petersburg Nuclear Physics Institute, St. Petersburg, 188350 Gatchina, Russiav Institute for High Energy Physics, 142281 Protvino, Moscow region, Russia

w Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germanyx Istituto Nazionale di Fisica Nucleare, Sezione Roma 1, Gruppo Sanità, and Physics Laboratory,

Istituto Superiore di Sanità, 00161 Roma, Italyy Department of Physics, Simon Fraser University, Burnaby, British Columbia, V5A 1S6, Canada

z TRIUMF, Vancouver, British Columbia, V6T 2A3, Canadaaa Department of Physics, Tokyo Institute of Technology, 152 Tokyo, Japan

ab Department of Physics and Astronomy, Vrije Universiteit, 1081 HV Amsterdam, The Netherlandsac Andrzej Soltan Institute for Nuclear Studies, 00-689 Warsaw, Poland

ad Yerevan Physics Institute, 375036 Yerevan, Armenia


Editor: V. Metag

Abstract

The influence of the nuclear medium on lepto-production of hadrons was studied in the HERMES experimDESY in semi-inclusive deep-inelastic scattering of 27.6 GeV positrons off deuterium, nitrogen and kryptonThe differential multiplicity for krypton relative to that of deuterium has been measured for the first time forous identified hadrons (π+, π−, π0, K+, K−, p and p) as a function of the virtual photon energyν, the frac-tion z of this energy transferred to the hadron, and the hadron transverse momentum squaredp2

t . The multiplic-ity ratio is strongly reduced in the nuclear medium at lowν and high z, with significant differences among thvarious hadrons. The distribution of the hadron transverse momentum is broadened towards highp2

t in the nuclear

HERMES Collaboration / Physics Letters B 577 (2003) 37–46 39

ith nu-
medium, in a manner resembling the Cronin effect previously observed in collisions of heavy ions and protons wclei. 2003 Elsevier B.V. All rights reserved.
PACS: 13.87.Fh; 13.60.-r; 14.20.-c; 14.40.-n

sesn,arehisrksnc-

of

estsestelyu-ge i

therk

nu-a-gy[2].in-here-onter-ion,re-ex-g”hattheoniza-

iume-te

ur--venu-ndc-ngd-al

delsionvy-aron-theingoion

ol-in-astg, inar-is

tiesar

ep-ted

ypen a

ic

stualles

ion.

The phenomenon of confinement in QCD impoitself dynamically in the process of hadronizatioi.e., the mechanism by which final-state hadronsformed from a quark that has been struck hard. Tprocess, also known as the fragmentation of quainto hadrons, can be described by fragmentation futionsDh

f (z), denoting the probability that a quarkflavor f produces a hadron of typeh carrying a frac-tion z of the energy of the struck quark in the target rframe. In the nuclear medium additional soft procesmay occur before the final-state hadron is compleformed. The nuclear environment may thereby inflence the hadronization process, e.g., cause a chanthe quark fragmentation functions, in analogy toEMC finding of a medium modification of the quadistribution functions [1].

The understanding of quark propagation in theclear medium is crucial for the interpretation of ultrrelativistic heavy ion collisions, as well as high enerproton–nucleus and lepton–nucleus interactionsQuark propagation in the nuclear environmentvolves processes like multiple interactions with tsurrounding medium and induced gluon radiation,sulting in energy loss of the quark. If the final hadris formed inside the nucleus, the hadron can inact via the relevant hadronic interaction cross sectcausing a further reduction of the hadron yield. Thefore, quark and hadron propagation in nuclei arepected to result in a modification, i.e., a “softeninof the leading-hadron spectra [3] compared to tfrom a free nucleon. By studying the properties ofleading-hadrons emerging from nuclei, informationthe characteristic time-distance scales of hadrontion can be derived.

The hadronization process in the nuclear medis traditionally described in the framework of phnomenological string models [4–7] and final sta

* Corresponding author.E-mail address: [email protected] (D. Ryckbosch).

n

interactions of the produced hadrons with the srounding medium [8]. Alternatively, in-medium modifications of the quark fragmentation functions habeen proposed, either expressed in terms of theirclear rescaling [9,10], or parton energy loss [11] ahigher-twist contributions to the fragmentation funtions [12], or in terms of a gluon-bremsstrahlumodel for leading hadron attenuation [13]. The moels of Refs. [10,13] also incorporate hadronic finstate interactions. These recent QCD-inspired moprovide a theoretical description of the hadronizatprocess in deep-inelastic scattering, relativistic heaion collisions [12] and Drell–Yan reactions on nucletargets [11,14]. Moreover, some of these models ctain a so-far untested QCD prediction, i.e., thatinduced radiative energy loss of a quark traversa lengthL of hot or cold matter is proportional tL2 [15] due to the coherence of the gluon radiatprocess [16].

Semi-inclusive deep-inelastic lepton–nucleus clisions are most suitable to obtain quantitativeformation on the hadronization process. In contrto hadron–nucleus and nucleus–nucleus scatterindeep-inelastic scattering no deconvolution of the pton distributions of the projectile and target particlesneeded, so that hadron distributions and multiplicifrom various nuclei can be directly related to nucleeffects in quark propagation and hadronization.

The experimental results for semi-inclusive deinelastic scattering on nuclei are usually presenin terms of the hadron multiplicity ratioRh

M , whichrepresents the ratio of the number of hadrons of th produced per deep-inelastic scattering event onuclear target of massA to that from a deuteriumtarget (D). The ratioRh

M depends on the leptonvariablesν andQ2, whereν = E − E′ and−Q2 =q2 = (k − k′)2 are the energy in the target reframe and the squared four-momentum of the virtphoton, respectively, and on the hadronic variabz = Eh/ν andp2

t , wherept is the hadron momentumcomponent transverse to the virtual photon direct


iveton

tron,ced

onhe

a

nr

n-atL].

21]en-

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ataith

eu-s.cepeum

edtiong aer

nsma-a

re-ses

t ofpi-

areando-be-

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Fig. 1. Kinematic planes for hadron production in semi-inclusdeep-inelastic scattering and definitions of the relevant lepand hadron variables. The quantitiesk (k′) and E (E′) are the4-momentum and the energy of the incident (scattered) posiandph andEh are the 4-momentum and the energy of the produhadron.

Fig. 1 illustrates the definition of the relevant leptand hadron kinematic variables for this analysis. Tmultiplicity ratio is defined as:

(1)RhM

(z, ν,p2

t ,Q2) =

Nh(z,ν,p2t ,Q

2)

Ne(ν,Q2)

∣∣A

Nh(z,ν,p2t ,Q

2)

Ne(ν,Q2)

∣∣D

,

whereNh is the yield of semi-inclusive hadrons ingiven (z, ν, p2

t , Q2)-bin, andNe the yield of inclusivedeep-inelastic scattering leptons in the same (ν, Q2)-bin. The ratioRh

M is usually evaluated as a functioof ν and z only, while integrating over all othekinematic variables, as existing data forRh

M show aweak dependence on eitherQ2 or p2

t [17,18].In the past, semi-inclusive leptoproduction of u

differentiated hadrons from nuclei was studiedSLAC with electrons [19], and at CERN and FNAwith high-energy muons by EMC [18] and E665 [20Recently, HERMES reported more precise data [on the production of charged hadrons, as well as idtified π+ andπ− mesons, in deep-inelastic positrscattering on nitrogen relative to deuterium. A signcant difference was found between the multiplicitytio of positive and negative hadrons, while the muplicity ratio for identified pions was found to be thsame for both charges. In order to clarify this issadditional measurements ofRh

M with identification ofother hadron species have been performed at HMES.

In this Letter we present results on the hadron mtiplicities on krypton relative to deuterium, providing the first measurements of the multiplicity ratio fidentified pions, kaons, protons and antiprotons. A

ditionally the nitrogen data for charged hadrons aidentified pions are reevaluated, now covering a wikinematic range than in Ref. [21]. The measuremedescribed were performed with the HERMES sptrometer [22] using the 27.6 GeV positron beam stoin the HERA ring at DESY. The spectrometer consiof two identical halves located above and belowpositron beam pipe. Both the scattered positronsthe produced hadrons were detected simultaneowithin an angular acceptance of±170 mrad horizon-tally, and±(40–140) mrad vertically.

The data were collected using krypton and dterium gas targets internal to the positron storage rEither polarised deuterium or unpolarised high dsity krypton gas was injected into a 40 cm long tublar open-ended storage cell. Target areal densitieto 1.4 × 1016 nucleons/cm2 were obtained for krypton. During these high-density runs HERA operain a dedicated mode for the HERMES experimeThis made it possible to accumulate the krypton stistics within a few days in 1999. The deuterium dwere collected over a period of one year (1999) wa lower-density polarised target. The yields from dterium were averaged over the two spin orientation

The positron trigger was formed by a coincidenbetween signals from three scintillator hodoscoplanes, and a lead-glass calorimeter where a minimenergy deposit of 3.5 GeV (1.4 GeV) for unpolaris(polarised) target runs was required. The identificaof the scattered positrons was accomplished usintransition-radiation detector, a scintillator preshowcounter, and an electromagnetic calorimeter.

The identification of charged pions, kaons, protoand antiprotons was accomplished using the infortion from the RICH detector [23], which replacedthresholdCerenkov counter used in the previouslyported measurements on14N [21]. This detector usetwo radiators, a 5 cm thick wall of silica areogel tilfollowed by a large volume of C4F10 gas, to provideseparation of pions, kaons, and protons over mosthe kinematic acceptance of the spectrometer. Theons and kaons identified by the RICH detectoranalysed in the momentum region between 2.515 GeV, while for the identified protons and antiprtons the momentum region is restricted to the rangetween 4 and 15 GeV in order to reduce possible cominations from misidentified hadrons. The identifiction efficiencies and contaminations for pions, kao


in aontoreri-r-heyron

u-u-ns.en-edri-mialrre-

ck-n-ererge

the

on

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eiontoring

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-No

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tive

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ingar

protons and antiprotons have been determinedMonte Carlo simulation as a function of the hadrmomentum and multiplicity in the relevant detechalf. These RICH performance parameters were vfied in a limited kinematical domain using known paticle species from identified resonance decays. Twere used in a matrix method to unfold the true haddistributions from the measured ones.

The electromagnetic calorimeter [24] provided netral pion identification by the detection of two netral clusters originating from the two decay photoEach of the two clusters was required to have anergy Eγ 0.8 GeV. The background was evaluatin each kinematic bin by fitting the two-photon invaant mass spectrum with a Gaussian plus a polynothat fits the shape of the background due to uncolated photons. The number of detectedπ0 mesons wasobtained by integrating the peak, corrected for baground, over the±2σ range with respect to the cetroid of the Gaussian. The identified neutral pions wanalysed in the same momentum range as the chapions, i.e., between 2.5 and 15 GeV.

Scattered positrons were selected by imposingconstraintsQ2 > 1 GeV2, W =

√2Mν +M2 −Q2

> 2 GeV for the invariant mass of the photon–nuclesystem whereM is the nucleon mass, andy = ν/E <

0.85 for the energy fraction of the virtual photoThe requirements onW andy are applied to excludnucleon resonances and to limit the magnitude ofradiative corrections, respectively. In the previoureported data on14N [21] an additional constraintx =Q2/(2Mν) > 0.06 for the Bjorken scaling variablwas applied, in order to exclude the kinematic regwhere an anomalous ratio of the longitudinaltransverse cross sections for deep-inelastic scattefrom 14N appeared. Since that report this anomwas found to be due to a peculiar local instrumeninefficiency, for which corrections have now beevaluated [25]. By applying these correctionsx-range was extended down tox = 0.02 both for thenew data and for the previously published14N data.

Contributions from target fragmentation were supressed by requiringz > 0.2.

Thez-acceptance is restricted to rather large vaas ν decreases due to the lower constraint onhadron momentum. Hence, to ensure that theν-depen-dence of the multiplicity ratio could not be attribute

d

to a strong variation of the meanz-value, the presendata were confined toν > 7 GeV.

Under the kinematic constraints described abothe number of selected deep-inelastic scattering evis 8.2(7.3)× 105 for krypton (deuterium). The number of charged pions is 11.3(13.5)× 104, while thenumber of neutral pions is 1.9(2.3)× 104. The num-ber of kaons is 2.1(2.3)× 104, and the number of protons and antiprotons is 1.1(1.1)× 104.

The data have been corrected for radiative proceinvolving nuclear elastic, quasi-elastic and inelasscattering, using the codes of Refs. [26,27]. The cof Ref. [27] was modified to include the measursemi-inclusive deep-inelastic scattering cross sectiThe size of the radiative corrections applied toRh

M wasfound to be negligible in most of the kinematic rangwith a maximum of about 7% at the highest valueν, as most of the radiative contributions cancel inmultiplicity ratio [28].

The charged pion sample is contaminated byons originating from the decay of heavier mesons.main effect on the pion multiplicities is due to the dcay of exclusively producedρ0 vector mesons, whichmay affect the multiplicities by an amount rangifrom about 1% at lowz up to 30% (45%) at highz forpositive (negative) pions, as has been estimated froMonte Carlo simulation. The effect on the multipliciratioRh

M is smaller, but does not cancel as theρ0 vec-tor meson are also attenuated in the nuclear medBy taking into account the measuredρ0 nuclear trans-parency [29], the remaining effect onRh

M has been estimated and included in the systematic uncertainty.correction was applied toRh

M . Pions resulting fromthe decay ofρ0 mesons formed in the fragmentatioprocess are included inRh

M .The systematic uncertainty is reduced due to

fact that multiplicity ratios of semi-inclusive aninclusive yields are measured. The contributionsthe systematic uncertainty ofRh

M arise from radiativecorrections (< 2%), hadron identification (1.5% foneutral pions, 0.5% for kaons, 1% for protons andfor antiprotons), overall efficiency (< 2%), andρ0-meson production for positive (0.3–4%) and nega(0.3–7%) pions [28].

The geometric acceptance for semi-inclusive hron production has been verified to be the sameboth the krypton and deuterium targets by studythe multiplicity ratio as a function of the hadron pol


redel

Cties,solidrves

the

a

c-

-opther

ata

as ind the

heea-oet-cat-

forntal

n-

ionr re-

-lcu-

Fig. 2. Charged hadron multiplicity ratioRhM

as a function ofν forz > 0.2. In the upper panel HERMES data on Kr are compato SLAC [19] and CERN [18] data on Cu. In the lower panthe HERMES data on14N are compared with CERN and SLAdata on12C. The error bars represent the statistical uncertainand the systematic uncertainty is shown as the band. Thecurves are calculations from Ref. [10] and the dot-dashed cuare calculations from Ref. [12].

angle. This ratio was found to be constant withinexperimental precision.

The multiplicity ratio has been determined asfunction of eitherz, ν or p2

t , while integrating overall other kinematic variables. In Fig. 2 the multipliity ratios for all charged hadrons withz > 0.2 are pre-sented as a function ofν together with data of previous experiments on nuclei of similar size. In the tpanel the HERMES data on Kr are compared withSLAC [19] and CERN [18] data for Cu. In the lowepanel the reevaluated HERMES data on14N are dis-played together with data on12C [18,19]. Due to theextension down tox = 0.02, the14N data shown inFig. 2 have a higher statistical accuracy than the dreported in Ref. [21]. The HERMES data forRh

M areobserved to increase with increasingν, roughly ap-

Fig. 3. Charged hadron multiplicitiesRhM

as a function ofz forν > 7 GeV. The data are compared to the same calculationsFig. 2. The error bars represent the statistical uncertainties ansystematic uncertainty is shown as the band.

proaching the EMC results at higher values ofν. Thediscrepancy with the SLAC data is partially due to tfact that semi-inclusive cross section ratios were msured at SLAC instead of multiplicity ratios. Thus ncorrections in the SLAC data were made for the targmass dependence of the inclusive deep-inelastic stering cross section, as discussed in Ref. [21].

A stronger attenuation is observed for Kr than14N, the average ratios and the total experimeuncertainties beingRh

M = 0.802± 0.021 andRhM =

0.954± 0.023, respectively. Fig. 3 shows the depedence onz of the same multiplicity ratios forν >

7 GeV. This figure includes the regionz < 0.2, whichcontains contributions from both target fragmentathadrons and leading hadrons decelerated in nucleascattering. Qualitatively, the dependences onν andzof the Kr data resemble those of the14N data, but thefeatures are more pronounced.

The measuredν- andz-dependences for both krypton and nitrogen are compared to several model ca


ee

thick (thin)protons

Fig. 4. Multiplicity ratios for identified pions, kaons, protons and antiprotons from a Kr target as a function ofν for z > 0.2 (left), and as afunction of z for ν > 7 GeV (right). In the upper right panel the multiplicity ratio for identified pions from a14N target are also shown. Thclosed (open) symbols represent the positive (negative) charge states, and the crosses representπ0 mesons. In the bottom panels the averagzandν values are displayed: pions and kaons (protons and antiprotons) are shown as closed (open) circles; the averageQ2 values are indicatedby the open stars referring to the right-hand scales. The inner (outer) error bars represent the statistical (total) uncertainties. Thesolid curves represent the calculations of Ref. [10] for positive (negative) charge states. Multiplicity ratios for negative kaons and antiatthe highestz-bins are not displayed due to their poor statistical significance.

nddi-ter-nta-. Inm-ently-

dta

sticul-

theas-

uon

lations shown in Figs. 2 and 3 as solid curves [10], adot-dashed curves [12]. In Ref. [10] the nuclear mofication of hadron production in deep-inelastic scating is described as a rescaling of the quark fragmetion functions, supplemented by nuclear absorptionthis model the nuclear absorption contribution is doinated by the string interaction, while the subsequinteraction of the fully formed hadron contributes ona few percent toRh

M for krypton. The calculation over

estimates the14N attenuation, but gives a fairly gooaccount of both theν andz dependences of the Kr dafor 0.2 < z < 0.9. In Ref. [12] nuclear modificationof the quark fragmentation process in deep-inelascattering has been evaluated taking into account mtiple parton scattering and induced energy loss inmedium. The only free parameter of this model wtuned to reproduce the14N data, and the derived energy loss has been used to determine the initial gl


el

l-d

, asng

er-

f thes of

tedle

ee-

der-eg--be-the

and

-

sge

vedgis

rkusthen

ncesinndon

edd

tionerandive

onetion.tede ofghtthefa]tionablear

x-ed toop-theveds. Ae

er--

le

ion

density in the Au+ Au collision data collected bythe PHENIX Collaboration at RHIC [30]. The modroughly reproduces the changes inRh

M when goingfrom nitrogen to krypton.

For the first time theν-dependences of the mutiplicity ratio were studied for identified neutral ancharged pions, kaons, protons and antiprotonsshown in the left part of Fig. 4. The correspondiz-dependences ofRh

M with ν > 7 GeV are shown inthe right part of Fig. 4. In the bottom panels the avage values forQ2 andz or ν are displayed for all thepresented data. The results for both charge states opion and the kaon are compared to the calculationRef. [10]. A good description for theπ± andK+ datais observed, while the attenuation is under-predicfor theK− data. No model predictions are availabfor protons and antiprotons. AverageRh

M values areobtained by integrating yields overν andz. The resultspresented in Fig. 4 and the averageRh

M values reportedin Table 1 forz > 0.2, show that the multiplicity ratiosfor positive and negative pions are similar, in agrment with what was already found on14N [21]. In ad-dition, the multiplicity ratio for neutral pions is founto be consistent, within the total experimental unctainties, with that for charged pions as well as for native kaons. However,Rh

M for positive kaons is significantly larger. An even larger difference is observedtween protons and their antiparticles compared tomeson case. These differences inRh

M of positive andnegative kaons, as well as those between protonsantiprotons, are still present atz > 0.5. This is shownin the last column of Table 1, where the averageRh

M

values are reported forz > 0.5, i.e., when emphasising leading hadrons. In addition thez > 0.5 range ismost suitable to compareRh

M of mesons and baryonas this comparison is performed at the same averaνas shown in the bottom right panel of Fig. 4.

It has been suggested [12] that the obserdifferences inRh

M can be attributed to the mixinof quark and gluon fragmentation functions. Thmixing gives a different modification of the quaand antiquark fragmentation functions in nuclei, thleading to a more significant difference betweenmultiplicity ratio of protons and antiprotons thabetween those of mesons. The observed differein the multiplicity ratios can also be interpretedterms of different formation times of baryons amesons [31], or in terms of different hadron–nucle

Table 1Multiplicity ratio values for krypton and deuterium yields integratoverz andν > 7 GeV. Total experimental uncertainties are quote

h-type 〈RhM

〉〈RhM

〉z > 0.2 z > 0.5

π+ 0.775± 0.019 0.712± 0.023π− 0.770± 0.021 0.731± 0.031π0 0.807± 0.022 0.728± 0.024K+ 0.880± 0.019 0.766± 0.024K− 0.783± 0.021 0.668± 0.036p 0.977± 0.027 0.816± 0.029p 0.717± 0.038 0.705± 0.067

interaction cross sections [32]. While this cross secis similar for positive and negative pions, it is largfor negative kaons as compared to positive kaons,even larger for antiprotons than protons, in qualitatagreement with the trend shown by the data.

The data for identified charged pions producedKr and 14N for z > 0.5 were used to estimate thmass-number dependence of the nuclear attenuaThe nitrogen data, measured in a more restricmomentum range between 4–13.5 GeV due to usthe Cerenkov detector, are shown in the upper ripanel of Fig. 4. By using the same constraints onkrypton data and assuming a simpleAα-dependence othe nuclear attenuation 1–Rh

M , the experimental datare found to be closer to theA2/3-dependence [28predicted in Ref. [12], than theA1/3-dependence thafollows from models based on nuclear absorpteffects only. Data on more nuclei are needed to ensystematic studies of theA-dependence of the nucleattenuation effects.

Thept distribution of the observed hadrons is epected to be broadened on a nuclear target compara proton target due to multiple scattering of the pragating quark and hadron. This effect is known asCronin effect [33] and has previously been obserin heavy-ion and hadron–nucleus induced reactionnuclear enhancement at highp2

t is also observed in thHERMES data shown in Fig. 5 both for14N and Kr nu-clei. In this plot the EMC [18] data on Cu which cova differentν-range, 10< ν < 80 GeV, are also displayed. The data forp2

t < 0.7 GeV2 show the attenuation previously discussed, while the data forp2

t 0.7GeV2 reflect thept -broadening ascribed to multipscattering effects. The events atp2

t 0.7 GeV2 con-tribute less than 5% to the total statistics; in addit


matic

at-

n–t ispre-],sticataona

igi-

nsonsthe

rastns,

nceults

theonion

edofss.on

onhayto

ningtioned

l-ir-s-geffsir

hendOP,efürleal

enceda-ar-nd

nce

83)

Fig. 5. Multiplicity ratio for charged hadrons versusp2t for

ν > 7 GeV andz > 0.2. The HERMES data on Kr and14N are com-pared to the EMC [18] data for Cu in the range 10< ν < 80 GeV.The error bars represent the statistical uncertainties. The systeuncertainty for Kr (14N) is shown as the lower (upper) band.

the effect of the restrictionp2t < 0.7 GeV2 on the mul-

tiplicity ratio has been evaluated and found to bemaximum 1% in the lastν bin, well inside the statistical and systematic uncertainty.

This effect is similar to the one reported for protonucleus and nucleus–nucleus collisions [34] busmaller in magnitude. The enhancement is alsodicted to occur at apt -scale of about 1–2 GeV [35,36in agreement with the semi-inclusive deep-inelascattering data shown in Fig. 5. The HERMES dmay help to interpret the new relativistic heavy-iresults from SPS [37] and RHIC [30], which showweakerpt enhancement than expected from the ornal Cronin effect.

In summary, the multiplicities of charged hadroand of identified pions, kaons, protons and antiproton krypton relative to deuterium were measured forfirst time. The data show that the multiplicity ratioRh

M

is reduced at lowν and highz. Different multiplicityratios were observed for various hadrons. In contto the similarity between positive and negative pioa significant difference inRh

M is found betweenpositive and negative kaons and a larger differebetween protons and antiprotons. The different res

for various hadrons may reflect differences inmodification of quark and antiquark fragmentatifunctions [12] and/or in the hadron nucleon interactcross sections.

The hadron multiplicity is observed to be enhancat highp2

t in the nuclear medium, showing evidencethe Cronin effect in deep-inelastic scattering proceThis effect is similar to the one observed in hadrnucleus scattering, with a rise ofRh

M to values aboveunity for p2

t 1 GeV2.Additional measurements of differential hadr

multiplicities on both light and heavy nuclei witpion, kaon and proton identification are underwat HERMES. Such measurements will also helpclarify the issues raised by the present data concerthe mass-number dependence of the hadronizaprocess and of the Cronin effect for various identifihadrons.

Acknowledgements

We thank A. Accardi, F. Arleo, W. Cassing, T. Fater, B.Z. Kopeliovich, U. Mosel, J. Nemchik, H.J. Pner and X.N. Wang for many interesting discusions on this subject. We gratefully acknowledthe DESY management for its support, the staat DESY, and the collaborating institutions for thesignificant effort. This work was supported by tFWO-Flanders, Belgium; the Natural Sciences aEngineering Research Council of Canada; the ESINTAS and TMR network contributions from thEuropean Union; the German BundesministeriumBildung und Forschung; the Italian Istituto Nazionadi Fisica Nucleare (INFN); Monbusho InternationScientific Research Program, JSPS and Toray SciFoundation of Japan; the Dutch Foundation for Funmenteel Onderzoek der Materie (FOM); the UK Pticle Physics and Astronomy Research Council; athe US Department of Energy and National ScieFoundation.

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b

ted withfound thattonergies



n–p Pairing—diagonal matrix elements: Wigner energy,symmetry energy and spectroscopy

R.R. Chasmana,b

a Physics Division, Argonne National Laboratory, Argonne, IL 60439-4843, USAb Department of Particle Physics, Weizmann Institute of Science, 76100 Rehovot, Israel

Received 16 June 2003; received in revised form 18 September 2003; accepted 3 October 2003

Editor: W. Haxton

Abstract

The role of diagonal matrix elements in n–p pairing is investigated. It is found that diagonal matrix elements, calculareasonable two-body interactions, explain the Wigner energy and the symmetry energy in a transparent way. It is alsothe diagonal matrix elements explain most of the changes in level density near ground ofN = Z odd–odd nuclei as comparedN = Z + 2 odd–odd nuclei. In addition, it is found that diagonal matrix elements have a major effect on the excitation eof particle states relative to hole states in odd–mass nuclides near theN = Z line. 2003 Published by Elsevier B.V.

fi-re.tud-p-of

ntialsi-

odel

n-twopof

Ineu-ber

-dv-

ted,sin-

the

edus

For nuclides near theN = Z line, in addition tolike particle pairing, n–p pairing effects play a signicant role in determining low-energy nuclear structuThe interplay of these pairing modes has been sied in the framework of extended quasi-particle aproximations [1–5] and in terms of exact solutionsthe degenerate model [6–10]. There is a substaamount of ongoing work in both the extended quaparticle approach [11–14] and in the degenerate mapproach [15,16].

In a previous study [17] of n–p pairing, we costructed wavefunctions that take the two neutron–proton ‘alpha particle’ correlations, implicit in n–pairing, explicitly into account. A second feature

E-mail address: [email protected] (R.R. Chasman).


this approach is triple projection before variation.addition to the exact projection of both proton and ntron particle numbers, we project exactly the numparity of theT = 0 andT = 1 n–p pairs.Q = 1 de-fines a solution in which the number of n–pT = 0pairs is even andQ = 2 is a solution with odd numbers ofT = 0 pairs. In a later work [18], we extendethis method to include blocked levels, i.e., Nilsson leels with an odd number of particles. We also nothe occurrence ofΩ-blocking in Nilsson levels, i.e.a Nilsson level occupied by a single neutron and agle proton both with the same value ofΩ . The pair-ing matrix element for such pairs was taken to besame as that of otherT = 0 diagonal pairing matrixelements.

In this Letter, we consider a slightly extendversion of the Hamiltonian used in our previo


48 R.R. Chasman / Physics Letters B 577 (2003) 47–53

p-

is

eingver,them

ine

t isWeical

nts

et ofore

ion

il-ro-fual

areds–oth

cedtingff-e

tstrix

ghanthe

h

c-ntsa-

ts.ionsde-y-Shena-

ghnts.v-

ndt of

ndsle-anat

ons, we

studies of n–p pairing.

H =∑k>0

εk(a†kak + a

†−ka−k + b

†kbk + b

†−kb−k)

−∑i,j

GT =1i,j [A†

i Aj + B†i Bj + C

†i Cj ]

−∑i,j

GT =0i,j

[D

†i Dj + (M

†i Mj + N

†i Nj )

(1)× δ(Ωi,j )],

wherea†k (b

†k) denotes a neutron (proton) creation o

erator;Ai† = (a

†i a

†−i ) andBi

† = (b†i b

†−i ). TheT = 1

n–p pair creation operator isCi† = (1/

√2)[a†

i b†−i +

a†−ib

†i ] and theT = 0 n–p pair creation operator

Di† = (1/

√2)[a†

i b†−i − a

†−ib

†i ].

The new terms in our Hamiltonian areM†i =

(a†i b

†i ) andN

†i = (a

†−ib

†−i ). The importance of thes

terms has long been recognized [4] for finite crankfrequencies. In the absence of cranking, howethese terms are relevant only for levels havingsame value ofΩ , the projection of angular momentuon the nuclear symmetry axis. The factorδ(Ωi,j )

denotes this fact. The other two-body interactionsthe Hamiltonian are not limited in this way, so wassume that theM† andN† terms will not give riseto important collective correlations atω = 0.

However, there is one set of these terms thaimportant—namely the diagonal matrix elements.take these diagonal matrix elements to be identwith diagonal matrix elements for theT = 0 D† pairs.This is motivated by the fact that the matrix elemeare the same when calculated with aδ-interactionor a density-dependentδ-interaction. The existencof these terms was recognized in our treatmenΩ-blocked pairs. Here, we treat these terms mconsistently and fully.

Our ordering convention is to put neutron creatoperators before proton creation operators in theC†,D†, M† andN† operators that appear in the Hamtonian and in the wavefunctions. We define the pton wavefunction with positivejz as the negative othe equivalent neutron wavefunction to retain the usplus sign inC†.

In the Hamiltonian, the single-particle energiesunderstood to be eigen-states of a deformed WooSaxon potential. As we are interested in the smo

features of n–p pairing, we assume equally spaNilsson levels, each level capable of accommodatwo neutrons and two protons. We further take all odiagonalT = 0 pairing matrix elements to be the samand all T = 1 off-diagonal pairing matrix elemento be the same (the usual constant pairing maelement approximation). As the 0+ state is the groundstate in the odd–odd nucleus60Ga and the 1+ stateis the ground state in the odd–odd nucleus58Cu, itis reasonable to equate theT = 1 andT = 0 pairingmatrix elements in theA ∼ 60 region. As we are usinequally spaced levels in our calculations, rather tthe actual levels, we use the symbol EE to denoteelement withZ = 30 and OO for the element witZ = 31.

A study of pairing matrix elements [19] in the atinides showed that diagonal pairing matrix elemeare roughly twice as large as off-diagonal pairing mtrix elements on average, using either aδ or a density-dependentδ-interaction to calculate matrix elemenWe have repeated this analysis using wavefunctfor orbitals relevant to theA ∼ 60 mass region and finthat the ratio of diagonal to off-diagonal matrix elments is 1.9 for aδ-interaction and 1.94 for a densitdependentδ-interaction. Using the more realistic D1Gogny interaction [20], this ratio is 2.4 and this is tratio that we have adopted in our calculations. By alyzing nuclides far from theN = Z line, Satula andWyss found [21] an empirical value for the pairinstrength that is 19/A. However, they do not distinguisbetween diagonal and off-diagonal matrix elemeThe Gogny interaction gives 0.316 MeV for the aerage off-diagonal pairing matrix element atA = 60,in agreement with the empirical analysis of Satula aWyss. It gives an average diagonal matrix elemen0.758 MeV. As pairing forces roughly follow a 1/Adependence, it is useful to note that this correspoto a 45.5/A dependence for the diagonal matrix ements. Using a Woods–Saxon potential, we foundaverage single particle level spacing of 0.85 MeVA = 60 and this is the spacing used in the calculatidescribed below. In the calculations presented hereuse 30 Nilsson levels.

Our variational wavefunction is a product form

(2)Θ =k∏

Ψk

m∏Φm

s∏Ξs |0〉,

R.R. Chasman / Physics Letters B 577 (2003) 47–53 49

s,x

ion

ene-

in-in

e

gu-

ra-

the].

rero-is

the

ose—BEedto

antieslaterctsrgy,rgy

efultantthelaten.ed

ed

n-ngrre-

telateil-

thethe

ew.90–

-ange

where the indexk runs over the unblocked orbitalthe indexm runs over all blocked orbitals, the indes runs overΩ-blocked orbitals and|0〉 is the physicalvacuum.

For the unblocked orbitals,Ψk is given by

Ψk = [1+ U(1, k)A†

k + U(2, k)B†k + U(3, k)C†

k

(3)+ U(4, k)D†k + U(5, k)(W†

k )],

whereU(i, k) are variational amplitudes.W†k denotes

the configuration in which levelk is occupied by twoneutrons and two protons. The ordering of creatoperators inW† is A†B†.

For the blocked orbitals,Φm is given by

Φm = [V (1,m)a†

m + V (2,m)b†m + V (3,m)A†

mb†m

(4)+ V (4,m)a†mB†

m

],

whereV (i,m) are variational amplitudes. It should bnoted that there is pair scattering between the oparticle and the three particle configurations inΦm,but there is no scattering between configurationsΦm0 and configurations inΨm0, because the twobody interaction preserves particle number parityall levels.

Finally for theΩ-blocked orbitals, considering th+Ω configuration, one has

Ξs = [a†s b

†s ].

We next evaluate the diagonal energy of each confiration.

(5)E(Ai†) = E(Bi

†) = E(Ci†) = 2εi − GT =1

i,i ,

(6)E(Di†) = 2εi − GT =0

i,i ,

(7)E(Wi†) = 4εi − 3∗ (

GT =0i,i + GT =1

i,i

).

Note that diagonal contributions fromM†i Mi and

N†i Ni are included inE(Wi

†). For Ω blocked con-figurations,

(8)E(Mi†) = E(Ni

†) = 2εi − GT =0i,i .

For the levels having odd number parity configutions, the diagonal energies are

(9)E(ai†) = E(bi

†) = εi

and

E(Ai†bi

†) = E(ai†Bi

†)

(10)= 3εi − 3

2

(GT=0

i,i + GT =1i,i

).

The Wigner energy anomaly is a sharp increase inbinding energy ofN = Z even–even nuclei [21–24It has been noted that a similar effect inδV (N,Z),defined below, occurs far from theN = Z line [26,27].In light nuclei, where shell model calculations afeasible, the Wigner energy anomaly can be repduced [24,27] by shell model calculations. In thcommunication, we consider only nuclides nearN = Z line.

To understand the Wigner energy, we decompthe binding energies (BE) of nuclei into two termsthe Slater BE and the correlation BE. The Slateris the binding energy of the configuration obtainby filling the lowest single-particle orbitals subjectconstraints onQ, the number parity ofT = 0 n–ppairs. The energy of this single Slater determinwavefunction is just the sum of the diagonal energenumerated above. We refer to this energy as the Senergy or zeroth-order energy. Correlation effeincrease the binding energy. The correlation eneis defined as the difference between the total eneand the Slater energy. This decomposition is usbecause the correlation energy is essentially consfrom one even–even nucleus to the next whensingle particle levels are equally spaced. We calcuthis correlation energy at two levels of approximatioThe first approximation is to use the energy obtainfrom the variational wavefunction of Eq. (2), denotasΘVar.

At the next level of approximation, we do a cofiguration interaction calculation. We vary the pairiinteraction strengths associated with each of the colated modesA†, B†, C† andD† separately to generaa series of wavefunctions. For example, we calcua ground state variational wavefunction for a Hamtonian in which all of the interaction strengths aresame as those of the physical Hamiltonian, withexception ofGn–n. We take a value ofGn–n that is suf-ficiently smaller than the true value to generate a nvariational state that has an overlap in the range 00.95 withΘVar. This might be denoted asΘ1. We thentake a value ofGn–n that is sufficiently large to generate yet another state that has an overlap in the r


r-l-ys-he

ntoela-tatessteare.

hety,

to

is

ionenst.

is

y

al

e

y

gies

dd

ior.

ra-xi-

e

0.90–0.95 withΘVar, Θ2. We repeat this procedure foGp–p, Gn–p,T =1, andGn–p,T=0. This gives eight wavefunctions in addition toΘVar. We then do a diagonaization of these nine wavefunctions, using the phical values of the pairing interaction strengths. Tnon-orthogonality of the basis states is fully taken iaccount. This gives a better estimate of the corrtion energy. When there are nearly degenerate swith the same value ofQ, the diagonalization involve9n basis states, wheren is the number of degenerastates. The correlation energies given in this Letterobtained from configuration interaction calculations

The Wigner energy [24] is defined in terms of tBE of various combinations of nuclei in the quantiδV (N,Z), where

δV (N,Z) = 1

4

[BE(N,Z) − BE(N − 2,Z)

− BE(N,Z − 2)

(11)+ BE(N − 2,Z − 2)].

ForN andZ even, the Slater energy approximationδV (N,Z) is

(12)δV (N,Z) = 1

4

(GT =1

i,i + 3GT=0i,i

)for N = Z

and

(13)δV (N,Z) = 0 for N = Z.

Within the accuracy of our calculations, thereno change inδV (N,Z) arising from the correlationenergy corrections, for the values ofN and Z thatconcern us. Specifically, the configuration interactresults give a correlation energy varying betwe6.49 and 6.56 MeV for the ground states of intereAlthough the correlation energy is fairly large, itessentially constant.

For N and Z odd, the relevant Slater energapproximations toδV (N,Z) are

(14)δV (N,Z) = 1

2G>

i,i for N = Z

and

δV (N = Z + 2,Z) = 1

8GT =1

i,i + 3

8GT =0

i,i − 1

4G>

i,i

(15)for N = Z + 2,

where G>i,i denotes the larger of the two diagon

pairing matrix elements. In theA = 60 region we have

taken theT = 0 andT = 1 pairing strengths to bthe same. In this case, we getδV (N = Z + 2,Z) =(1/4)Gi,i .

For even–even nuclei [24], the Wigner energy is

W(A) = δV

(A

2,A

2

)

(16)

− 1

2

[δV

(A

2,A

2− 2

)+ δV

(A

2+ 2,A

)].

For odd–odd nuclei, the Wigner energy is

W(A) = 1

2

[δV

(A

2− 1,

A

2− 1

)

+ δV

(A

2+ 1,

A

2+ 1

)]

(17)− δV

(A

2+ 1,

A

2− 1

).

Note thatW(A) for odd–odd nuclei involves onleven–even nuclei, and there are no changes inW(A)

from correlation energies, as the correlation enerare essentially the same.

There is a second combination ofδV (N,Z) termsthat contributes to the Wigner energy in odd–onuclei.

d(A) = 2

[δV

(A

2,A

2− 2

)+ δV

(A

2+ 2,

A

2

)]

(18)− 4δV

(A

2+ 1,

A

2− 1

).

The first two terms ind(A) involve binding energies inodd–odd nuclides. The values ofd(A) extracted fromexperimental data are quite irregular [24] in behavFor 62OO, we get a value of−0.32 MeV for thecorrelation energy contribution tod(A).

Plugging in the energies of the relevant configutions, we immediately get the Slater energy appromations toW(A) andd(A) as

(19)W(A)e–e = 1

4

(3∗ GT =0

i,i + GT =1i,i

),

(20)W(A)o–o = 1

4

(3∗ GT =0

i,i + GT =1i,i

),

(21)d(A) = 1

2

(GT =0

i,i + GT =1i,i

) + (GT =0

i,i − G>i,i

).

The fact that theT = 0 matrix elements dominate thexpression forW(A) does not mean thatT = 0 pairing


e

toe-e-

-e

x-tan-

–

theIn

ndter

nthe

,lys of

thergymtheandP

twolledhich

s.

la-

dn

fortsuseingnalre

ngns

diesr.

ionrgy.r

correlations are more important than theT = 1 pairingcorrelations in these nuclei.

TakingGT =1i,i = GT =0

i,i , all three quantitiesW(A)e–e

andW(A)o–o andd(A) have the same numerical valuin the Slater energy approximation, i.e.,Gi,i which is45.5/A MeV. The correlation energy contributionW(A) is zero. This is in extraordinarily good agrement with the empirically determined [24] smooth dpendence of 47/A MeV. In [21], it was noted that the1/A dependence ofW(A) may be an artifact. Our result explains the reason for a 1/A dependence of thWigner energy. The value ofd(A), after including thecorrelation energy contributions, is 0.44 MeV. The etracted values are very irregular, but all are substially less thanW(A).

We turn next to the excitation energies ofQ = 2states relative to theQ = 1 state in odd–odd and evenevenN = Z nuclides. In an odd–oddN = Z nucleus,theQ = 1 andQ = 2 states are degenerate whenT = 0 andT = 1 pairing strengths are the same.lowest order, theQ = 2 excited state of anN = Z

even–even nucleus differs from theQ = 1 ground stateby breaking the quartet in the last occupied level apromoting a n–p pair to the next level. The Slaenergy approximation for this energy difference is

BE(Q = 2) − BE(Q = 1)

(22)= 2)ε + 2[GT =0

i,i + GT =1i,i

].

Taking )ε of 0.85 MeV and Gi,i = 0.76 MeV,this gives a value of 4.74 MeV for the excitatioenergy. This is in moderately good agreement withsmoothed empirical value [25] given as

(23)BE(T = 0) − BE(T = 1) = 150

A+ 24√

A

which gives 5.6 MeV atA = 60. The correlationenergy is comparable for theQ = 1 and Q = 2states of theN = Z even–even nuclei. Actuallythere are twoQ = 2 states near 5 MeV. Crudespeaking, these two states are linear combinationtwo configurations:

(1) aD† n–p pair in level 15 and aC† n–p pair in level16 and;

(2) a C† n–p pair in level 15 and aD† n–p pair inlevel 16.

Fig. 1. Excitation energy ofQ = 2 states inN = Z nuclei. Theexcitation energy is plotted as a function ofGT=0 for GT=1 fixedat 0.316 MeV. The solid lines show the excitation energy ofQ = 2 states in60EE. The dashed line shows the excitation eneof the lowestQ = 2 state in62OO. The results are obtained froa configuration interaction calculation. In the box, we showSlater determinant approximation for the distribution of protonsneutrons forQ = 1 andQ = 2 in the even–even case. The letter(N) above a line indicates a proton (neutron) in that level. Thelevels shown are levels 15 and 16. All levels below level 15 are fiin this order. The energy expressions are the Slater energies, wconsist of single particle energies plus diagonal pairing energie

We have carried out configuration interaction calcutions of the splittings of theQ = 2 andQ = 1 states inN = Z nuclei. The splittings are calculated for fixeGT =1, while varyingGT =0. The results are shown iFig. 1.

In Figs. 2 and 3, the low-lying states are shownN = Z andN = Z + 2 odd–odd nuclei. The resuldiffer somewhat from those shown earlier [18] becaof changes in the single-particle spacings, pairstrengths and the inclusion of the additional diagoterms in the Hamiltonian. Qualitatively, the results aquite similar to the earlier calculations. The strikifeature is that the lowest blocked level configuratioare at an excitation of roughly 3 MeV in62OOwhile in 64OO a blocked configuration is the grounstate. When there is blocking, correlation energin blocked and unblocked configurations will diffeHere, there is a contribution to the relative excitatenergies due to differences in the correlation eneThis difference is∼ 1 MeV. Differences in Slateenergies give rise to somewhat larger shifts. In62OO,


senalof

nant

given

s

ird

erein

ble

rgeearted.hernearetionleole

neelsing

x,own,ter

ma-is

eerstorrgywo

ing6.in

gu-ther-

, theicle

ngf us-

Fig. 2. Excitation energies ofQ = 1, Q = 2 and blocked statein 62OO. GT=0 and GT =1 have the value of 0.316 MeV. Tharrowhead on the left of all blocked levels indicates an additiofactor of two in the number of levels coming from the two valuesΩ with Ω = |Ω1±Ω2|. TheΩ-blocked levels in theQ = 1 columnare marked with an asterisk. In the box, the Slater determioccupations of levels 16 and 17 are shown, for the lowestQ = 1state and the lowest blocked state. The Slater energies are also

the excitation energy of the blocked configuration i

(24)E(BL) − E(Q = 1) = )ε + Gi,i + )ECorrelation.

The first two terms contribute 1.6 MeV and the thone∼ 1 MeV. In 64OO,

(25)E(Q = 1) − E(BL) = )ε + Gi,i − )ECorrelation.

In the Slater approximation to the ground state thare three nucleons in level 16 and one nucleonlevel 17. The relevant energy is 3ε(16) + ε(17) −3Gi,i . In the lowest collective state, the comparaenergy is 2ε(16) + 2ε(17) − 2Gi,i . We use Gi,i

without a superscript here, as we have taken theT = 0andT = 1 matrix elements to be the same. These lachanges in level densities [28] of odd–odd nuclei nground, shown in Figs. 2 and 3 have been documen

Large diagonal matrix elements give rise to anotunusual spectroscopic effect in odd mass nuclidestheN = Z line. In the61EE, the lowest excited statis a particle state and the first hole state excitais at roughly twice the excitation of the first particstate. In the Slater energy approximation, the first h

.

Fig. 3. Excitation energies ofQ = 1, Q = 2 and blocked states i64OO. Off-diagonalGT =0 and GT=1 matrix elements have thvalue of 0.316 MeV. The arrowhead on the left of all blocked levindicates an additional factor of two in the number of levels comfrom the two values ofΩ with Ω = |Ω1 ± Ω2|. The Ω-blockedlevels in theQ = 1 column are marked with an asterisk. In the bothe Slater determinant occupations of levels 16 and 17 are shfor the lowestQ = 1 state and the lowest blocked state. The Slaenergies are also given.

state is even higher in energy. The Slater approxition to the excitation energy of the first particle stateε(17) − ε(16). For the first hole state, there are thrconfigurations with similar Slater energies. The fitwo configurations consist of promoting a protona neutron to level 16 from level 15. The Slater eneapproximation to the excitation energy in these tcases isε(16)− ε(15)+ 2Gi,i . This is 2.35 MeV. Thethird zeroth-order configuration consists of promottwo protons and a neutron from level 15 to level 1The Slater approximation to the excitation energythis case is 3ε(16) − 3ε(15). This is 2.55 MeV. InFig. 4, we show the spectra before and after confiration interaction effects are taken into account. Innucleus63OO, the relative excitation energies of paticle and hole states are reversed. In this nucleusfirst excited state is a hole state and the first partexcited state is∼ 1 MeV above it.

In conclusion, we find that large diagonal pairimatrix elements are an inevitable consequence o


ass

ls tohow

ther. Inromionence

s.ner

e-rgedd–

ar-nu-

e

udeson-s-

esels,for

s-b-g

n. Ins.s ofedDi-

63.

71)

84

84

11.

4)

Fig. 4. Excitation energies of particle and hole states in the odd mnucleus61EE. Off-diagonalGT=0 andGT =1 matrix elements havethe value of 0.316 MeV. We assume a value ofΩ , the projection ofangular momentum on the symmetry axis, for each of the levedifferentiate particle and hole states. In the first column, we sthe Slater determinant level occupations in the ground state. Insecond column, we show the excitation spectrum in this ordethe third column, we show the excitation spectrum obtained fconfiguration interaction calculations. The difference in excitatenergies of the first particle and first hole states are a consequof the diagonal pairing matrix elements.

ing semi-realistic or realistic two-body interactionThese diagonal matrix elements explain the Wigenergy anomaly and account for most of the symmtry energy. These matrix elements explain the lachanges in the level density near ground of the oodd nucleiN = Z + 2 compared toN = Z. Finally,these matrix elements give rise to a large shift of pticle states relative to hole states in the odd-massclides near theN = Z line. Although we have set thT = 0 matrix elements equal to theT = 1 matrix el-ements, moderate changes in the relative magnitof these matrix elements should not change the cclusions of this Letter substantially. However, it is esential to include theW† configuration explicitly forunblocked levels in order to take the effects of thmatrix elements fully into account. In blocked levethe three nucleon configurations must be includedthe same reason.

Acknowledgements

I thank I. Talmi for very several valuable discusions on n–p pairing and J.L. Egido and L.M. Roledo for providing me with a program for calculatinpairing matrix elements using the Gogny interactiothank A. Volya and W. Satula for useful conversatioThe calculations were carried out on the computerthe MCS Division at Argonne. This work is supportby the US Department of Energy, Nuclear Physicsvision, under Contract No. W-31-109-ENG-38.

References

[1] A. Goswami, Nucl. Phys. 60 (1964) 228.[2] A. Goswami, L.S. Kisslinger, Phys. Rev. B 26 (1965) 140.[3] P. Camiz, A. Covello, M. Jean, Nuovo Cimento 36 (1965) 6[4] A.L. Goodman, Adv. Nucl. Phys. 11 (1979) 263.[5] H.H. Wolter, A. Faessler, P.U. Sauer, Nucl. Phys. A 167 (19

108.[6] B.H. Flowers, S. Szpikowski, Proc. Phys. Soc. London

(1964) 193.[7] B.H. Flowers, S. Szpikowski, Proc. Phys. Soc. London

(1964) 673.[8] K.T. Hecht, Phys. Rev. B 139 (1965) 794.[9] J.C. Parikh, Nucl. Phys. 63 (1965) 214.

[10] J.N. Ginocchio, Nucl. Phys. 74 (1965) 321.[11] A.L. Goodman, Phys. Rev. C 63 (2001) 044325.[12] S. Frauendorf, J.A. Sheikh, Phys. Rev. C 59 (1999) 1400.[13] W. Satula, R. Wyss, Phys. Rev. Lett. 87 (2001) 052504.[14] K. Neergaard, Phys. Lett. B 537 (2002) 287.[15] J. Engel, K. Langanke, P. Vogel, Phys. Lett. B 389 (1996) 2[16] J. Dobes, S. Pittel, Phys. Rev. C 57 (1998) 688.[17] R.R. Chasman, Phys. Lett. B 524 (2002) 81.[18] R.R. Chasman, Phys. Lett. B 553 (2003) 581.[19] R.R. Chasman, Phys. Rev. C 14 (1976) 1935.[20] J.F. Berger, M. Girod, D. Gogny, Nucl. Phys. A 428 (198

23c.[21] W. Satula, R. Wyss, Nucl. Phys. A 676 (2000) 120.[22] E.P. Wigner, E. Feenberg, Rep. Prog. Phys. 8 (1941) 274.[23] I. Talmi, Rev. Mod. Phys. 34 (1962) 704.[24] W. Satula, et al., Phys. Lett. B 407 (1997) 103.[25] A.O. Macchiavelli, et al., AIP Conf. Proc. 656 (2003) 241.[26] N. Zeldes, Phys. Lett. B 429 (1998) 20.[27] D.S. Brenner, et al., Phys. Lett. B 243 (1990) 1.[28] D.G. Jenkins, et al., Phys. Rev. C 65 (2002) 064307.

b

lane

areddictions

ular,f.



The Cronin effect, quantum evolution and the colorglass condensate

Jamal Jalilian-Mariana, Yasushi Narab, Raju Venugopalanc

a Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USAb Department of Physics, University of Arizona, Tucson, AZ 85721, USA

c Physics Department & RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA

Received 1 July 2003; received in revised form 1 September 2003; accepted 19 September 2003

Editor: J.-P. Blaizot

Abstract

We show that the numerical solution of the classical SU(3) Yang–Mills equations of motion in the McLerran–Venugopamodel for gluon production in central heavy ion collisions leads to a suppression at lowpt and an enhancement at thintermediatept region as compared to peripheral heavy ion andpp collisions at the same energy. Our results are compto previous, color glass condensate inspired calculations of gluon production in heavy ion collisions. We revisit the preof the color glass condensate model forpA (dA) collisions in leading order and show that quantum evolution—in particthe phenomenon of geometric scaling and change of anomalous dimensions—preserves the Cronin enhancement opA crosssection (when normalized to the leading twist term) in the leading order approximation even though thept spectrum can changeWe comment on the case when gluon radiation is included. 2003 Published by Elsevier B.V.

sol-a

s ine-n-un-ntly,-sh

cts.pec-] inceer-ultsckghe in-ion

n,

ns,

1. Introduction

The Relativistic Heavy Ion Collider (RHIC) haopened a new frontier in high energy heavy ion clisions. The first data from RHIC which showedlarge suppression in the ratio of produced hadronAA and pp collisions [1] has created much excitment in the heavy ion community. It has led to itense theoretical and experimental work in order toderstand and characterize the outcome. More recehadron spectra indA collisions at RHIC were measured [2] in order to clarify the role of and distingui

E-mail address:[email protected] (Y. Nara).


between initial state and final state (plasma) effeWhether the observed suppression of hadronic stra [3] and disappearance of back to back jets [4central Au+ Au collisions, as well the large elliptiflow [5], in heavy ion collisions at RHIC is due to thquark–gluon plasma is still in need of further expimental investigation. Nevertheless, the recent resfrom thedA collisions at RHIC and the apparent laof strong initial state effects in mid-rapidity and at hipt appear to necessitate the presence of final statteractions in the partonic matter created in heavycollisions at RHIC [6].

Even though the Cronin effect [7] (the observatioat fixed target experiments, that the ratio ofpA andpp cross sections, scaled by the number of collisio


J. Jalilian-Marian et al. / Physics Letters B 577 (2003) 54–60 55

yossts,

des,

inginof

l in-w

ills–

theeniredninlieru-nonre-ag-

cales-olor

ian-

anere.vers ofof

inu-ur

ills

(3)

. (The

the

-re-

ngg–ce,

heis

mb

d

s

li-

es,

is above unity at some intermediatept while belowone at lowpt ) is likely small in high energy heavion collisions as compared to parton energy leffects, it is one of the two main nuclear effecalong with shadowing, expected in high energypA

(dA) collisions. SincepA collisions were proposein order to clarify the role of initial and final stat(medium) effects in high energy heavy ion collisionit is extremely important to have a firm understandof the physics of shadowing and the Cronin effectorder to have a precise understanding of the roleparton energy loss effects in heavy ion collisions.

The Cronin effect in high energypA andAA colli-sions has been the subject of renewed theoreticaterest recently [8–10]. In this brief Letter, we shothat the numerical solution of the classical Yang–Mequations of motion [11,12,14] in the McLerranVenugopalan model [15] does indeed includeCronin effect. We point out the differences betwethis numerical approach and other saturation inspmodels [17,18] which led to the absence of the Croeffect in these models. We revisit some of our earresults forpA collisions and show that quantum evoltion and the so-called geometric scaling phenome[19,20] (plus change of anomalous dimension) pserves the Cronin enhancement even though its mnitude and peak may change.

2. The Cronin effect in AA collisions

In the McLerran–Venugopalan model, the classiYang–Mills equations of motion are solved in the prence of external sources of color charge. These ccharges can be thought of as the highx quarks and glu-ons in the wavefunction of a nucleus and are Gaussdistributed with a characteristic scaleΛs . (In practice,Λs ≈ Qs , the saturation scale.) In principle,Λs can bedetermined from nuclear gluon distributions. It isexternal parameter in the calculations described hPhysical quantities are computed by averaging othe Gaussian-distributed color charges. The detailthese computations for the real time gluodynamicsnuclear collisions can be found in Refs. [11,12,14].

Briefly, the numerical lattice calculationsRef. [12] impose color neutrality condition at the ncleon level and realistic nuclear density profiles. In ocomputations, we first solve the classical Yang–M

Fig. 1.RCP from the McLerran–Venugopalan model for an SUgauge theory. HereΛs0 = 2 GeV, whereΛ2

s0 is the color chargesquared per unit transverse area in the center of each nucleusvalue ofΛs averaged over the entire nucleus is smaller∼ 1.4 GeV.)This result is obtained for a 256× 256 lattice.

equations on the lattice for the two nuclei beforecollision. In the radiation gauge (x+A− +x−A+ = 0),the initial conditions of gauge fieldsAµ for nucleus–nucleus collisions atτ = 0 can be obtained by matching the solutions in the space-like and time-likegions. Requiring that the gauge fields be regular atτ =0, DµiF

µi = 0 andDµ+Fµ+ = J+ for x−, x+ → 0gives the boundary conditions atτ = 0:

Ai(0, xT ) = Ai1(0, xT )+ Ai

2(0, xT ) (i = x, y),

A±(0, xT ) = ±x± i

2

[Ai

1(0, xT ),Ai2(0, xT )

].

Here,Ai1,2 are the pure gauge fields for two incomi

nuclei. Using these initial conditions, classical YanMills equations are solved, assuming boost invarianon a 2-dimensional lattice. The definition of tnumber distribution in the non-perturbative regiondiscussed in detail in [11]. In the transverse Coulogauge∇⊥ ·A = 0, it is

N(k) =√

〈|φ(k)2|〉〈|π(k)|2〉,whereφ(k) andπ(k) correspond to the potential ankinetic terms in the Hamiltonian, respectively.

In Fig. 1, we plotRCP, the ratio of produced gluonin head-on (b = 0 fm) and in peripheral (b = 11 fm)Au–Au collisions normalized by the number of colsionsNcoll, for an SU(3) gauge theory.Ncoll is com-puted self-consistently in our framework and agre

56 J. Jalilian-Marian et al. / Physics Letters B 577 (2003) 54–60

edh

lann in

e.ltsance

r re-ger

he

ults

ba-

er-tin

heitych

udeu-ght

e-

rre-f thettersub-thedi-

ce., isal-tedhe

e bead-

vetherf-utal

ttertemly.

fi-deswn

entbe-ers

Fig. 2. RAA for an SU(2) gauge theory.RAA is the ratio of thept distribution of gluons for Au–Au collisions (Λs0 = 2 GeV)divided by p–p collisions (Λs0 = 0.2 GeV) and normalized bythe ratio of their asymptotic values at largept . Here MV denotesthe McLerran–Venugopalan model with color neutrality imposglobally; Color Neutral I & II impose color neutrality on eacconfiguration at the nucleon level—see text for discussion.

for instance, with Ref. [16]. The ratioRCP is belowunity at low pt and above unity at intermediatept .This shows that the original McLerran–Venugopamodel indeed has the Cronin enhancement. One caprinciple show that this ratio goes to unity at highpt ,but this is numerically intensive and not shown her

Instead, for simplicity, we show in Fig. 2, resufrom a computation of the real time evolution ofSU(2) gauge theory. There is no qualitative differenbetween the SU(2) case and the SU(3) case. Ousults for the SU(2) gauge theory are obtained for lar(512×512) lattices relative to the (256×256) latticesin the SU(3) case. Plotted in Fig. 2, is the ratio of tpt distribution of gluons from Au–Au collisions (withΛs0 = 2 GeV) to that inp–p collisions, normalized tothe ratio of their asymptotic values (Ncoll) at highpt .Thep–p results here are taken to be the lattice resfor the very small value ofΛs0 = 0.2 GeV. The latticeresult in the latter case is equivalent to the perturtive tree level result up to very smallpt ’s. The reasonRAA deviates from unity is due to the multiple scatting (“Cronin”) effect illustrated in Fig. 3—this poinwill be discussed further shortly. The three curvesFig. 2 correspond to the following: MV denotes tMcLerran–Venugopalan model with color neutralimposed only globally over the entire nucleus in ea

Fig. 3. Schematic diagram of mono-jet gluon production amplitin kt factorized form (left figure) vs. the non-factorized contribtions arising from solutions of classical Yang–Mills equations (rifigure).

configuration. Color Neutral I & II correspond to thmore stringent condition where color neutrality is imposed on the scale of a nucleon. The former cosponds to the case where monopole component onucleon color charge is subtracted while in the lacase, both monopole and dipole components aretracted. As has been noted previously in Ref. [12],effect of these more stringent color neutrality contions is to induce a power law dependencepn

t at lowpt

for the correlator of color charges in momentum spaThis dependence, albeit non-perturbative in originsimilar to that induced by perturbative color neutrity which arises from the color screening of saturagluons generated in the quantum evolution [19]. Tsoftening of the Cronin enhancement can thereforunderstood as resulting from color screening or “showing” of the initial gluon distributions.

In a nice paper, Kovchegov and Mueller hashown that the choice of gauge can determine wheinteractions are “initial state” or “final state” efects [21]. In our numerical computations (carried oin Aτ = 0 gauge) initial state as well as some finstate interactions are included. We qualify the labecause due to the strong expansion of the syswith time, gluon field strengths decrease very quickHigh pt modes (pt > Λs0) in particular are linearizedat very early times and therefore, suffer no furthernal state interactions. On the other hand, soft mostill interact with each other for a long time as shoin Ref. [13]. Therefore, the lattice result ofRCP > 1in Fig. 1 can be regarded as the Cronin enhancemresulting from these rescatterings. The interactiontween hard and soft modes for occupation numb


eseap-achre-is

hesown

.for

n

4.

lassthe

ion

ted

theustives1],the

asbles

inereumheionhis

doheeforerngsnintionaree

iningefor

tsd

.inn

of

oss

f 1 remains an outstanding problem. Naively, thinteractions are of higher order in the classicalproach but at late times, with the classical approbreaking down, they become competitive. Despitecent progress [22], a full treatment of this problemlacking.

We now compare our treatment to other approacin saturation based models. Since there is no kncompleteanalytical solution for the collision of twonuclei [23,24], asimplifiedmodel was used in [16]In this “kt factorized” approach, the cross sectiongluon productions is given by

Edσ

d3p= 4πNc

N2c − 1

1

p2t

×p2t∫dk2

t αsφA

(x1, k

2t

)φA

(x2, (pt − kt )

2),whereφA(x,pt ) is the unintegrated gluon distributiofunction of a nucleus

GA(x,Q2) ≡

Q2∫dk2

t φA(x, kt ).

This equation describes mono-jet production in thektfactorized form and can be visualized as in Fig.Radiation of additional jets are down by powers ofαs .The connection to gluon saturation and the color gcondensate is phenomenological and comes fromassumed form of the unintegrated gluon distributφA(x, kt) in the transverse momentum regionk2

t Q2

s . In the perturbative region, wherek2t Q2

s ,

(1)φA

(x1, k

2t

) ∼ 1/k2t ,

while in the saturation region, wherek2t Q2

s ,

(2)φA

(x1, k

2t

) ∼ 1/αs.

In [16] these two asymptotic forms of the unintegragluon distribution are then matched atQs . In thisapproach, there is only a single scattering inkt > Qs region and multiple scatterings at scales jaboveQs are not included. Since the non-perturbatinput in the form of the “gluon liberation factor” iincluded from the numerical lattice simulations [1this approach likely includes phenomenologicallyphysics of the CGC for global observables suchthe centrality and rapidity dependence of observa(further discussed in the next section).

Fig. 4. Mono-jet production cross section inkt factorized form.

The samekt -factorized formalism is consideredRef. [17]. The authors however additionally considthe effects, at moderatept ’s, due to the change in thunintegrated gluon distributions arising from quantevolution. In particular, they take into account tchange in the distributions due to the modificatof the anomalous dimensions in the evolution. Tchange leads to a scaling withNpart as opposedto Ncoll scaling. (Note that these modificationsnot affect the prior results of Ref. [16] since tmultiplicities, at thept ’s at which they occur, arrather small.) However, the Cronin enhancementpt distributions is missed in [16,17]. On the othhand, in our numerical computations, all rescatteriare included at the classical level leading to the Croenhancement. Note though that quantum evoluis absent in our lattice calculations—its effectsonly implicitly included through the magnitude of thsaturation scale.

In addition to their importance for the Croneffect, the non-factorized contributions illustratedFig. 3 likely play a significant role in determininthe total gluon multiplicity as well. This can bunderstood by comparing the numerical resultsthe gluon liberation coefficientfN [11,14] whichgive fN = 0.3–0.5, in contrast to analytical resulfor this coefficient that include only the factorizecontributions and is roughly 3 to 4 times larger [24]

A possible way of including this enhancementthe kt factorized form through quantum evolutiois discussed in [25]. A similar approximationφA(x, kt) in the context ofpA collisions [18] alsoleads to a lack of Cronin enhancement in the cr


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section. It would be interesting to include quantuevolution effects in addition to the Cronin effectour numerical work to quantify the importance of tenergy loss contribution. This work is in progress awill be reported shortly [26]. Below, we considerpAscattering and explicitly show that inclusion of highorder scatterings leads to the Cronin effect.

3. The Cronin effect in pA collisions

Even though the Cronin effect in a high enerheavy ion collision is quite small at highpt ascompared to the parton energy loss effects, it is qimportant in a proton (deuteron) nucleus collisisince energy loss effects in the hot medium produin a heavy ion collision, are absent in apA collision.In this section, we revisit the color glass condensresults for a quark or gluon scattering on a nucleusand show that the recent phenomenon of geomescaling and changing of anomalous dimension dnot affect our conclusions as long as we dividepA cross section by its leading twist limit (rather thpp).

Scattering of a quark or gluon on a nucleus usthe color glass condensate formalism and its relato DIS was discussed in [8,9]. It was shown thatscattering cross section is given by

dσqA→qX

d2pt dp− d2bt

= 1

(2π)2δ(q− − p−)

(3)×∫

d2rt eipt ·rt [2− σdipole(x, rt , bt )

]

with

σdipole(x, rt , bt )

(4)≡ 1

Nc

Tr⟨1− V

(bt + rt

2

)V †(bt − rt

2

)⟩ρ,

whereq− (p−) is the longitudinal momentum of thincoming (outgoing) quark, with a similar equatiofor gluon scattering. This is the multiple scatterigeneralization of quark–gluon scattering in pQCD aunlike the leading twist (single scattering) result,finite aspt → 0 due to higher twist effects. In additio

defining

(5)γ (x,pt , bt ) ≡∫

d2rt eipt ·rt [2− σdipole(x, rt , bt )

]

and using the fact thatσdipole(x, rt = 0, bt) = 0, we seethatγ satisfies the following sum rule:

(6)∫

d2pt γ (x,pt , bt ) = 2(2π)2,

for fixed bt . It is clear from this sum rule that if thcross section in (3) is suppressed at lowpt , it must beenhanced at highpt in order to compensate for the lopt suppression so that the sum rule holds.1 The Croninpeak moves to higherpt as one goes to higher ener(or more forward rapidities as well as more centcollisions).

The effects of quantum evolution on our classiresults can be investigated using the renormalizagroup equations [27], and in particular the BalitskKovchegov (BK) [28] equation for the dipole crosection in the largeNc limit. It is straightforward toapply the BK equation to theqA (or gA) scatteringcross section in order to prove that quantum evolupreserves the sum rule in (6). For our purposessuffices to notice thatσdipole(x, rt = 0, bt ) = 0 at anyx(energy) so that the sum rule is preserved by quanevolution and therefore, the Cronin enhancemenstill present. Nevertheless, thept spectra will lookdifferent at different energies since the locationthe Cronin peak as well as its magnitude chanas one goes to higher energies (see, for examFig. 4 in the last paper of [9]). In addition, thchange of the anomalous dimensionγ could modifythe magnitude of the Cronin effect. Nevertheless, sithe BK equation preserves the sum rule in (6) atpartonic level, this modification in the highpt regionwill be compensated by an analogous modificationthe lowpt region so that the sum rule is not violated

One should keep in mind that at RHIC and fmid rapidity and highpt processes (such as thsuppression of hadron yields) the effectivex of thepartons is quite large. For example, forpt ∼ 5–10GeV in mid rapidity, thex range is ∼ 0.05–0.1.

1 In the first paper of [8], a careless wording of the paragrafter Eq. (24) gives the impression that there is no Cronin effThis is not the case and theqA scattering cross section, first derivethere, does have the Cronin enhancement.


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91

91

91

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90

The only potential evidence for gluon saturation ageometrical scaling in hadrons is from HERA whesaturation models work very well only forx < 0.01and fail at higherx. In the case of nuclei, thieffectivex may be slightly higher but cannot be tomuch higher since otherwise, strong gluon shadowwould manifest itself in theF2 structure functionwhich shows no strong shadowing effects at thex

range 0.05–0.1 and as a matter of fact, shows anshadowing! The color glass condensate model iseffective theory of QCD at smallx only and likelybreaks down at the highx ’s relevant for highpt

processes in mid rapidity at RHIC. (This situation wimprove as one goes to higher collision energiesstays in the lowpt region.)

Moving to more forward rapidities (in the projectifragmentation region) will make applications of tcolor glass condensate model more reliable sismaller values ofx in the target are probed. Thsaturation scale is larger, rendering weak coupmethods more reliable. In addition, the contributionhighx region to the cross section will be less importathan that in the mid rapidity region. Whether the mforward rapidities accessible at RHIC are large enofor the physics of gluon saturation to be the dominphysics remains to be seen.

4. Summary

We considered in this note gluon productionheavy ion collisions using the numerical simulatioof the color glass condensate. We showed that thetio of central to peripheral cross sections (or equilently, the ratio of central topp cross sections), normalized by the number of collisions, shows the Croenhancement at highpt as well the suppressionlow pt . We discussed other gluon saturation and coglass condensate inspired models and commentethe absence of the Cronin effect in these models.also consideredpA collisions and showed that, at thpartonic level and in leading order inαs , quantumevolution with energy and the change of anomaldimension preserves the Cronin enhancement (wnormalized to its leading twist term rather thanpp)due to a sum rule satisfied by the dipole cross stion even though the magnitude and location of Cropeak is energy-dependent. When divided by thepp

cross section as done experimentally, our ratiohave suppression at highpt in agreement with the results of Ref. [29].

Note added

After this work was completed, we were maaware of similar work by Kharzeev, Kovchegov aTuchin [29]. Although there is some overlap in odiscussion of thepA case (their focus here being ogluon production), they do not explicitly consider tCronin effect forAA collisions as we have.

Acknowledgements

J.J.-M. and Y.N. would like to thank the Institute fNuclear Theory at the University of Washington fhospitality and the Department of Energy for partsupport while this work was being completed. J.J.-and R.V. are supported by the US Department ofergy under Contract No. DE-AC02-98CH10886 aJ.J.-M. is supported in part by a Program DevelopmFund Grant from Brookhaven Science AssociaR.V. thanks the RIKEN-BNL Research Center at BNfor continued support. R.V. and Y.N. thank Alex Kranitz for discussions. Y.N.’s research is supported byDOE under Contract No. DE-FG03-93ER40792.

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b

lies onrapidlyers which



The low-lying glueball spectrum

Adam P. Szczepaniaka, Eric S. Swansonb,c

a Department of Physics and Nuclear Theory Center, Indiana University, Bloomington, IN 47405, USAb Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA

c Jefferson Lab, 12000 Jefferson Ave, Newport News, VA 23606, USA

Received 2 September 2003; accepted 4 October 2003

Editor: H. Georgi

Abstract

The complete low-lying positive charge conjugation glueball spectrum is obtained from QCD. The formalism rethe construction of an efficient quasiparticle gluon basis for Hamiltonian QCD in Coulomb gauge. The resultingconvergent Fock space expansion is exploited to derive quenched low-lying glueball masses with no free parametare in remarkable agreement with lattice gauge theory. 2003 Published by Elsevier B.V.

ntalerolian. It

andrgy

eenmryeenrk inenten

.

hoc[3],meithglu-delse toes.

[6],per-lityson-u-trym

rgeD

ion

1. Introduction

The scalar glueball has been called the fundameparticle of QCD [1]. Indeed, its existence and nonzmass are a direct consequence of the non-Abenature of QCD and the confinement phenomenonis clear that finding and understanding the scalar (other) glueballs is a vital step in mastering low-eneQCD.

Recently quenched lattice gauge theory has bable to determine the low-lying glueball spectruwith reasonable accuracy [2] (only very preliminadeterminations of other matrix elements have battempted). These data serve as a useful benchmathe development of a qualitative model of the emergproperties of low-energy QCD. The models may thbe used to guide experimental glueball searches.

E-mail address: [email protected] (A.P. Szczepaniak)


Previous models of glueballs have relied on adeffective degrees of freedom such as flux tubesbags [4], or constituent gluons [5]. We note that soof the models listed in Ref. [5] construct states wmassive gluons, while others either use transverseons or dynamically generated gluons masses. Moin the former category contain spurious states duthe presence of unphysical longitudinal gluon modSum rule computations of glueball properties existhowever, they are based on phenomenological proties of the spectrum. Finally, the conjectured duabetween supergravity and large-N gauge theories habeen used to compute the glueball spectrum in nsupersymmetric Yang–Mills theory by solving the spergravity wave equations in a black hole geome[7]. Unfortunately all of these approaches suffer froweak or conjectured connections to QCD.

We present a computation of the positive chaconjugation glueball spectrum which arises from QCand is systematically improvable. The computat


62 A.P. Szczepaniak, E.S. Swanson / Physics Letters B 577 (2003) 61–66

[8]eisall

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2].heour

en

---

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be

b

othat

the[8,

ticatic

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ofow

he

is based on the formalism presented in Ref.in which the QCD Hamiltonian in Coulomb gaugis employed as a starting point. Coulomb gaugeefficacious for the study of bound states becausedegrees of freedom are physical (there are no gfields in this gauge) and a positive definite noexists [9]. Furthermore, resolving the Coulomb gauconstraint produces an instantaneous interactionnon-Abelian analogue of the Coulomb interactiowhich, as shown in Ref. [8] may be used to generbound states. Because the temporal component ovector potential is renormalization group invariantCoulomb gauge (this is not true in other gaugethe instantaneous potential does not depend onultraviolet regulator or the renormalization scale [1This fact permits a physical interpretation of tinstantaneous potential which is a central aspect offormalism.

The pure gauge QCD Hamiltonian may be writtas [9]HQCD =H0 + δH with

H0 = 1

2

∫dx

[E2 + B2]

(1)+ 1

2

∫dx dyρa(x)K(0)(x − y)ρa(y)

and

(2)δH = V3g + V4g + VJ + VC.HereB = ∇ × A is the Abelian part of the chromomagnetic field andE = −∂/∂tA is the chromoelectric field. The third term inH0 represents the nonAbelian, instantaneous Coulomb interaction betwcolor charges,ρa = −f abcEb · Ac, mediated by an effective potentialK0 computed by taking a vacuum epectation value of the Coulomb kernel,

K0(x − y)δab

(3)

= g2〈Ψ |[(∇ · D)−1(−∇2)(∇ · D)−1]x,a;y,b|Ψ 〉,

with Dab = δab∇ − gf abcAc being the covarianderivative in the adjoint representation. For the vuum wave functional,Ψ [A] = 〈A|Ψ 〉 we take a varia-tional ansatz,

(4)Ψ [A] = exp

(−1

2

∫d3k(2π)3

Aa(k)ω(k)Aa(−k)),

with the variational parameterω(k) determined byminimizing the vev ofH . The correction terms inδH include V3g and V4g which are the three- anfour-gluon operators originating from the differenbetween the full and the Abelian chromomagnefield. VJ denotes a contribution from the FaddeePopov determinant in the kinetic term. The effeof VJ and the Faddeev–Popov determinant infunctional integrals have recently being studiedRef. [10] where it was found that its effects caneffectively included in the variational parameterω(k).Finally, VC is the difference between the Coulomoperator and its vev,K0. In the calculation of theglueball spectrum it results in operators mixing twand three, quasiparticle wave functions. We noteafter renormalization the couplingg is absorbed intothe Faddeev–Popov operator, which then definesCoulomb gauge analog of a ghost propagator10]. The renormalized effective potentialK0 is fixedby comparing with the quenched lattice QCD stapotential. A very accurate representation of the stconfinement potential is achieved [8].

The variational vacuum defined above also spifies a Fock space of quasiparticle excitations cresponding to effective gluonic degrees of freed(which we call quasigluons). Such quasigluons o“massive” dispersion relation in the variational vauum and therefore improve the description of gluobound states since mixing between states with difent number of quasiparticles is suppressed due toeffective mass.

The calculation of the vev of the Hamiltonian athe properties of the quasiparticle excitations wdiscussed in Refs. [8,10,11]. These require solvinset of coupled integral Dyson equations and as a reone finds that the functionω(k), which in a free theoryis given byω(k) = k, becomes finite ask → 0. Thevalueω(0) can be related to the slope of the stapotential at large distances.

2. Fock space expansion and the glueballspectrum

The quasigluons which emerge in the analysisRef. [8] set the QCD scale parameter via the lmomentum dispersion relationr0ω(k → 0) = 1.4,wherer0 is the lattice Sommer parameter. Using t

A.P. Szczepaniak, E.S. Swanson / Physics Letters B 577 (2003) 61–66 63

nt

aandeenptge

ue-bu-oneral

s areer-lly,e to

n inall

thehasondentsl of

enssedces

e ason

the

Regge string tension orρ mass to fix the scale thegivesω(0) = 600–650 MeV. It is natural to interprethis scale as a dynamical gluon mass.1 Thus theformalism of Ref. [8] provides a justification ofFock space expansion in terms of quasigluonsgives the leading instantaneous interaction betwthe quasigluons. In view of this it is natural to attema description of low-lying glueballs in the pure gausector of QCD.

In this approach positive charge conjugation glballs are dominated by the two quasigluon contrition. These may mix with three and higher quasiglustates via transverse gluon exchange (and, in genvia any term inδH ). Mixing with single quasigluonstates is excluded because color nonsinglet stateremoved from the spectrum due to infrared divgences in the color nonsinglet spectrum [11]. Finathe scalar glueball is orthogonal to the vacuum duthe form of the gap equation.

The resulting bound state equations are showEq. (5). There is one orbital component of gluebwave function forJP = 0+ and two forJP = (even2)+. These are denoted byψi(k), i = 1,2. The firstterm on the right-hand side of Eq. (5) representsquasigluon kinetic energy (the gluon gap equationbeen employed to simplify the expression), the secterm is the quasigluon self energy, and third represthe interaction between quasigluons in the channeinterest.∫k2dk

(2π)32ω(k)|ψi(k)|2

+ NC

2

∑i

∫k2dk

(2π)3q2dq

(2π)3ω(k)

ω(q)

×[

4

3V0 + 2

3V2

]|ψi(k)|2

− NC

4

∫k2dk

(2π)3q2dq

(2π)3(ω(k)+ω(q))2ω(k)ω(q)

×ψ∗i (q)Kij (q, k)ψj (k)

(5)=E

∫k2dk

(2π)3|ψi(k)|2,

1 The relationship of a dynamical gluon mass to vortex-drivconfinement and gauge symmetry breaking is thoroughly discuby Cornwall; see, for example, the second and third referenof [5].

,

with

(6)

K11 = 3J 2 + 3J − 2

(2J − 1)(2J + 3)VJ

+ J (J − 1)

2(2J − 1)(2J + 1)VJ−2

+ (J + 1)(J + 2)

2(2J + 3)(2J + 1)VJ+2,

(7)

K22 = 3(J + 2)(J − 1)

(2J − 1)(2J + 3)VJ

+ (J + 2)(J + 1)

2(2J + 1)(2J − 1)VJ−2

+ J (J − 1)

2(2J + 1)(2J + 3)VJ+2

and

K12 =K21

= √(J − 1)J (J + 1)(J + 2)

(8)

×[

1

2(2J + 3)(2J + 1)VJ+2

+ 1

2(2J + 1)(2J − 1)VJ−2

− 1

(2J + 3)(2J − 1)VJ

].

The bound state equations for other glueballs arin Eq. (5), with the exception that the wave functiindex takes on a single value. For these casesinteraction kernels are as follows:JP = (odd 3)+ (there is no 1+ gg glueball):

(9)K = J + 2

2J + 1VJ−1 + J − 1

2J + 1VJ+1;

JP = (even 0)−:

(10)K = J

2J + 1VJ−1 + J + 1

2J + 1VJ+1;

JP = 0+:

(11)K = 2

3

(V0 + V2

2

).

In all these relations the interaction is defined as

(12)VL(q, k)= 2π

1∫−1

dx K(0)(q, k, x = k · q)PL(x)


k

oflic-

oru-ur-

s in

r is

tur-i-ree--nt.

henex-desex-

toartth aveion

r ofesale

ther

thatould

andwnthed to

hisgeheblered.

os-re-ara-upn toeuewith

.5).tateras

eest-t

hate-

ese

atesentheel

ex-eVctsgy

and the potentialK(0)(q, k, x) is that derived inRef. [8] with the QCD scale chosen to beω(0) =600 MeV. Finally we note that there are noJP =(odd)−, orC = − glueballs at lowest order in the Focspace expansion.

3. Higher order corrections

It is of course desirable to test the efficacythe Fock space expansion employed here by expitly checking the effect of coupling to the threehigher quasigluon spectrum. This is a difficult copled channel problem and we therefore content oselves with a perturbative evaluation of these effectthis initial study. Specifically, the energy shiftδEn =∑m |〈gg|δH |m(ggg)〉|2/(En − Em) must be evalu-

ated. Duality implies that when the energy transfelarge,(En −Em) > Λ, whereΛ is of the order of theQCD scale, this sum may be evaluated in its perbative form (with partonic gluons in the intermedate state). We compute here the effects of the thgluon coupling fromδH . This is the leading interaction in terms of expansion in the coupling constaAfter renormalizationg2/4π → α(p2) wherep2 rep-resents a characteristic momentum in integrals wcomputing matrix elements. The running couplingpansion for the remaining sum over low energy mois certainly less justifiable, however as shown inamples in Ref. [8], such soft corrections also seembe small. For numerical efficiency the low energy pof the guasigluon exchange was approximated wilocal four-gluon interaction (we note that this effectiinteraction also accounts for the four-gluon interactpresent in the Hamiltonian)

Vc = C(Λ)f abcf ade∫

d3k1

(2π)3d3k2

(2π)3d3k3

(2π)3d3k4

(2π)3

× (2π)3δ(k1 + k2 + k3 + k4)

× exp(−(

k21 + k2

2 + k23 + k2

4

)/Λ2)

(13)×Abi (k1)Acj (k2)A

di (k3)A

ej (k4),

whereC is a dimensionless parameter of the ordeg2(Λ)∼ 1. Standard effective field theory techniquwere subsequently employed: the factorization scΛ was chosen and the couplingC was fixed bycomparison to the lattice scalar glueball mass. Omass predictions then follow. The scaleΛ was then

varied to ensure that the procedure is stable andthe coupling remains “natural” (of order unity). Tmaintain consistency the effect of these terms shobe incorporated into the quasigluon gap equationthe gluon self energy. However, it may be shothat the effect of contact terms are canceled inbound state equation when the gap equation is usesimplify the quasigluon kinetic and self energies. Tis not true for the high-momentum gluon exchanterms which add a UV dominated correction to tsingle gluon kinetic energy. These have negligieffect on low energy spectrum and have been igno

4. Results and conclusions

The lowest order predictions for the quenched pitive charge conjugation glueball spectrum are psented in Table 1. We stress that there are no free pmeters in this computation; the renormalization groparameters and the scale were fixed by comparisothe Wilson loop static interaction [8]. Although onmay anticipate splittings on the order of 100 MeV dto coupled channel effects, the general agreementlattice data is quite good (theχ2 per degree of freedomfor the six measured lowest spin-parity states is 1Nevertheless we note that the authors of Ref. [2] sthat the 3++ may have significant mixing with highestates and the quoted 4++ mass should be regardedpreliminary.

Although it appears to be difficult to push latticmass computations above 4 GeV it would be intering to measure the quenched 4−+ glueball mass to testhe prediction made in Table 1. Lastly we note tall radial excitations lie roughly 1 GeV above their rspective ground states, except the 4++. We have noexplanation for this curiosity, but note that it implithat lattice extractions of the 4++ mass must be madwith great care.

We note that the degeneracy between parity streported in the first reference of [5] is not sehere. We suspect that the degeneracy is due tononrelativistic expansion of the interaction kernmade in that reference.

As stated above, coupled channel effects arepected to modify the spectrum at the 10–100 Mlevel. As an initial estimate of the size of these effewe simply setC = 0 (Eq. (13)) and evaluate the ener

A.P. Szczepaniak, E.S. Swanson / Physics Letters B 577 (2003) 61–66 65

the

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hlyhatllsck

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1)

Table 1Glueball spectrum

State This work LGT (GeV) Ref.(no mixing)

0++ 1.98 1.73(5)(8) [2]a1.754(85)(86) [15]1.627(83) [16]1.686(24)(10) [19]1.645(50) [18]1.61(7)(13) [17]

0++′ 3.26 2.67(18)(13) [2]2++ 2.42 2.40(2.5)(12) [2]

2.417(56)(117) [15]2.354(95) [16]2.26(12)(18) [17]2.380(67)(14) [19]2.337(100) [18]

2++′ 3.11 3.499(43)(35) [13]0−+ 2.22 2.59(4)(13) [2]

2.19(26)(18) [17]0−+′ 3.43 3.64(6)(18) [2]2−+ 3.09 3.10(3)(15) [2]2−+′ 4.13 3.89(4)(19) [2]3++ 3.33 3.69(4)(18)b [2]3++′ 4.294++ 3.99 3.65(6)(18) [14]4++′ 4.284−+ 4.274−+′ 4.98

a The first error is combined statistical and systematic,second is from scale fixing.

b Possible mixing with higher states.

shift due to perturbative one-gluon exchange. Aspected, the scalar glueball mass experiences the lashift, with a reduction in mass of roughly 200 Me(from 1980 to 1790 MeV). It is gratifying that thibrings the scalar glueball into excellent agreemwith lattice gauge theory. We proceed by incorporing the effective contact interaction. The factorizatscale was varied between 0.25 and 10 GeV, stable results were found between 1 and 8 GeV, with a vaof C given roughly by−0.4 in this range. We findthat the tensor glueball mass is reduced by roug100 MeV, while other masses experience somewsmaller shifts. Thus it appears that low-lying gluebaare indeed dominated by their two-quasigluon Focomponents. However it is clear that a careful exanation of coupled channel effects and better lattice dare required to make a definite statement about theficacy of our approach.

t

Fluctuations of the topological charge density hapseudoscalar quantum numbers. This raises thesibility that the QCD anomaly affects the lightest 0−+glueball mass. Topological effects have so far not bincorporated into our formalism. Doing so would rquire modification of the vacuum ansatz to reflectidentification of gauge equivalent field configuratioat the boundary of the fundamental modular regiThis allows contributions from field configurationwith nonzero topological charge. Indeed a cross-obetween the 0−+ and 2++ glueball masses has beobserved on the lattice as a function of the renormized coupling [20] if boundary conditions are impose

Further aspects of the gluonic structure laid ouRef. [8] may be investigated by an examinationthe adiabatic potential surfaces of heavy quarkbrids (this probes nonperturbative gluon-confinempotential couplings). Extensions to the light hybspectrum will prove of interest to searches for thnew states at Jefferson Lab. Finally, the short rastructure of the meson sector is dominated by cpled channel effects and nonperturbative gluodynics. The wealth of experimental information in thsector will provide a definitive test of the dynamibeing advocated in our approach.

Acknowledgements

This work was supported by DOE under contraDE-FG02-00ER41135, DE-AC05-84ER40150 (E.Sand DE-FG02-87ER40365 (A.S.).

References

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,

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9)

7.17;0)

02)

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43.

26

597

l,09

ys.

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(2001) 413.[17] M.J. Teper, hep-lat/9711011.[18] G.S. Bali, K. Schilling, A. Hulsebos, A.C. Irving, C. Michae

P.W. Stephenson, UKQCD Collaboration, Phys. Lett. B 3(1993) 378.

[19] W.J. Lee, D. Weingarten, hep-lat/9805029;H. Chen, J. Sexton, A. Vaccarino, D. Weingarten, Nucl. PhB (Proc. Suppl.) 34 (1994) 357.

[20] B. van den Heuvel, Nucl. Phys. B 488 (1997) 282;P. van Baal, Nucl. Phys. B (Proc. Suppl.) 63 (1998) 126.

b

ix

d foundattempt

keep thent and



Renormalization of the Cabibbo–Kobayashi–Maskawa matrin standard model

Yong Zhou

Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China

Received 3 August 2003; received in revised form 23 September 2003; accepted 4 October 2003

Editor: T. Yanagida

Abstract

We have investigated the present renormalization prescriptions of Cabibbo–Kobayashi–Maskawa (CKM) matrix, anthere is still not an integrated prescription to all loop levels in the on-shell renormalization scheme. In this Letter weproposing a new prescription designed for all loop levels in the present perturbative theory. This new prescription willunitarity of the CKM matrix and make the amplitude of an arbitrary physical process involving quark mixing convergegauge independent. 2003 Published by Elsevier B.V.

PACS: 11.10.Gh; 12.15.Lk; 12.15.Hh

],wa

c-el-e-Ms re-er-

ndandre-ng

dis-lex-n-on-ned.this

-

nya-elp-

uge

As an important part of standard model (SM) [1the renormalization of Cabibbo–Kobayashi–Maska(CKM) quark mixing matrix is a matter of great acount in theory. At present, along with the devopment of exact determination of CKM matrix elments [2], the importance of renormalization of CKmatrix becomes more and more apparent. This waalized for the Cabibbo angle with two fermion genations by Marciano and Sirlin [3] and for the CKMmatrix of the three-generation SM by Denner aSack [4] more than a decade ago. Though DennerSack’s prescription is very delicate and simple, itduces the physical amplitude involving quark mixi

E-mail address: [email protected] (Y. Zhou).


gauge dependent [5]. Recently many authors havecussed this problem [5,6], but because of its compity all of them are limited to one-loop level and an itegrated prescription beyond one-loop level in theshell renormalization scheme has been not obtaiSo we want to propose a new prescription to solveproblem.

As we know a CKM matrix renormalization prescription must satisfy the three conditions [6]:

(1) In order to keep the transition amplitude of aphysical process involving quark mixing ultrviolet finite, the CKM counterterm must cancout the ultraviolet divergence left in the loocorrected amplitude.

(2) It must guarantee such transition amplitude gaparameter independent [7].


68 Y. Zhou / Physics Letters B 577 (2003) 67–70

its

M

al-o-cal-ndeandhentill

tlyfs

d

8].

and

e

theto

ar-3),new

ur

se-

t of

(3) SM requires the bare CKM matrixV 0 is unitary,

(1)∑k

V 0ikV

0∗jk = δij ,

with i, j , k the generation index andδij theunit matrix element. If we split the bare CKMmatrix element into the renormalized one andcounterterm

(2)V 0ij = Vij + δVij

and keep the unitarity of the renormalized CKmatrix, Eq. (1) requires

(3)∑k

(δVikV

∗jk + VikδV

∗jk + δVikδV

∗jk

)= 0.

In order to satisfy these conditions we will renormize the CKM matrix through two steps. First we intrduce a CKM counterterm which makes the physiamplitude ofW+ → uidj convergent and gauge independent below certain loop levels. Next we meit to satisfy the unitary condition of Eq. (3) below thloop levels, and simultaneously keep the divergentgauge-dependent (if it has) part of it unchanged. Tby recursion we construct the CKM countertermsinfinite loop levels.

In order to elaborate our idea clearly we firsintroduce then-loop (n 1) decay amplitude oW+ → uidj as follows (here all of the contributionof the counterterms lower thann-loop level have beenincluded in the formfactors):

Tnij =AL

[FLnij + Vij

(δgn

g+ 1

2δZWn

)

+ 1

2δZuL

nikVkj + 1

2VikδZ

dLnkj + δVnij

](4)+ARFRnij +BLGLnij +BRGRnij ,

with g and δg the SU(2) coupling constant anits counterterm,δZW the W boson wave-functionrenormalization constant (WRC),δZuL andδZdL theleft-handed up-type and down-type quark’s WRC [The added denotationn represents then-loop result,and

AL = g√2ui(p1)/εγLνj (q −p1),

(5)BL = g√2ui(p1)

ε · p1

MW

γLνj (q − p1),

with εµ theW boson polarization vector,γL andγRthe left-handed and right-handed chiral operators,MW theW boson mass. Similarly, replacingγL withγR in Eq. (5) we getAR andBR , respectively.FL,RandGL,R are four formfactors. Here we will only carabout the coefficient ofAL which contains then-loopCKM counterterm. The simplest method to makeamplitudeTn convergent and gauge independent ismake the coefficient ofAL equal to zero, i.e.,

δVnij = −FLnij − Vij

(δgn

g+ 1

2δZWn

)

(6)− 1

2δZuL

nikVkj − 1

2VikδZ

dLnkj .

Obviously such CKM counterterm cannot be guanteed to satisfy the unitary condition of Eq. (so needs to be mended. Here we introduce aset of denotation:δVn, to denote the amended CKMcounterterm which satisfies the unitary condition. Omethod is to constructδVn throughδVn, δVn−1, . . . ,

δV1. Here we state thatδVn is obtained by usingδVn−1, . . . , δV1 as the lower-loop CKM countertermin Eq. (6). Now the unitary condition of Eq. (3) bcomes

δV1V† + V δV

†1 = 0,

δV2V† + V δV

†2 = −δV1δV

†1 ,

δV3V† + V δV

†3 = −δV1δV

†2 − δV2δV

†1 ,

...

δVnV† + V δV †

n = −δV1δV†n−1 − δV2δV

†n−2 · · ·

− δVn−2δV†2 − δVn−1δV

†1 ,

(7)...

In order to solve these equations, we introduce a sesymbolsBn

B1 = 0,

(8)Bn =n−1∑i=1

−δViδV †n−i .

ObviouslyBn satisfies

(9)Bn = B†n.

Assuming the CKM countertermsδV1, δV2, . . . , δVn−1and δVn have been obtained, then-loop amended

Y. Zhou / Physics Letters B 577 (2003) 67–70 69

:

l’sM

lling

he-

ngonnrt off

t oruseeight

) isnd

.

rt--he

n-mal-

in-as

ionicalourof

nly

mal-of

di-uld

-ow-tionn-

eryxt

istheheely

CKM countertermδVn can be determined as follows

(10)δVn = 1

2

(δVn − V δV †

n V +BnV).

This method takes example by Diener and Kniehprescription [6]. It is easy to check that such CKcounterterm satisfies Eqs. (7) atn-loop level. Since thecountertermsδg andδZW are both real in the on-sherenormalization scheme, we can obtain the followresult from Eq. (10) and Eq. (6)

δVnij = 1

2

(∑kl

VikF∗LnlkVlj − FLnij

)

+ 1

4

∑k

(δZuL∗

nki − δZuLnik

)Vkj

+ 1

4

∑k

Vik(δZdL∗

njk − δZdLnkj

)

(11)+ 1

2

∑k

BnikVkj .

The remaining problem is to test whether tamended CKM countertermδVn has the same divergent and gauge-dependent part asδVn, which is the re-quirement of making the physical amplitude involviquark mixing finite and gauge independent. Basedthe renormalizability and predictability of SM, we capredict that the divergent and gauge-dependent paδVn (if it has) must satisfy the unitary condition oEq. (3) atn-loop level

(12)δV DGn V † + V δV DG†

n = BDGn ,

where the superscript DG denotes the divergengauge-dependent part of the quantity. This is becaif not so the unitary condition of Eq. (3) will requirthe divergent or gauge-dependent part of the rCKM counterterm different fromδVn, thus will reducethe physical amplitude ofW+ → ui dj divergent orgauge dependent (see Eq. (4)). In fact Eq. (12satisfied at one-loop level [4,6]. From Eqs. (10) a(12), it is easy to obtain(δV DG

n − δV DGn

)V †

(13)= 1

2

(BDGn − δV DG

n V † − V δV DG†n

)= 0.

Times CKM matrixV at the right-hand side of Eq(13), we have

(14)δV DGn = δV DG

n .

Now we have obtained the proper CKM counteerm at n-loop level. We can construct CKM counterterms till infinite loop levels by recursion, whicwill satisfy the unitary condition of Eq. (3) and makthe physical amplitude involving quark mixing covergent and gauge independent. Since the renorization of CKM matrix is a very complex problem(one can see it from the fact that at present antegrated prescription applicable to all loop levels hnot been obtained in the on-shell renormalizatscheme), our solution is quite simple and pract(see Eq. (11)). On the other hand, we supposeprescription will not break the present symmetriesSM, e.g., Ward–Takahashi identity, because it ochanges the values of CKM matrix elements fromV 0

ij

to Vij + δVij .Lastly we want to point out that the proble

of infrared divergence is unclear in our renormization prescription. As we know, the correctionEq. (4) to the amplitude ofW+ → uidj has theinfrared divergence coming from the Feynmanagrams including photons. This divergence shobe cancelled in the inclusive decay widthW+ →(ui dj , ui dj γ , ui djγ γ, . . .) by the corresponding divergence of the real photon emission processes. Hever, there are no a priori reasons for the cancellaof this divergence in the proposed CKM matrix couterterm, Eqs. (10), (11). Since this problem looks vdifficult to be solved, we want to leave it for the nework.

Acknowledgements

The author thanks professor Xiao-Yuan Li for huseful guidance and the referee for pointing outproblem of infrared divergence in our manuscript. Tauthor also thanks Dr. Hu Qingyuan for his sincerhelp (in my life).

Appendix A

In this appendix we give the explicit result ofδV1.From Eqs. (11) and (8), we obtain

70 Y. Zhou / Physics Letters B 577 (2003) 67–70

1)t

sult

52.

54

00)

75)

6)

02)

δV1ij = 1

2

(∑kl

VikF∗L1lkVlj − FL1ij

)

+ 1

4

∑k

(δZuL∗

1ki − δZuL1ik

)Vkj

(A.1)+ 1

4

∑k

Vik(δZdL∗

1jk − δZdL1kj

),

which is gauge independent sinceδV1ij is gaugeindependent in Eq. (6) [5] and Eq. (10). Eq. (A.is similar as Eq. (12) of Ref. [6]. The ultravioledivergence ofδV1ij is

δV1ij∣∣UV

= 3α∆

64πM2Ws

2W

×[−2

∑k,l =j md,jm

2u,kVilV

∗klVkj

md,l −md,j

+ 2∑

k,l md,jm2u,kVilV

∗klVkj

md,l +md,j

− 2∑

k =i,l mu,im2d,lVilV

∗klVkj

mu,k −mu,i

+ 2∑

k,l mu,im2d,lVilV

∗klVkj

mu,k +mu,i

+ Vij

(∑k

VikV∗ikm

2d,k

(A.2)

+∑k

VkjV∗kjm

2u,k − 2m2

d,j − 2m2u,i

)],

with α the fine structure constant,sW the sine ofthe weak mixing angleθW , and∆ = 2/(D − 4) +γE − ln(4π) + ln(M2

W/µ2) (D is the space–time

dimensionality,γE is the Euler’s constant, andµ is anarbitrary energy scale).mu,i andmd,j , etc. are up-typeand down-type quark’s masses. TheRξ -gauge and thedimensional regularization have been used. This reagrees with the results of Refs. [4,5] and [6].

References

[1] N. Cabibbo, Phys. Rev. Lett. 10 (1963) 531;M. Kobayashi, K. Maskawa, Prog. Theor. Phys. 49 (1973) 6

[2] Particle Data Group, Phys. Rev. D 66 (2002) 1;M. Battaglia, et al., hep-ph/0304132;Z. Xiao, C.-D. Lü, L. Guo, hep-ph/0303070.

[3] W.J. Marciano, A. Sirlin, Nucl. Phys. B 93 (1975) 303.[4] A. Denner, T. Sack, Nucl. Phys. B 347 (1990) 203.[5] P. Gambino, P.A. Grassi, F. Madricardo, Phys. Lett. B 4

(1998) 98;A. Barroso, L. Brücher, R. Santos, Phys. Rev. D 62 (20096003;Y. Yamada, Phys. Rev. D 64 (2001) 036008;D. Espriu, J. Manzano, Phys. Rev. D 63 (2001) 073008.

[6] K.-P.O. Diener, B.A. Kniehl, Nucl. Phys. B 617 (2001) 291.[7] C. Becchi, A. Rouet, R. Stora, Commun. Math. Phys. 42 (19

127;C. Becchi, A. Rouet, R. Stora, Ann. Phys. (N.Y.) 98 (197287.

[8] D. Espriu, J. Manzano, P. Talavera, Phys. Rev. D 66 (20076002;Y. Zhou, J. Phys. G 29 (2003) 1031.

b

eory

ible lowoundaryonditions

nsionalry gives

n thehamperedn which

lkgroundsle matterugh the

, ratherrequire

here areents ofant role.

sic



Boundary terms for eleven-dimensional supergravity and M-th

Ian G. Moss

School of Mathematics and Statistics, University of Newcastle Upon Tyne, NE1 7RU, UK

Received 2 September 2003; accepted 9 October 2003

Editor: P.V. Landshoff

Abstract

A new action for eleven-dimensional supergravity on a manifold with boundary is presented. The action is a possenergy limit of M-theory. Previous problems with infinite constants in the action are overcome and a new set of bconditions relating the behaviour of the supergravity fields to matter fields are obtained. One effect of these boundary cis that matter fields generate gravitational torsion. 2003 Elsevier B.V. All rights reserved.

One of the phenomenologically interesting low energy limits of M-theory corresponds to eleven-dimesupergravity on a manifold with a ten-dimensional boundary. Horava and Witten have argued that this theothe strongly coupled limit of theE8 × E8 heterotic string [1,2]. The gauge and matter fields propagate oboundary and couple to the bulk supergravity. Previous attempts to construct these couplings have beenby the appearance of the square of the Dirac delta function. This Letter presents an improved constructioresults in a consistent set of interaction terms.

The interaction terms in the model are constructed as an expansion inκ2/3, whereκ is the eleven-dimensionagravitational coupling constant. At leading order, the theory is eleven-dimensional supergravity on the bacR10×S1/Z2. Since the orbifoldS1/Z2 is identical to an intervalI , with the covering spaceS1, the background haa boundary consisting of two timelike ten-dimensional surfaces or branes. One of these contains the visibwith which we are familiar and the other contains hidden matter. Gravitational forces are transmitted throinterior which is often called the bulk.

The modified theory described here is presented from the point of view of the manifold with a boundarythan the covering space. The action allows for the possibility that the boundary may curve, as we wouldfor descriptions of cosmology. The main innovations appear in the boundary conditions. In the first place tcorrections to the chirality condition on the gravitino, which are to a large extent forced by the requiremsupersymmetry. There are also boundary conditions for the supergravity three-form which play an importThe resulting theory is supersymmetric at ordersκ0, κ2/3 andκ4/3.

The notation used here is based on [3]. The metric signature is− + · · ·+. Vector indices areI, J, . . . in thebulk, A,B, . . . on the boundary andN in the (unit) normal direction. The outward going normal has extrin

E-mail address: [email protected] (I.G. Moss).

0370-2693/$ – see front matter 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2003.10.027


72 I.G. Moss / Physics Letters B 577 (2003) 71–75

sfy

etry of

tionovariant

elikeoundary,as been

n ontries

e

ditions.required

curvatureKAB . The exterior derivative of ann-form α is (dα)I1...In+1 = (n + 1)−1∂[I1αI2...In+1] and the wedgeproduct(α ∧ β)I1...Im = mCn α[I1...InβIn+1...Im] wheremCn is a binomial coefficient. The gamma matrices satiΓI ,ΓJ = 2gIJ andΓ I...K = Γ [I ...Γ K]. The spinors are Majorana, andψ =ψT Γ 0.

The action will be presented first, followed by an account of the boundary conditions. The supersymmthe action will be discussed at the end. The supergravity part contains the metricg, gravitinoψI and three-formC(with field strengthG= 6dC) [4]. The usual supergravity action is

SSG = 2

κ2

∫M

dµ

(−1

2R − 1

2ψI Γ

IJKD(Ω∗)

JψK − 1

48GIJKLG

IJKL

(1)

−√

2

192

(ψIΓ

IJKLMPψP + 12ψJ Γ KLψM)G∗JKLM −

√2

10! εI1...I11(C ∧G∧G)I1...I11

).

In the 1.5 order formalism used here, the spin connectionΩ is varied as an independent field. The combinaΩ∗ = (Ω + Ω)/2, where hats denote a standardised subtraction of gravitino terms to make a supercexpression.

The background for the low energy limit of M-theory of interest here contains a manifold with timboundaries. The boundary conditions are fixed by symmetries on the covering space. On a manifold with bthe Einstein action is supplemented by an extrinsic curvature term [5–7]. The supersymmetric version hfound previously [8]. The full boundary term with the extrinsic curvature and supersymmetry corrections is

(2)S0 = 2

κ2

∫∂M

dµ

(K − 1

4ψAΓ

ABψB + 1

2ψAΓ

AψN

).

Variation of the actionSSG + S0 gives a boundary condition on the extrinsic curvature and a chirality conditiothe gravitinoP+ψA = 0, whereP+ = (1+ ΓN)/2. These boundary conditions are consistent with the symmeof the orbifoldS1/Z2. The Bianchi identity implies an additional boundary conditionGABCD = 0 which cannotbe derived from the action.

The gauge multiplet contains anE8 gauge fieldAaA and chiral fermionsχa in the adjoint representation. Thaction is based on the Yang–Mills action with an interaction term involving the supercurrent,

S1 = −2ε

κ2

∫∂M

dµ

(1

4FaABF

aAB + 1

2χaΓ ADA(Ω)χ

a + 1

4ψAΓ

BCΓ AFa∗BCχ

a

(3)+ 1

192χΓABCχψDΓ

ABCDEψE

).

The constantε sets the relative scale of the matter coupling. The total actionS = SSG + S0 + S1. Note thatF ∗ = (F + F )/2, where

(4)F aAB = FaAB − ψ[AΓB]χa.The complicated four Fermi interaction in the action is required for obtaining supercovariant boundary con

One boundary condition is imposed as a constraint. The tangential components of the three form will beto satisfycABC = 0, where

(5)cABC = CABC +√

2

12εωABC +

√2

48εχaΓABCχ

a.

This boundary condition contains the Chern–Simons form,

(6)ω= tr

(A∧ dA+ 2

3A∧A∧A

).

I.G. Moss / Physics Letters B 577 (2003) 71–75 73

check

rn–gy withtheetry. This

xpansion

he

gauge

brane

uction ofaffects

in the

ach

We shall see shortly how this boundary condition is fixed by supersymmetry, but first it is interesting toconsistency with the gauge symmetry. Under a non-Abelian gauge transformation withδAaA = −DAεa , thevariation in the Chern–Simons form becomesδω= d(εaF a). The non-Abelian gauge transformation of the CheSimons form can therefore be absorbed by an Abelian gauge transformation of the three-form (in analoYang–Mills supergravity [9]). However, theC ∧G ∧G term in the supergravity action is not invariant underAbelian gauge transformation, and a quantum gauge anomaly has to be used to restore the gauge symmis the generalised Green–Schwarz [10] mechanism described by Horava and Witten [2], and it fixes the eparameter,

(7)ε = 1

4π

(κ

4π

)2/3

.

There are also gravitational anomalies which addR ∧ R terms to the boundary condition (5). However, for tpresent we shall restrict attention to the low curvature regime and ignoreR ∧R terms.

The remaining boundary conditions can be obtained by finding the extremal of the action. Leaving themultiplet fixed for the moment, the relevant boundary terms in the variation of the action are

(8)δS = 2

κ2

∫∂M

dµ(δgABp

AB + δψiθi),

with

(9)pAB = −1

2

(KAB −KgAB

) + 1

4κ2T AB,

(10)θA = −Γ ABP+ψB − ε

4Γ BCΓ AF aBCχ

a − ε

96Γ ABΓ CDEψBχΓCDEχ,

whereT AB is the surface stress energy tensor.The boundary conditionpAB = 0 corresponds, in the covering space, to a junction condition across the

[7]. The boundary conditionθA = 0 is a chirality condition on the gravitino

(11)P+ψA = ε

12

(ΓA

BC − 10δABΓ C)F aBCχ

a − ε

96χΓBCDχΓ

BCDP−ψA.

This boundary condition represents a significant difference between the present model and the constrHorava and Witten.1 One significant difference is that torsion can be generated by the matter fields. Thisthe connectionΩ which is governs the motion of gauginos.

The chirality condition on the gravitino and the boundary condition on the three form play a special rolesupersymmetry of the theory. The supersymmetry transformation rules are almost conventional,

(12)δgIJ = ηΓ(IψJ ),

(13)δψI =DI (Ω)η+√

2

288

(ΓI

JKLM − 8δIJ Γ KLM

)ηGJKLM,

(14)δCIJK = −√

2

8ηΓ[IJψK] +

√2

4ε∂[I fJK],

(15)δAaA = 1

2ηΓAχ

a,

(16)P−δχa = −1

4Γ ABF aABη.

1 The supersymmetry transformation of the chirality conditionΓ11ψA = ψA used by Horava and Witten [2] in the covering space approis ambiguous because the supersymmetry transformation of the gravitino is discontinuous across the brane.

74 I.G. Moss / Physics Letters B 577 (2003) 71–75

s less(11),

is

ymmetryry

form in

ulation

stly

ing them thecancel.

–Millse termtion of

metric

ofcountered

The two-formf will be explained below. The restriction on the chirality of the supersymmetry parameter iconventional, but is determined by the need to ensure supercovariance of the fermion boundary condition

(17)P+η = − ε

96χΓABCχΓ

ABCP−η.

This can be regarded as a modification of the projection operatorP+. The chirality condition on the gauginosimplyP+χ = 0 and is not affected by any modification due to a convenient Fierz rearrangement.

We shall consider the supersymmetry of the boundary conditions first, and then move on to the supersof the action. The variation ofCABC introduces a two-formf , which can be any two-form with the boundacondition

(18)fAB = 2Aa [AδAaB].

The two-form is needed to cancel a gauge non-invariant term from the variation of the Chern Simonsthe boundary condition (5). The remaining terms in the variation ofCABC depend only onP+ψA, allowing us touse the gravitino boundary condition to show consistency with the variation of the remaining terms. A calchas been done to confirm that the boundary condition (5) is supersymmetric toall orders inε. A more detaileddiscussion will be presented in a longer publication.

Taking the exterior derivative ofcABC = 0 and making use of (11) puts the boundary condition in manifegauge invariant (and supercovariant) form,

(19)GABCD = −3√

2εF a [ABF aCD] + √2εχaΓ[ABCDD](Ω)χa +

√2

4εχaΓ[ABCΓ EFψD]F aEF .

This can be used to check the supersymmetry of the gravitino boundary condition (11).The variation of the action under the supersymmetry transformations can be obtained by combin

boundary terms (8) with terms from the variation of the matter multiplet and with terms which arise frointerior. The invariance of 11-dimensional supergravity ensures that the volume terms in the variationBoundary terms arise from the interior when partial integration has to be used.

If we write the gravitino variation in the interior in the formδψILI , then integration by parts adds a termηLNto the other boundary terms in (8), where

(20)LN = −ΓNΓ ABDA(Ω)ψB −√

2

96ΓNΓ

ABCDEψAGBCDE +√

2

8ΓNΓ

ABψCGABCN .

A slight rearrangement gives

ηLN = ηDA(Ω)θA + 1

2KACηΓ

ABΓ CψB + 1

4εηDA(Ω)

(Γ BCΓ AFBCχ

) −√

2

96ηΓ ABCDEψAGBCDE

(21)+√

2

8ηΓ ABψCGABCN.

We see clearly the term which cancels the extrinsic curvature in (9) and a term involving the Yangsupercurrent which partially cancels the variation of the Yang–Mills part of the action. The penultimatcancels the variation of the supercurrent (using (19)) and the final term partially cancels with the variaCABC .

The three-form and gravitino boundary conditions have to be imposed in order to obtain a supersymaction. After some calculation, the action is found to be supersymmetric up to terms of orderε3 (equivalent toκ2).At this order there are terms arising from the variation of theC∧G∧G term in the action and no obvious sourceterms for these to cancel. This is an advance over previous attempts to construct the action which have eninfinite terms at orderκ4/3.

I.G. Moss / Physics Letters B 577 (2003) 71–75 75

the lowt orderenergyith

The action and boundary conditions provide a supersymmetric theory which is a natural candidate forenergy limit of M-theory. Further work is needed to investigate fully what happens to the supersymmetry aκ2 and to complete the supersymmetry variation of the gravitino boundary condition. Going beyond the lowlimit, it would be desirable to include theR ∧ R curvature terms which are significant in compactifications wCalabi–Yau manifolds [11–15].

References

[1] P. Horava, E. Witten, Nucl. Phys. B 460 (1996) 506.[2] P. Horava, E. Witten, Nucl. Phys. B 475 (1996) 94.[3] E. Bergshoeff, M. de Roo, B. de Ditt, P. van Nieuwenhuisen, Nucl. Phys. B 195 (1982) 97.[4] E. Cremmer, B. Julia, J. Scherk, Phys. Lett. B 76 (1978) 409.[5] J.W. York, Phys. Rev. Lett. 28 (1972) 1082.[6] G.W. Gibbons, S.W.H. Hawking, Phys. Rev. D 15 (1977) 2752.[7] H.A. Chamblin, H.S. Reall, Nucl. Phys. B 133 (1999) 133.[8] H.C. Luckock, I.G. Moss, Class. Quantum Grav. 6 (1989) 1993.[9] G. Chapline, N.S. Manton, Phys. Lett. B 120 (1983) 105.

[10] M.B. Green, J.H. Schwarz, Phys. Lett. B 149 (1984) 117.[11] E. Witten, Nucl. Phys. B 471 (1996) 135.[12] T. Banks, M. Dine, Nucl. Phys. B 479 (1996) 173.[13] A. Lukas, B.A. Ovrut, K.S. Stelle, D. Waldram, Phys. Rev. D 59 (1999) 086001.[14] A. Lukas, B.A. Ovrut, K.S. Stelle, D. Waldram, Nucl. Phys. B 552 (1999) 246.[15] J. Ellis, Z. Lalak, S. Pokorski, W. Pokorski, Nucl. Phys. B 540 (1999) 149.

b

aryingwe deriveof non-for the



Background field quantization and non-commutativeMaxwell theory

Ashok Dasa, J. Frenkelb, S.H. Pereirab, J.C. Taylorc

a Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627-0171, USAb Instituto de Física, Universidade de São Paulo, São Paulo, SP 05315-970, Brazil

c Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

Received 25 September 2003; received in revised form 8 October 2003; accepted 9 October 2003

Editor: M. Cvetic

Abstract

We quantize non-commutative Maxwell theory canonically in the background field gauge for weak and slowly vbackground fields. We determine the complete basis for expansion under such an approximation. As an application,the Wigner function which determines the leading order high temperature behavior of the perturbative amplitudescommutative Maxwell theory. To leading order, we also give a closed form expression for the distribution functionnon-commutativeU(1) gauge theory at high temperature. 2003 Published by Elsevier B.V.

inriesr-ncefest.on-

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1. Introduction

Background field techniques are quite usefulthe study of conventional non-Abelian gauge theo[1,2]. In particular, they simplify calculations enomously, since in a background field gauge, invariaunder background gauge transformations is maniOn the other hand, canonical quantization of nAbelian gauge theories within such a frameworkhighly non-trivial [3]. The difficulty comes from thefact that a complete basis for the field equation ofquantum gauge field is not easy to determine in geral. The only known example of a successful canocal quantization is for the case where the backgrofield strength is a constant [3]. However, there

E-mail address: [email protected] (A. Das).


many physical situations where the background fican be considered to be weak and the variations inbackground field less rapid than the variations inquantum field. In such a case, we show that cancal quantization in the background field gauge cancarried out and, in fact, we demonstrate this witthe context of non-commutative Maxwell theory. (Tquantization goes through unchanged even in the pence of fermion fields.)

The high temperature behavior of a plasma [4constitutes an example where the external fieldassumed to be weak with slow variations compawith the quantum fields. Namely, in the hard thermloop approximation, it is normally assumed that

(1)p k ∼ T ,

where p represents a typical external momentuwhile k denotes an internal loop momentum. O


A. Das et al. / Physics Letters B 577 (2003) 76–82 77

chn-

theinisutweof

hadlarthethemge.anteateeblein

Intheingell

3anthld.eerior

andanding

rmon

ofn-s,we

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method finds a natural application in the study of susystems and we derive the Wigner function for nocommutative photons which, in turn, determinesleading high temperature behavior of amplitudesthis theory. In an earlier work [8], we had studied thquestion through the use of Wigner function (withothe use of the background field method), wherehad noted some peculiarity of non-covariancethe results under a gauge transformation andargued for a covariant completion of a particuform. In the present approach, we show thatcovariance of the results is manifest and thatparticular covariantization found earlier, results frothe proper quantization in the background field gauThis, therefore, clarifies the meaning of the covaricompletion found in [8]. When working within thframework of background field method, an alternand simpler definition of Wigner function (to thleading order) is possible. Using this, we are also ato determine the leading order distribution functiona closed form at one loop.

The organization of our results is as follows.Section 2, we briefly recapitulate the basics ofbackground field method. Considering the leadorder behavior of the equation of motion as was the background gauge condition, in Sectionwe determine a complete basis for the covariD’Alembertian operator in this approximation whicallows for an expansion of the quantum gauge fieAs an application of our method, in Section 4 wintroduce an alternate, simpler definition of the Wignfunction which describes the leading order behavof the amplitudes through a transport equationshow that the calculations are manifestly covariantagree with the perturbative results. Furthermore, usthis Wigner function, we determine a closed foexpression for the leading order distribution functiat the one loop level.

2. Background field method in non-commutativeMaxwell theory

In this section, we review very briefly the basicsbackground field method within the context of nocommutative Maxwell theory. For our conventionnotations and the definitions of star product etc.,

refer the reader to [8] as well as the vast literaturethe subject of non-commutative field theories [9,10

Non-commutativeU(1) gauge theory (Maxweltheory) is described by the action

(2)S[A] =∫

d4x

(−1

4Fµν Fµν

),

where

(3)Fµν = ∂µAν − ∂νAµ − ie[Aµ,Aν].Here, the commutator stands for the Moyal brackethe fields. We now make the expansion

(4)Aµ = Aµ + aµ, 〈aµ〉 = 0,

whereAµ is the background field satisfying

Dµ(A)Fµν(A)

(5)= DµF µν = ∂µF µν − ie[Aµ, F µν

] = 0,

aµ is the quantum field and〈aµ〉 denotes the expectation value of the quantum field in any given staThen, it follows that

(6)Fµν = Fµν + Dµaν − Dνaµ − ie[aµ, aν].In such a case, the action (2) can be expanded as

S[A + a]

(7)

=∫

d4x

[−1

4Fµν F µν

− 1

2

(Dµaν − Dνaµ

) Dµaν

+ ieF µν aµ aν

+ ie(Dµaν − Dνaµ

) aµ aν

+ e2

2

[aµ, aν

] aµ aν

],

where linear terms in the quantum field do not ocby virtue of the equations of motion (5) for thbackground field.

The advantage of the background field methodin the fact that the original gauge invariance of ttheory under

(8)δAµ(x) = ∂µε(x) − ie[Aµ(x), ε(x)

],

can be viewed in one of two ways. First, this canthought of as a quantum gauge invariance under

78 A. Das et al. / Physics Letters B 577 (2003) 76–82

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inge

um

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calandch14)

inein

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oft usauge

8])

ge,

eld

transformations,

δAµ(x) = 0,

(9)δaµ(x) = ∂µε(x) − ie[Aµ(x) + aµ(x), ε(x)

],

or as a background gauge invariance under

δAµ(x) = ∂µε(x) − ie[Aµ(x), ε(x)

],

(10)δaµ(x) = −ie[aµ(x), ε(x)

].

Namely, under a quantum gauge transformation,background field is inert while the quantum fietransforms like a gauge field. On the other hand, una background gauge transformation, the backgrofield transforms like a gauge field while the quantufield transforms in the adjoint representation. Ittherefore, possible to take advantage of this andthe gauge fixing and the ghost actions

SGF + Sghost

(11)

=∫

d4x

[− 1

2ξ(D · a) (D · a)

+ Dµc (∂µc − ie[Aµ + aµ, c])

],

which break the quantum gauge invariance (9), butinvariant under the background gauge transforma(10) with ghosts transforming in the adjoint represtation. As a result, calculations carried out with sua background gauge fixing will lead to results thatmanifestly invariant under background gauge transmations.

The part of the total action quadratic in the quantfields is responsible for the one loop results and hasform

(12)

Sq =∫

d4x

[−1

2

(Dµaν − Dνaµ

) Dµaν

+ ieF µν aµ aν

− 1

2ξ(D · a) (D · a) + Dµc Dµc

].

Here ξ represents the gauge fixing parameter andthe limit ξ → 0 we have the background field gaucondition,

(13)D · a = Dµaµ = ∂µaµ − ie[Aµ, aµ

] = 0.

In this gauge, the equation of motion for the quantfield (at the one loop level) follows from (12) to be

(14)DνDνaµ = 2ie

[F µν, aν

].

It can be easily checked that (13) and (14)compatible.

3. Quantization

To quantize the gauge field, we have to determinbasis satisfying both (13) and (14). This is, in genea very hard problem and a solution in a factorizaform may not always exist. We, therefore, look fosolution of these equations in the approximation tthe background fields are weak and slowly varycompared to the quantum fields. As we have poinout in the introduction, there are various physiphenomena of interest that satisfy such conditionsin the next section we will have an application to sua physical situation. With these assumptions, Eq. (reduces in the leading order to

(15)D2aµ = DνDνaµ = 0.

Thus, in this approximation, it is essential to determa basis for the covariant D’Alembertian operatororder to quantize the gauge field. Furthermore, siaµ transforms covariantly under a background gatransformation (10), the basis function must reflthis. We know that the plane waveseik·x represent abasis for the D’Alembertian operator in the absenceany background gauge fields. Correspondingly, ledenote the basis in the presence of background gfields aseik·X

.To determine this basis, let us define (see also [

(16)Aµ = Aµ + 1

k · D Fµνkν = 1

k · D ∂µ(k · A).

It is clear that this transforms like a background gaufield under (10). We note from (16) that, in general

(17)k · A = k · A.

Furthermore, we see from (16) that in the gauge

(18)k · A = 0,

Aµ vanishes so that it must be a pure gauge fisatisfying

(19)k · A = iΩ−1 k · ∂Ω.

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This can also be equivalently written as

k · ∂Ω + ieΩ k · A = 0,

(20)k · ∂Ω−1 − iek · A Ω−1 = 0.

The solution of (19) (or equivalently of (20)) cabe determined easily in terms of link operators andthe form

(21)Ω(x) = U(A)(−∞, x) = P

(e−ie

∫ 0−∞ duk·A(x+ku)

),

where the integration is along a straight path parato kµ from −∞ to xµ. For simplicity, we have takethe reference point to be at−∞ although this isnot necessary. We note here that open Wilson liof the form in (21) play an important role in noncommutative gauge theories from various pointsview at zero temperature [9–11] (including in tconstruction of gauge invariant observables [12])well as at finite temperature in the constructioneffective actions [13]. From the form of the solutioin (21) as well as the properties of star productsimmediately follows that

Ω−1(x) eik·x Ω(x)

= U(A)(x,−∞) U(A)(−∞, x + θk) eik·x

(22)= U(A)(x, x + θk) eik·x,

where we have introduced the notation

(23)(θk)µ = θµνkν,

and used the property

(24)eik·x f (x) e−ik·x = f (x + θk).

From the transformation properties of the link opetors, we see that the combination of factors on the lhand side of (22) transforms covariantly under (10)

From the definition in (19) (or (20)) as well as thfact thatk2 = 0, it follows that

k · D(Ω−1(x) eik·x Ω(x)

)(25)= 0 = k · D(

U(A)(x, x + θk) eik·x).With this, we now see that, to leading order in oapproximation,

D2(U(A)(x, x + θk) eik·x)(26)= ik · D(

U(A)(x, x + θk) eik·x) = 0,

where we have neglected the term where the covaderivative acts on the link operator since the momtum of the background field is sub-leading compato k. Thus, we see that to leading order in our apprimation, a basis for the covariant D’Alembertian opator can be written as

(27)fk(x) = eik·X = U(A)(x, x + θk) eik·x.

This transforms covariantly under (10) and reduto ordinary plane waves whenA = 0 (and, thereforeA = 0 or whenθµν = 0). We also note that followingthe derivation in [11] (where an integrated form of trelation is obtained), it is easy to show that

(28)U(A)(x, x + θk) eik·x = ei(k.x+ek×A(x)) ,

where we have used the notation standard in ncommutative field theories,

(29)A × B = θµνAµBν.

Eq. (28) represents precisely the covariantizationtor determined earlier in [8] from different considertions and this derivation clarifies the origin of suchfactor, showing that we can think ofXµ (see (27)) asthe appropriate covariant coordinate for the problemhand.

The basis for the covariant D’Alembertian operaallows us to make an expansion of a covariant (frthe non-commutativeU(1) point of view) scalar field.However, the expansion of a gauge field must,addition, satisfy (13). To that end, we note that inleading order of our approximation, Eq. (13) canwritten as

(30)∂µaµ(x) = 0,

which is the Landau gauge. Correspondingly, expsion in terms of the usual transverse polarization vtors is sufficient to satisfy the gauge condition in tleading order. We would like to emphasize that,general, the polarization vector can have sub-leadterms that are not necessarily factorizable (whichbeen checked to lowest orders) which is anotherson why quantization in the background field methis highly non-trivial in general. With all this, we canow expand the quantum fields (in the leading or


that

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6).ri-p-

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dhob-on.ni-bil-n-ncehe

inor-useors.ies(if

senerthexi-

a-e

om

henyn,

of our approximation) as

(31)

aµ(x) =∑s

∫d3k

(2π)3√

2k0εµ(k, s)

× (a(k, s)e−ik·X

+ a†(k, s)eik·X

),

where we have assumed without loss of generalitythe polarization vector is real and

(32)k0 = |k|, k · ε(k, s) = 0.

The quantum field can now be quantized andphysical Hilbert space identified in the standard mner [14].

4. Application

As an application of the background field quatization of the previous section, we will now derivthe Wigner function [15] which determines the leaing order high temperature behavior of the amptudes in non-commutative QED. We note that coventionally the covariant Wigner function for the nocommutative photon is defined as (see [8])

(33)

Wµν(x, k) =∫

d4y

(2π)4e−iy·kG(+)µλ (x) Gλ(−)

ν (x),

where

G(±)µν (x) = U(A)(x, x±) Fµν(x±) U(A)(x±, x),

(34)x± = x ± y

2.

On the other hand, within the framework of thbackground field method an alternate and simpdefinition of the covariant Wigner function [16], whicdescribes the leading order behavior in the hthermal loop approximation, is possible and hasform

(35)

wµν(x, k) =∫

d4y

(2π)4e−iy·kG(+)

µ (x) G(−)ν (x),

(36)

G(±)µ (x) = U(A)(x, x±) aµ(x±) U(A)(x±, x).

There are several things to note from (35) and (3First, the Wigner function in (35) transforms covaantly under (10) independent of whether the link oerator in (36) is defined with respect to the compl

gauge fieldAµ or with respect to the backgroungauge fieldAµ. However, we have defined it witrespect to the background field to avoid some prlems that arise otherwise in a practical calculati(Such problems also arise in the conventional defition and need various assumptions on the factorizaity of thermal correlation functions. However, a defiition such as in (36) avoids such assumptions.) Sithe Wigner function (35) is already quadratic in tquantum fields, at one loop level, the gauge fieldsthe link operators would factor out of the thermal crelation functions as background fields even if wethe complete gauge field to define the link operatHowever, keeping an eye on the potential difficultthat may arise at higher loop level from such termsdefined with a complete gauge field), we have chothe particular definition in (36). Second, the Wignfunction in (35) can be easily seen to be related toone in (33) in the leading hard thermal loop appromation as

ηµν⟨wµν(x, k)

⟩

(37)= − limk2→0

ηµν

2k2

(⟨Wµν(x, k)

⟩ − Wµν(x, k)),

where〈·〉 denotes thermal average.Following the derivation in [8], the transport equ

tion for wµν can now be derived. In fact, if we definthe distribution function

(38)F(x, k) = ηµν⟨wµν(x, k)

⟩,

then, it can be easily shown that (this also follows frEq. (33) derived in [8] and the identification in (37))

k · DF(x, k)

= e

2

∂

∂kσ

kρ

(39)

×[Fρσ F +F Fρσ

− 2∫

d4y

(2π)4e−iy·k⟨G(+)µ Fρσ Gµ(−)

⟩].

By iteratively solving the transport equation (39), tdistribution function (38) can be determined to aorder in the leading approximation. This would, the


li-n.ss

art

antayes

inop-

al[5]

der.eseser,

stly1),, inbene

onion

onderor

eectlyard

iveeldak

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ar-mnti-av-

d-nsba-ormonghon-ed

sisinnd)

ter-c-e-

orartell

determine the current defined as

(40)Jµ(x) = −e

∫d4k θ

(k0)kµ

(F(x, k) −F(x,−k)

),

which, in turn, would yield the leading order amptudes of the theory through functional differentiatio(By leading order in this context, we refer to the claof terms inside the curly bracket in (40) which, apfrom a δ(k2), are functions of zero degree ink. Inconventional QCD, this class yields all the domincontributions, but in non-commutative QED, this mnot give the complete contribution for arbitrary valuof the non-commutative parameterθµν as discussedin [13].) The anti-symmetrization in the definition(40) is to ensure the correct charge conjugation prerty [17] of the current as discussed in [8].

With the field expansion given in (31), the thermaverages can be calculated in the physical spacesatisfying

(41)∑s=1,2

εµ(k, s)εµ(k, s) = −2,

and the current can be determined order by orIt is straightforward to check that this coincidwith the results obtained in [8] (which also givthe appropriate perturbative amplitudes). Howevunlike the earlier work, here the results are manifecovariant at any order with the expansion in (3without any need for covariantization. Furthermorethis case, the distribution function in (38) can evenobtained in a closed form in the leading order at oloop and has the form

F(x, k) = 2∫

d4y

(2π)4e−iy·k

∫d4k

(2π)3δ(k2)nB

(∣∣k0∣∣)

(42)

× θ(k0)(ey·D/2

eik·X

)(e−y·D/2 e−ik·X

)+ (k ↔ −k)

,

wherenB(|k0|) denotes the Bose–Einstein distributiand the covariant translation (for a covariant functunder the non-commutativeU(1)) is explicitly givenby

(43)e±y·D/2 f (x) = U(A)(x, x±) f (x±) U(A)(x±, x).

Using the transport equation (39), the distributifunction in (42) can be systematically expanded orby order in the number of background fields (

powers ofe) and substituted into the definition of thcurrent in (40). We have verified explicitly, up to ththree photon amplitude, that this reproduces correthe perturbative results in the leading order in the hthermal loop approximation.

5. Conclusion

In this Letter, we have quantized non-commutatU(1) gauge theory canonically in the background fimethod using the background field gauge for weand slowly varying background fields. We have demined a (covariant) basis for the covariant D’Alembertian operator which indeed coincides with the pticular covariantization factor determined earlier frodifferent considerations. We have applied our quazation method to study the high temperature behior of non-commutative Maxwell theory in the leaing order using the Wigner function. The calculatioare manifestly covariant and agree with the perturtive results. We have also determined a closed fexpression for the distribution function for the photin the leading approximation at one loop. Althouour discussion has been within the context of ncommutative Maxwell theory, this can be generalizto conventional QCD as well. In particular, a bafor the covariant D’Alembertian operator can agabe constructed in terms of a pure gauge (backgroufield Aµ defined in (16). This can then be used to demine, in principle, the leading order distribution funtion in QCD. This is an interesting question that dserves further study.

Acknowledgements

One of us (J.F.) would like to thank F.T. Brandt fhelpful discussions. This work was supported in pby US DOE Grant No. DE-FG 02-91ER40685 as was by CNPq, FAPESP and CAPES, Brazil.

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[13] F.T. Brandt, A. Das, J. Frenkel, S. Pereira, J.C. Taylor, PRev. D 67 (2003) 105010.

[14] T. Kugo, I. Ojima, Prog. Theor. Phys. 60 (1978) 1869;T. Kugo, I. Ojima, Prog. Theor. Phys. Suppl. 66 (1979) 1.

[15] H.T. Elze, U.W. Heinz, Phys. Rep. 183 (1989) 81.[16] H.Th. Elze, Z. Phys. C 47 (1990) 647.[17] M.M. Sheikh-Jabbari, Phys. Rev. Lett. 84 (2000) 5265.

b

rove the

subjectcts of

cture of,12]. It

theories–16]. Thealization

In fact,orders.

,

da



On the finiteness of noncommutative supersymmetric QED3in the covariant superfield formulation

A.F. Ferraria, H.O. Girottia, M. Gomesb, A.Yu. Petrovb,1, A.A. Ribeiroa, A.J. da Silvab

a Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre, RS, Brazilb Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970 São Paulo, SP, Brazil

Received 9 September 2003; received in revised form 8 October 2003; accepted 9 October 2003

Editor: M. Cvetic

Abstract

The three-dimensional noncommutative supersymmetric QED is investigated within the superfield approach. We pabsence of UV/IR mixing in the theory at any loop order and demonstrate its one-loop finiteness. 2003 Published by Elsevier B.V.

During last years noncommutative gauge theories have been intensively studied. The interest in thishas deep motivations coming mainly from string theory [1] (for a review see [2,3]). Different aspenoncommutative gauge theories were discussed in [4–11].

One of the most remarkable properties of noncommutative theories consists of an unusual strudivergences, the so-called UV/IR mixing, that could lead to the appearance of infrared divergences [4should be noticed that the cancellation of quadratic and linear ultraviolet divergences in commutativedoes not guarantee the absence of harmful infrared divergences in their noncommutative counterparts [13elimination of such divergences is crucial since they may obstruct the development of a sound renormscheme, leading to the breakdown of the perturbative series.

Based on experience, it is natural to expect that supersymmetry could improve this situation [4,17].the Wess–Zumino model [14] and the three-dimensional sigma-model [18] are renormalizable at all loopThis is furtherly supported by the results of [19] according to which the one-loop effective action inN = 1,2super-Yang–Mills theory contains only logarithmic divergences while forN = 4 the theory is one-loop finite [1920].

E-mail addresses:[email protected] (A.F. Ferrari), [email protected] (H.O. Girotti), [email protected] (M. Gomes),[email protected] (A.Yu. Petrov), [email protected] (A.Yu. Petrov), [email protected] (A.A. Ribeiro), [email protected] (A.J.Silva).

1 Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634041, Russia.



84 A.F. Ferrari et al. / Physics Letters B 577 (2003) 83–92

QEDll also

llutativity,

ses

In this Letter we employ the covariant superfield formalism to study noncommutative supersymmetric3.We will prove that this theory is free of nonintegrable UV/IR divergences at any loop order. We shademonstrate that the model is one-loop finite.

The action of the three-dimensionalN = 1 noncommutative supersymmetric QED is [21]

(1)S = 1

2g2

∫d5zWα ∗Wα,

where

(2)Wβ = 1

2DαDβAα − i

2

[Aα,DαAβ

]− 1

6

[Aα, Aα,Aβ

]is a superfield strength constructed from the spinor superpotentialAα . Hereafter it is implicitly assumed that acommutators and anticommutators are Moyal ones. In this work we consider only space–space noncommto evade unitarity problems [22]. This action is invariant under the gauge transformations

(3)δAα =DαK − i[Aα,K].Then, we must add a gauge fixing term which we choose to be

(4)SGF=− 1

4ξg2

∫d5z

(DαAα

)D2(DβAβ

),

leading to the quadratic action

(5)S2= 1

2g2

∫d5z

[1

2

(1+ 1

ξ

)AαAα − 1

2

(1− 1

ξ

)Aαi∂αβD

2Aβ

].

The free gauge propagator is

(6)⟨Aα(z1)A

β(z2)⟩= ig2

2

[Cαβ 1

(ξ + 1)− 1

2 (ξ − 1)i∂αβD2]δ5(z1− z2),

whereCαβ =−Cαβ is the second-rank antisymmetric symbol defined with the normalizationC12= i. The mostconvenient choice for the gauge fixing parameter isξ = 1, the Feynman gauge, in which the propagator collapto

(7)⟨Aα(z1)A

β(z2)⟩= ig2Cαβ 1

δ5(z1− z2).

The interaction part of the classical action in the pure gauge sector is

Sint = 1

g2

∫d5z

[− i

4DγDαAγ ∗

[Aβ,DβAα

]− 1

12DγDαAγ ∗

[Aβ, Aβ,Aα

]− 1

8

[Aγ ,DγA

α] ∗ [

Aβ,DβAα

]+ i

12

[Aγ ,DγA

α] ∗ [

Aβ, Aβ,Aα]

(8)+ 1

72

[Aγ ,

Aγ ,A

α] ∗ [

Aβ, Aβ,Aα]].

The action of the associated Faddeev–Popov ghosts reads

(9)SFP= 1

2g2

∫d5z

(c′DαDαc+ ic′ ∗Dα[Aα, c]

),

implying in the propagator

(10)⟨c′(z1)c(z2)

⟩=−ig2D2δ5(z1− z2).

A.F. Ferrari et al. / Physics Letters B 577 (2003) 83–92 85

ergenceom

noticeg loop,

rnalthing

t

-

torFig. 1

(a) (b) (c)

Fig. 1. Superficially linearly divergent diagrams contributing to the two-point function of the gauge field.

We assume that the ghosts are in the adjoint representation. The total action is, then, given by

(11)Stotal= S + SGF+ SFP.

To study the divergence structure of the model we shall start by determining the superficial degree of divω associated to a generic supergraph. Explicitly,ω receives contributions from the propagators and implicitly frthe supercovariant derivatives. This last dependence can be unveiled by the use of the conversion rule

(12)DαDβ = i∂αβ −CαβD2

and the identity(D2)2= . Each loop contributes two power of momentum. To see how this come about,that each integration overd3k is decreased by one power of momentum when contracting the correspondininto a point. It can be seen that, ifV3,V2,V1, andV0 are, respectively, the number ofpuregauge vertices with threetwo, one and none spinor derivatives, then, they altogether will contribute3

2V3+ V2+ 12V1 to ω. Furthermore,Vc

gauge-ghost vertices will increaseω by 12Vc. Each gauge propagator (let their number bePA) lowersω by two,

each ghost propagator (let their number bePc) lowersω by one. Moving a supercovariant derivative to an extefield decreasesω by 1

2 (letND be the number of spinor derivatives moved to the external fields). Putting everytogether we may conclude thatω is given by

(13)ω= 2L+ 3

2V3+ V2+ 1

2(V1+ Vc)− 2PA −Pc − 1

2ND.

The number of the ghost vertices is equal to the number of the ghost propagators,Pc = Vc, since the ghospropagators only form closed loops. Thus, after using the topological identityL+ V − P = 1 with P = PA + PcandV = Vc + V0+ V1+ V2+ V3, we obtain

(14)ω= 2− 1

2Vc − 2V0− 3

2V1− V2− 1

2V3− 1

2ND.

This power counting relationship characterizes noncommutative supersymmetric QED3 as an UV superrenormalizable theory. It is easy to realize that linear divergences may come only from the graphs withV3 = 2,or V2 = 1, orVc = 2. These graphs are depicted in Fig. 1, they contribute to the two-point functions ofAα field.In these graphs, a crossed line corresponds to a factorDα acting on the ghost propagator. A trigonometric faceik∧l − eil∧k = 2i sin(k∧ l) originates from each commutator. By denoting the contributions of the graphs inby I1a, I1b, andI1c, respectively, we have

I1a= 1

32

∫d3p

(2π)3d2θ1d

2θ2

∫d3k

(2π)3sin2(k ∧ p)k2(p− k)2 A

β(−p, θ1)Aβ ′(p, θ2)

(15a)

×[−DγDα

(Cγγ ′

ξ + 1

k2+ kγ γ ′ ξ − 1

k4D2

)Dα′Dγ ′δ12

×Dβ

(Cαα′

ξ + 1

k2 + (p− k)αα′ξ − 1

(p− k)4D2)Dβ ′δ12

+DγDα

(Cγα′

ξ + 1

k2+ kγα′ ξ − 1

k4D2

)Dβ ′δ12

×Dβ

(Cαγ ′

ξ + 1

k2 + (p− k)αγ ′ξ − 1

(p− k)4D2)Dα′Dγ ′δ12

]+ · · · ,


assmannonll shortly. After

utative

thato-d UV/IRed

o beprototype

I1b= 1

3(ξ + 1)

∫d3p

(2π)3d2θ1

∫d3k

(2π)3sin2(k ∧ p)

k2

× [Aβ(−p, θ1)Aβ(p, θ1)CγαD

γDαδ12∣∣θ1=θ2

−Aβ(−p, θ1)Aα(p, θ1)CγβDγDαδ12

∣∣θ1=θ2

]+ 1

3(ξ − 1)

∫d3p

(2π)3d2θ1

∫d3k

(2π)3sin2(k ∧ p)

k4

× [Aβ(−p, θ1)Aβ(p, θ1)kγαD

γDαD2δ212

∣∣θ1=θ2

−Aβ(−p, θ1)Aα(p, θ1)kγβDγDαD2δ12

∣∣θ1=θ2

]− 1

4(ξ + 1)

∫d3p

(2π)3d2θ1

∫d3k

(2π)3sin2(k ∧ p)

k2 Aγ (−p, θ1)Aβ(p, θ1)δ

ααDγ1Dβ2δ12

∣∣∣∣θ1=θ2

(15b)

− 1

4(ξ − 1)

∫d3p

(2π)3d2θ1

∫d3k

(2π)3sin2(k ∧ p)

k2 Aγ (−p, θ1)Aβ(p, θ1)k

ααDγ1D

2Dβ2δ12

∣∣∣∣θ1=θ2

+ · · · ,

(15c)I1c= 1

2

∫d3p

(2π)3d2θ1d

2θ2

∫d3k

(2π)3sin2(k ∧ p)k2(k + p)2 Aα(−p, θ1)Aβ(p, θ2)D

α1D

2δ12D2D

β2 δ12.

Where not otherwise indicated it must be understood that the supercovariant derivatives act on the Grvariableθ1, alsoδ12= δ2(θ1 − θ2). In the expressions for theI1’s the terms where covariant derivatives actexternal fields were omitted because they do not produce linear divergences and UV/IR mixing (as we shaverify, such terms give only finite contributions). In the formulae above they are indicated by the ellipsissome D-algebra transformations we arrive at

(16a)I1a=−1

2ξ

∫d3p

(2π)3d2θ1

∫d3k

(2π)3sin2(k ∧ p)

k2Aβ(−p, θ1)Aβ(p, θ1)+ · · · ,

(16b)I1b= 1

2(1+ ξ)

∫d3p

(2π)3d2θ1

∫d3k

(2π)3sin2(k ∧ p)

k2 Aβ(−p, θ1)Aβ(p, θ1)+ · · · ,

(16c)I1c=−1

2

∫d3p

(2π)3d2θ1

∫d3k

(2π)3sin2(k ∧ p)

k2 Aβ(−p, θ1)Aβ(p, θ1)+ · · · .

Hence, the total one-loop two-point function of the gauge superfield, given byI1 = I1a+ I1b+ I1c, is free fromboth UV and UV/IR infrared singularities. The same situation takes place in the four-dimensional noncommsupersymmetric QED [15,16]. It is also easy to show that the logarithmically divergent parts ofI1a, I1b andI1c,which involve derivatives of the gauge fields, turn out to be proportional to the integral

(17)∫

d3k

(2π)3kαβ sin2(k ∧ p)k2(k + p)2

and are therefore finite by symmetric integration. Thus, the logarithmic divergences inI1a, I1b, andI1c are alsoabsent, i.e., the two-point function ofAα field is finite in the one-loop approximation. We already mentionedlinear divergences are possible only forV2 = 1, or V3 = 2, or Vc = 2. Nevertheless, it is easy to see that twand higher-loop graphs satisfying these conditions are just vacuum ones. Then, there are no linear UV aninfrared divergences beyond one-loop and, as consequence,the Green functions are free of nonintegrable infrardivergences at any loop order.

We examine next the structure of potentially logarithmic divergent diagrams. They correspond to 0 ω < 1,which is possible ifV0= 1, orV1= 1, orV2= 2, orVc = 3,4, orVc = 2 with V2= 1, orV3= 2 with V2= 1, orV3= 2 with Vc = 2, orV3= 3,4, orV2= V3= 1. Notwithstanding, the contributions of these graphs turn out tvery similar among themselves so that the same mechanism of cancellation of divergences applies. As a


ds

isrmations,

tivityhich

fraredprovedr

Fig. 2. A typical logarithmically divergent diagram.

Fig. 3. Other superficially divergent contributions.

of this mechanism let us consider the supergraph withV3= 3 in Fig. 2. Its amplitude in the Feynman gauge rea

I2=−1

3

(i

2

)3 ∫d3p1d

3p2

(2π)6

∫d2θ1d

2θ2d2θ3

∫d3k

(2π)3sin(k ∧ p1)sin[k ∧ (p1+ p2)]sin[(k + p1)∧ p2]

k2(k +p1)2(k + p1+ p2)3

×Aβ(p1, θ1)Aβ ′(p2, θ2)Aβ ′′(−p1− p2, θ3)

(18)×DγDαDβ ′δ12Dγ ′Dα′Dβ ′′δ23D

γ ′′Dα′′Dβδ12Cγα′Cγ ′α′′Cγ ′′α.

By using the relationship (12) and the identityDα,D2 = 0 we find thatI2 vanishes. The fact that this graph

finite is actually a gauge independent statement. Indeed, in an arbitrary gauge and after D-algebra transfoI(ξ)2 is given by

I(ξ)2 = I2 − i

1

6

∫d2θ

∫d3p1d

3p2

(2π)6

∫d3k

(2π)3

[sin(p1∧ p2)−

3∑i=1

sin(2k ∧ pi + p1∧ p2)

]

× 1

k2(k + p1)2(k + p1+p2)3k2ξ

(ξ2− 1

)Aβ(p1, θ)Aβ ′(p2, θ)

(19)× [kβ′β ′′DβAβ ′′(p3, θ)+ kββ ′′Dβ ′Aβ ′′(p3, θ)+ kβ ′βDβ ′′Aβ ′′(p3, θ)

],

whose planar part is proportional to that of the integral in Eq. (17), which is finite. The nonplanar part ofI(ξ)2 is

composed of two terms, one proportional to

(20)∫

d3k

(2π)3kαβ cos(2k ∧ p)k2(k + p)2 ,

which is evidently finite, and the other proportional to a linear combination of integrals of the form

(21)∫

d3k

(2π)3kαβ sin(2k ∧ p)

k4 =− i

4π

pαβ√p2.

Here,pαβ = Θmnpn(σm)αβ , andΘmn is the constant antisymmetric matrix characterizing the noncommuta

of the underlying space–time. AsΘ0i = 0, this last expression does not produce logarithmic divergences, wconfirms the finiteness of the contributionI (ξ)2 .

The above mechanism also enforces the vanishing of UV logarithmic divergences and of UV/IR inlogarithmic singularities from the graphs in Fig. 3. The UV finiteness of all these one-loop graphs may bein an analogous way. For example, in the Feynman gauge the one-loop graph withV2 = 2 contains four spino


ation

rmne-loop. As itularities

ndutionsof two

remarke super-

r action

ls

egraphsd four

derivatives and its UV leading contribution is proportional to the finite integral in Eq. (17). A similar situarises for the one-loop graph withV2= V3= 1. The one-loop graph withV3= 2 andV2= 1 contains 8 D-factorsand, after using the identity(D2)2=, either a finite contribution proportional to that in Eq. (17) or a finite tein which some derivatives are moved to the external fields could emerge. The others potentially divergent ographs correspond toVc = 4 orV3= 4 and for them the same mechanism applies and, hence, they are finitecan be checked, the same happens in an arbitrary covariant gauge. The vanishing of UV/IR infrared singfor all these graphs has the same origin as that for the graph in Fig. 2.

Up to this point, the net result of our study is thatthe theory without matter turns out to be one-loop UV aIR finite. It is interesting to note that, in the framework of the background field method [21,23], all contribto the effective action are superficially finite. From a formal viewpoint this is caused by the presencespinor derivatives in the expression for the strengthWα in Eq. (2), which makesND 4 in Eq. (14), since loopcorrections must be at least of second order in the background strengths (compare with [19]). We alsothat Eq. (14) implies in the absence of divergences at three- and higher-loop orders, in agreement with threnormalizability of the theory. This concludes our analysis of theN = 1 supersymmetry.

We next study the interaction of the spinor gauge field with matter. To this end we add to (36) the matte

(22)Sm =−∫d5z

[1

2

(Dαφa + i

[φa,A

α]) ∗ (

Dαφa − i[Aα,φa])+mφaφa

].

Here,φa, a = 1, . . . ,N , are scalar superfields andφa their corresponding conjugate ones. We may also write

(23)Sm =∫d5z

[φa

(D2−m)

φa − i 12

([φa,A

α] ∗Dαφa −Dαφa ∗

[Aα,φa

])− 1

2

[φa,A

α] ∗ [Aα,φa]

].

The free propagator of the scalar fields is

(24)⟨φa(z1)φb(z2)

⟩= iδabD2+m−m2

δ5(z1− z2),

which, in momentum space, reads

(25)⟨φa(−k, θ1)φb(k, θ2)

⟩=−iδab D2+mk2+m2δ12.

The superficial degree of divergence when matter is present is given by

(26)ω= 2− 1

2Vc − 2V0− 3

2V1− V2− 1

2V3− 1

2Eφ − 1

2V Dφ −

1

2ND − V 0

φ ,

where, as before,Vi is the number of pure gauge vertices withi spinor derivatives,Eφ is the number of externascalar lines,ND is the number of spinor derivatives associated to external lines,V D

φ is the number of triple vertice

Aα ∗ φa ∗←→Dαφa , andV 0φ is the number of quartic verticesφa ∗ φa ∗Aα ∗Aα .

Graphs can now be split into those withEφ = 0 and those withEφ = 0. The leading UV divergence for thoswith Eφ = 0 isω= 3/2, corresponding to a tadpole graph which vanishes identically. What comes next arewith two externalAα legs which are UV linearly divergent. They are depicted in Fig. 4. Graphs with three anexternalAα legs are UV logarithmically divergent. The remaining ones are finite. As for the graphs withEφ = 0,only those withEφ = 2 are potentially UV logarithmically divergent, those withEφ > 2 are finite.

(a) (b)

Fig. 4. One-loop corrections to the self-energy of the spinor gauge field.


dy

arep graph

tion of

.

hethat

Graphs withEφ = 0 verify the conditionsV 0φ > 0 or VD

φ > 0 which, unless for the tadpole graph alrea

mentioned, imply that12VDφ + V 0

φ 1. On the other hand, if12VDφ + V 0

φ > 2, the corresponding supergraphssuperficially finite, according to (26). Since there are no external matter legs, each vertex of the one-loomust involve matter. Hence, we arrive at the following condition forω being nonnegative

(27)1 1

2VDφ + V 0

φ 2.

The lower limit of the inequality corresponds toω= 1, whereas the upper limit corresponds toω = 0.The UV linearly divergent case is only realized by the one-loop matter correction to the two-point func

the gauge fieldAα (Fig. 4). The graph (a) in Fig. 4 furnishes

I4a=−∫

d3p

(2π)3d2θ1d

2θ2

∫d3k

(2π)3Aα(−p, θ1)A

β(p, θ2)sin2(k ∧ p)(28)× [

Dα1⟨φa(1)φb(2)

⟩(Dβ2

⟨φa(1)φb(2)

⟩)− (Dα1Dβ2

⟨φa(1)φb(2)

⟩)⟨φa(1)φb(2)

⟩],

where the indices 1 and 2 in the supercovariant derivatives designate the field to which theD operator is appliedTaking into account the explicit form of the propagators, we found

I4a=N∫

d3p

(2π)3d2θ1d

2θ2

∫d3k

(2π)3Aα(−p, θ1)A

β(p, θ2)sin2(k ∧ p)

(29)×[Dα1(D

21 +m)

k2+m2δ12

(D21 +m)Dβ2

(k +p)2+m2δ12− Dα1(D

21 +m)Dβ2

k2+m2δ12

D21 +m

(k + p)2+m2δ12

],

which, after usingDβ2δ12=−Dβ1δ12, can be cast as

I4a=N∫

d3p

(2π)3d2θ1d

2θ2

∫d3k

(2π)3J (k,p)

(30)

× [2(D2

1 +m)δ12Dα1

(D2

1 +m)Dβ1δ12A

α(−p, θ1)Aβ(p, θ2)

+ (D2

1 +m)δ12

(D2

1 +m)Dβ1δ12

(DαAα

)(−p, θ1)A

β(p, θ2)],

where we have introduced the notation

(31)J (k,p)= sin2(k ∧ p)(k2+m2)[(k + p)2+m2] .

It is convenient to splitI4a into two parts,I4a= I (1)4a + I (2)4a , whereI (1)4a andI (2)4a are, respectively, associated to tfirst and second terms in the large brackets in the right-hand side of Eq. (30). It is straightforward to verify

I(1)4a = 2N

∫d3p

(2π)3d2θ

∫d3k

(2π)3J (k,p)

(32)×[−(k2+m2)CαβAα(−p, θ)Aβ(p, θ)+ (kαβ −mCαβ)

(D2Aα(−p, θ))Aβ(p, θ)

].

For the second term in the right-hand side of Eq. (30) one analogously finds

(33)I(2)4a =N

∫d3p

(2π)3d2θ

∫d3k

(2π)3J (k,p)

[DγDαAα(−p, θ)(kγβ −mCγβ)Aβ(p, θ)

].

By adding Eqs. (32) and (33) we can cast the contribution from the graph (a) in Fig. 4 as

I4a= 2N∫

d3p

(2π)3d2θ

∫d3k

(2π)3sin2(k ∧ p)

(k2+m2)[(k + p)2+m2]


riving

pdirect

integralnish in

g toumber ofgarithmicin

(34)

×[−(k2+m2)CαβAα(−p, θ)Aβ(p, θ)+ (kαβ −mCαβ)

[D2Aα(−p, θ)]Aβ(p, θ)

+ 1

2DγDαAα(kγβ −mCγβ)Aβ(p, θ)

].

The algebraic manipulations for the graph (b) in Fig. 4 are simpler and yield

(35)I4b= 2N∫

d3p

(2π)3d2θ

∫d3k

(2π)3sin2(k ∧ p)

(k + p)2+m2CαβA

α(−p, θ)Aβ(p, θ).

The complete correction to the two-point function is, therefore,

I4= 2N∫

d3p

(2π)3d2θ

∫d3k

(2π)3sin2(k ∧ p)

(k2+m2)[(k + p)2+m2](36)× (kγβ −mCγβ)

[(D2Aγ (−p, θ))Aβ(p, θ)+ 1

2DγDαAα(−p, θ)Aβ(p, θ)

].

We stress that the dangerous linear divergences have disappeared, i.e., the two-point function ofAα field turns outto be free of UV/IR infrared singularities and, moreover, finite. This two-point function can be used for dethe effective propagators in the1

Nexpansion [24].

It remains to consider the graphs withω = 0. It follows from (27), that the only remaining one-loologarithmically divergent graphs involving matter are those ones depicted in Fig. 5. Nevertheless, acalculation shows that the planar contributions of the first two of these supergraphs is proportional to thein Eq. (17) whose divergent part is known to vanish. The divergent parts of their nonplanar contributions vaa way similar to that of the graphs in Figs. 2 and 3. As for the third graph, it is evidently finite.

We shall next deal with the graphs withEφ > 0. Such graphs do not contain linear divergences, accordinEq. (26). Furthermore, the number of external scalar legs must be even since any vertex carries an even nscalar fields, and only an even number of them can be contracted into propagators. As stated before, the lodivergences in this case are possible only forEφ = 2,V D

φ = 2 and forEφ = 2,V 0φ = 1. These graphs are shown

Fig. 6. The graph (a) in Fig. 6 gives the contribution

I6a= 2g2∫

d3p

(2π)3d2θ1d

2θ2

∫d3k

(2π)3φa(−p, θ1)φa(p, θ2)

sin2(k ∧ p)k2[(k + p)2+m2]D

α(D2−m)

Dβδ12

(37)×[

1

2(ξ + 1)Cαβ + 1

2(ξ − 1)

kαβ

k2D2

]δ12+ · · · .

Fig. 5. Contributions to the three and four point functions of the spinor gauge field.

(a) (b)

Fig. 6. One-loop corrections to the self-energy of theφ field.


anyone or

V andtiondetailedmetry

SP) andort from12671-7.

As before, the ellipsis stands for manifestly finite terms. After some simplifications, one obtains

(38)I6a=−2ξg2m

∫d3p

(2π)3d2θ

∫d3k

(2π)3φa(−p, θ)φa(p, θ) sin2(k ∧ p)

k2[(k + p)2+m2] ,

which is finite. The second graph in Fig. 6 yields the amplitude

(39)I6b= (ξ − 1)∫

d3p

(2π)3d2θ1

∫d3k

(2π)3φa(−p, θ1)φa(p, θ2)

kαα

k4 sin2(k ∧ p)D2δ12

∣∣∣∣θ1=θ2

,

which vanishes identically because ofkαα = 0.Therefore the two-point function of the scalar field is free from UV/IR mixing and, moreover, finite in

covariant gauge. It follows from Eq. (26) that the supergraphs with two or more external scalar legs andmore gauge legs are also superficially finite.

To sum up we conclude thatthe three-dimensional noncommutative supersymmetric QED is one-loop UUV/IR infrared finite both without and with matter. A natural development of this work consists in the investigaof the possibility of appearance of divergences at two-loop order. Other possible developments are astudy of the 1/N expansion for the model involving many scalar fields and the analysis of spontaneous symbreaking and the Higgs mechanism.

Acknowledgements

This work was partially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPEConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). H.O.G. also acknowledges suppPRONEX under contract CNPq 66.2002/1998-99.A.Yu.P. has been supported by FAPESP, project No. 00/

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Search for the single production of doubly-charged Higgs bosand constraints on their couplings from Bhabha scattering

OPAL Collaboration

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K. Buesserx, H.J. Burckhartg, S. Campanad, R.K. Carnegief, B. Caronaa, A.A. Carterl,J.R. Cartere, C.Y. Changp, D.G. Charltona, A. Csillingab, M. Cuffianib, S. Dadot,

A. De Roeckg, E.A. De Wolfg,18, K. Deschx, B. Dienesac, M. Donkersf, J. Dubbertad,E. Duchovniw, G. Duckeckad, I.P. Duerdotho, E. Etzionu, F. Fabbrib, L. Feldi,P. Ferrarig, F. Fiedlerad, I. Flecki, M. Forde, A. Freyg, A. Fürtjesg, P. Gagnonk,J.W. Garyd, G. Gayckenx, C. Geich-Gimbelc, G. Giacomellib, P. Giacomellib,M. Giuntad, J. Goldbergt, M. Groll x, E. Grossw, J. Grunhausu, M. Gruwég,

P.O. Güntherc, A. Guptah, C. Hajduab, M. Hamannx, G.G. Hansond, K. Harderx,A. Harelt, M. Harin-Diracd, M. Hauschildg, C.M. Hawkesa, R. Hawkingsg,

R.J. Hemingwayf, C. Henselx, G. Herteni, R.D. Heuerx, J.C. Hille, K. Hoffmanh,D. Horváthab,2, P. Igo-Kemenesj, K. Ishii v, H. Jeremieq, P. Jovanovica, T.R. Junkf,

N. Kanayay, J. Kanzakiv,20, G. Karapetianq, D. Karleny, K. Kawagoev, T. Kawamotov,R.K. Keelery, R.G. Kelloggp, B.W. Kennedys, D.H. Kim r, K. Klein j,19, A. Klier w,S. Kluthae, T. Kobayashiv, M. Kobelc, S. Komamiyav, L. Kormosy, T. Krämerx,P. Kriegerf,11, J. von Kroghj, K. Krugerg, T. Kuhl x, M. Kupperw, G.D. Laffertyo,H. Landsmant, D. Lanskem, J.G. Layterd, A. Leinsad, D. Lellouchw, J. Letts14,L. Levinsonw, J. Lillich i, S.L. Lloydl, F.K. Loebingero, J. Luz,22, J. Ludwigi,

A. Macphersonaa,8, W. Maderc, S. Marcellinib, A.J. Martinl, G. Masettib,T. Mashimov, P. Mättig, W.J. McDonaldaa, J. McKennaz, T.J. McMahona,

R.A. McPhersony, F. Meijersg, W. Mengesx, F.S. Merritth, H. Mesf,1, A. Michelini b,S. Miharav, G. Mikenbergw, D.J. Millern, S. Moedt, W. Mohri, T. Mori v, A. Mutteri,

K. Nagail, I. Nakamurav,21, H. Nanjov, H.A. Nealaf, R. Nisiusae, S.W. O’Nealea,A. Ohg, A. Okparaj, M.J. Oregliah, S. Oritov,23, C. Pahlae, G. Pásztord,6, J.R. Patero,




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S. Rosatic, Y. Rozent, K. Rungei, K. Sachsf, T. Saekiv, E.K.G. Sarkisyang,9,A.D. Schailead, O. Schailead, P. Scharff-Hanseng, J. Schieckae, T. Schörner-Sadeniusg,

M. Schröderg, M. Schumacherc, C. Schwickg, W.G. Scotts, R. Seusterm,5,T.G. Shearsg,7, B.C. Shend, P. Sherwoodn, G. Sirolib, A. Skujap, A.M. Smithg,

R. Sobiey, S. Söldner-Remboldo,3, F. Spanoh, A. Stahlc, K. Stephenso, D. Stromr,R. Ströhmerad, S. Taremt, M. Tasevskyg, R.J. Taylorn, R. Teuscherh, M.A. Thomsone,

E. Torrencer, D. Toyav, P. Trand, I. Triggerg, Z. Trócsányiac,4, E. Tsuru,M.F. Turner-Watsona, I. Uedav, B. Ujvári ac,4, C.F. Vollmerad, P. Vanneremi,

R. Vértesiac, M. Verzocchip, H. Vossg,16, J. Vossebeldg,7, D. Wallerf, C.P. Warde,D.R. Warde, P.M. Watkinsa, A.T. Watsona, N.K. Watsona, P.S. Wellsg, T. Wenglerg,N. Wermesc, D. Wetterlingj G.W. Wilsono,10, J.A. Wilsona, G. Wolfw, T.R. Wyatto,

S. Yamashitav, D. Zer-Ziond, L. Zivkovic w

a School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UKb Dipartimento di Fisica dell’ Università di Bologna and INFN, I-40126 Bologna, Italy

c Physikalisches Institut, Universität Bonn, D-53115 Bonn, Germanyd Department of Physics, University of California, Riverside, CA 92521, USA

e Cavendish Laboratory, Cambridge CB3 0HE, UKf Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada

g CERN, European Organisation for Nuclear Research, CH-1211 Geneva 23, Switzerlandh Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637, USA

i Fakultät für Physik, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germanyj Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany

k Department of Physics, Indiana University, Bloomington, IN 47405, USAl Queen Mary and Westfield College, University of London, London E1 4NS, UK

m Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germanyn University College London, London WC1E 6BT, UK

o Department of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UKp Department of Physics, University of Maryland, College Park, MD 20742, USA

q Laboratoire de Physique Nucléaire, Université de Montréal, Montréal, Québec H3C 3J7, Canadar Department of Physics, University of Oregon, Eugene, OR 97403, USA

s CLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UKt Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israelu Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

v International Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113-0033,and Kobe University, Kobe 657-8501, Japan

w Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israelx Institut für Experimentalphysik, Universität Hamburg/DESY, Notkestrasse 85, D-22607 Hamburg, Germany

y Department of Physics, University of Victoria, PO Box 3055, Victoria BC V8W 3P6, Canadaz Department of Physics, University of British Columbia, Vancouver BC V6T 1Z1, Canada

aaDepartment of Physics, University of Alberta, Edmonton AB T6G 2J1, Canadaab Research Institute for Particle and Nuclear Physics, H-1525 Budapest, PO Box 49, Hungary

ac Institute of Nuclear Research, H-4001 Debrecen, PO Box 51, Hungaryad Ludwig-Maximilians-Universität München, Sektion Physik, Am Coulombwall 1, D-85748 Garching, Germany

aeMax-Planck-Institute für Physik, Föhringer Ring 6, D-80805 München, Germanyaf Department of Physics, Yale University, New Haven, CT 06520, USA


Editor: L. Rolandi


f Hcef thee-orcattering

Abstract

A search for the single production of doubly-charged Higgs bosons is performed using e+e− collision data collected bythe OPAL experiment at centre-of-mass energies between 189 GeV and 209 GeV. No evidence for the existence o±± isobserved. Upper limits are derived onhee, the Yukawa coupling of the H±± to like-signed electron pairs. A 95% confidenlevel upper limit ofhee< 0.071 is inferred forM(H±±) < 160 GeV assuming that the sum of the branching fractions oH±± to all lepton flavour combinations is 100%. Additionally, indirect constraints onhee from Bhabha scattering at centrof-mass energies between 183 GeV and 209 GeV, where the H±± would contribute viat-channel exchange, are derived fM(H±±) < 2 TeV. These are the first results both from a single production search and on constraints from Bhabha sreported from LEP. 2003 Published by Elsevier B.V.

dict

uth

ics,

s,

nd

to,

ny.d.

ity,

ne,

rt-

K),

sscha-ithbly-rrent

ly-air

eenrebly-

els.n-

ons

for

tobo-lessre-inlede-W

incea-es.

otso

1. Introduction

Some theories beyond the Standard Model prethe existence of doubly-charged Higgs bosons, H±±,

E-mail address:[email protected] (D.E. Plane).1 And at TRIUMF, Vancouver, Canada V6T 2A3.2 And Institute of Nuclear Research, Debrecen, Hungary.3 And Heisenberg Fellow.4 And Department of Experimental Physics, Lajos Koss

University, Debrecen, Hungary.5 And MPI München.6 And Research Institute for Particle and Nuclear Phys

Budapest, Hungary.7 Now at University of Liverpool, Department of Physic

Liverpool L69 3BX, UK.8 And CERN, EP Division, 1211 Geneva 23, Switzerland.9 And Manchester University.

10 Now at University of Kansas, Department of Physics aAstronomy, Lawrence, KS 66045, USA.

11 Now at University of Toronto, Department of Physics, ToronCanada.

12 Current address: Bergische Universität, Wuppertal, Germa13 Now at University of Mining and Metallurgy, Cracow, Polan14 Now at University of California, San Diego, CA, USA.15 Now at Physics Department Southern Methodist Univers

Dallas, TX 75275, USA.16 Now at IPHE Université de Lausanne, CH-1015 Lausan

Switzerland.17 Now at IEKP Universität Karlsruhe, Germany.18 Now at Universitaire Instelling Antwerpen, Physics Depa

ment, B-2610 Antwerpen, Belgium.19 Now at RWTH Aachen, Germany.20 And High Energy Accelerator Research Organisation (KE

Tsukuba, Ibaraki, Japan.21 Now at University of Pennsylvania, Philadelphia, PA, USA.22 Now at TRIUMF, Vancouver, Canada.23 Deceased.

including in left–right symmetric models [1], Higgtriplet models [2], and little Higgs models [3]. It habeen particularly emphasized that a see-saw menism used to obtain light neutrinos in a model wheavy right-handed neutrinos can lead to a doucharged Higgs boson with a mass accessible to cuand future colliders [4].

A review of experimental constraints on doubcharged Higgs bosons is presented in [5]. The pproduction of doubly-charged Higgs bosons has bconsidered in a previous OPAL publication [6], whemasses less than 98.5 GeV are excluded for doucharged Higgs bosons in left–right symmetric modDELPHI has obtained a limit of 97.3 GeV, indepedent of the lifetime of the H±± [7].

It has been noted that doubly-chargedHiggs bosmay be singly produced in eγ collisions, including ine+e− collisions where theγ is obtained from radiationfrom the other beam particle [8,9]. The diagramsthe direct production are shown in Fig. 1.

Doubly-charged Higgs bosons would decay inlike-signed lepton or vector boson pairs, or to a Wson and a singly-charged Higgs boson. For massesthan twice the W boson mass, they would decay pdominantly into like-signed leptons. Furthermore,most models the WW branching fraction is negligibeven for larger masses [9], therefore, the dominantcay mode, even for masses larger than twice theboson mass, is the decay to like-signed leptons. Sthe H±± naturally violates lepton number conservtion, it can have mixed lepton flavour decay modAdditionally, the Yukawa coupling of the H±± to thecharged leptons h is model dependent, and is ngenerally determined directly by the lepton mass,


ofth

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e

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n-t

ct

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ed

ha

].etes ofas-ag-d-plerith

ileeo-

ome-

all-turnis

-A)at-

it

Fig. 1. Feynman diagrams contributing to the single productionH−− bosons in e+e− collisions. The three additional diagrams wi“crossed” e+ lines are not shown.

decays to all lepton flavour combinations need toconsidered. It should be particularly noted that mixlepton flavour decays are severely constrained bydecay searches such asµ+ → e+e+e− andµ → eγ .

In this Letter, we search for the single productiof doubly-charged Higgs bosons, assuming the deH±± → ±′± using 600.7 pb−1 of e+e− collisiondata with centre-of-mass energies

√s = 189–209 GeV

collected by the OPAL detector. Since the productcross-section depends only onhee, the Yukawa cou-pling of the H±± to like-signed electron pairs, thsearch is sensitive to this quantity.

We assume that the decay of a doubly-charHiggs boson into a W boson and a singly-chargHiggs boson is negligible. We consider an H±± whichcouples to right-handed particles, but the resultsthe direct search quoted here are also valid forH±± which couples only to left-handed particles [9All lepton flavour combinations are considered in tH±± decay (ee,µµ, ττ , eµ, eτ , µτ ). The lifetime ofthe H±± can be important, and in particular is nonegligible for h < 10−7; however, our search is nosensitive to such small Yukawa couplings.

A doubly-charged Higgs boson would also affethe Bhabha scattering cross-section via thet-channelexchange diagram shown in Fig. 2, causing a chain rate and in the observed angular distribution of

Fig. 2. Feynman diagram contributing to the process e+e− → e+e−due to doubly-charged Higgs bosont-channel exchange.

outgoing electron. Constraints have been derivedthis process using data from lower energy collidersbut not previously from LEP.

In addition to the direct search results introducabove, we also derive indirect constraints onhee,the Yukawa coupling of H±± to electrons, usingthe differential cross-section of wide-angle Bhabscattering measured by OPAL in 688.4 pb−1 of datacollected at

√s = 183–209 GeV.

2. OPAL detector

The OPAL detector is described in detail in [10It is a multipurpose apparatus with almost complsolid angle coverage. The central detector consista silicon micro-strip detector and a system of gfilled tracking chambers in a 0.435 T solenoidal mnetic field which is parallel to the beam axis. A leaglass electromagnetic calorimeter with a presamsurrounds the central detector. In combination wthe forward calorimeters, the forward scintillating-tcounters, and the silicon–tungsten luminometer, a gmetrical acceptance is provided down to 25 mrad frthe beam direction. The silicon–tungsten luminomter measures the integrated luminosity using smangle Bhabha scattering events. The magnet reyoke is instrumented for hadron calorimetry, andsurrounded by several layers of muon chambers.

3. Direct search

3.1. Data samples and event simulation

The data samples are summarised in Table 1.The process e+e− → e∓e∓H±± is simulated with

the PYTHIA6.150 [11] event generator. In the simulation, the Equivalent Photon Approximation (EPis used to give an effective flux of photons origining from the electrons or positrons. The upper lim


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Table 1Data samples used in the direct search analysis

Ecm 〈Ecm〉 ∫L

(GeV) (GeV) (pb−1)

188–190 188.6 175.0190–194 191.6 28.9194–198 195.5 74.8198–201 199.5 78.1201–203 201.7 38.2203–206 205.0 79.4206–209 206.6 126.1

188–209 197.7 600.7

of the virtuality Q2 of the photon is given by thscale of the hard scattering process.24 The processe±γ → e∓H±± is simulated in a left–right symmetrimodel for an H±± which couples to right-handed paticles using the calculations from [8]. The contributifrom Z-exchange is negligible. In order to obtain tfull signal cross-section, a cut which PYTHIA appliby default at a minimum of 1 GeV on the transvemomentum of the lepton which radiates the H±± isexplicitly switched off. The cross-section and the agular distribution are checked with the calculations[9], using COMPHEP [12].

Separate samples are simulated with the 6 diffedecay modes (ee,µµ, ττ , eµ, eτ , µτ ). Samples of500 events each are generated for each of the avecentre-of-mass energies listed in Table 1 for H±±masses in 5 GeV steps from 90–200 GeV. For malarger than twice the W boson mass the decay H±± →W±W± is kinematically allowed. Its partial widthhowever, is negligible in most models [9]. In thLetter, the branching fraction BR(H±± → W±W±) isassumed to be zero.

The dominant Standard Model backgrounds in tanalysis are from the four-fermion processes

e+e− → +−′+′−,

including events from the so-called “multi-peripheradiagrams,

e+e− → e+e−γ (∗)γ (∗) → e+e−+−,

and lepton pairs,

24 Q2 is the negative squared four-momentum transfer.

e

e+e− → +−.

Four-fermion processes, except

e+e− → e+e−+− ( = e,µ, τ ),

e+e− → e+e−qq,

are simulated with the KORALW event generator [1The non-multi-peripheral part of the processes

e+e− → e+e−+−,

e+e− → e+e−qq,

is simulated with grc4f2.1 [14]. The multi-peripherdiagrams are simulated with the dedicated two-phoevent generators Vermaseren [15] for

e+e− → e+e−γ (∗)γ (∗) → e+e−e+e−,

and BDK [16] for

e+e− → e+e−γ (∗)γ (∗) → e+e−µ+µ−,

e+e− → e+e−γ (∗)γ (∗) → e+e−τ+τ−.

The Monte Carlo generators PHOJET [17] (forQ2 <

4.5 GeV2) and HERWIG [18] (forQ2 4.5 GeV2)are used to simulate hadronic events from two-phoprocesses. Lepton pairs are simulated using the K[19] generator forτ+τ−(γ ) andµ+µ−(γ ) events andNUNUGPV [20] for ννγ (γ ). Bhabha scattering isimulated with BHWIDE [21] (when both the electroand positron scatter at least 12.5 from the beam axisand TEEGG [22] (for the remaining phase space).

Multihadronic events, qq(γ ), are simulated usingKK2f [19]. RADCOR [23] is used to simulate multphoton events from QED processes. They maknegligible contribution to the background.

Generated signal and background events arecessed through the full simulation of the OPAL dettor [24] and the same event analysis chain was appto the simulated events as to the data.

3.2. Analysis

The signal final state consists of four chargleptons. Two like-sign leptons originate from the H±±decay and are expected to be visible in the detectomost cases. The electron or positron which originafrom the eeγ vertex (see Fig. 1) in general escapthrough the beampipe. The electron or positron whoriginates from the eeH±± vertex is also forward


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peaked; however, it enters the detector in a significfraction of signal events. The analysis is therefdivided into a two-lepton and a three-lepton analyThe final states in the three-lepton case contain thleptons visible in the detector, two of them havesame sign and could originate from the decay odoubly-charged Higgs boson. In the two-lepton catwo like-signed leptons are required, as expected indecay of a doubly-charged Higgs boson.

Leptons are identified as low multiplicity jets. Jeare reconstructed from charged particle tracks andergy deposits (clusters) in the electromagnetichadron calorimeters. Tracks and clusters are defito be of “good” quality using the requirements of [25After the jet reconstruction, double-countingof enebetween tracks and calorimeter clusters is correby reducing the calorimeter cluster energy byexpected energy deposition from associated chatracks [25], including particle identification information.

No explicit electron or muon identification is required, since it is found that the jet-based analytechnique retains high efficiency while reducing tbackground to an acceptable level. The same ansis is used to search for all 6 possible lepton flavcombinations, and the results are valid for all letonic decay modes of the H±±. The final backgroundis dominated by Standard Model processes contaifour charged leptons. The analysis cuts are listedlow. The cut values of the two-lepton and three-lepanalyses differ slightly.

The requirements for the two-lepton analysis ar

(2.1) The preselection requires low multiplicity even[26]. The events are additionally requiredhave at least two and less than nine chartracks. The sum of charged tracks and clusin the electromagnetic calorimeter must be lthan 16. Tracks and clusters are formed ijets using a cone algorithm [27] with a haangle of 20 degrees and a minimum jet energ2.5 GeV, and it is required that there be exactwo jets with polar angles25 satisfying|cosθ | <

25 OPAL uses a right-handed coordinate system where the+z

direction is along the electron beam and where+x points to thecentre of the LEP ring. The polar angleθ is defined with respect tothe +z direction and the azimuthal angleφ with respect to the+x

0.95, and which are not precisely back-to-ba(within 5). Finally, the sum of the energiesthe two jets reconstructed in the event mustgreater than 20% of

√s.

(2.2) Ordering the jet energies by their magnitu(Ejet1 > Ejet2), the following requirements armade:(a) Ejet1 > 0.1

√s;

(b) Ejet2 > 0.05√

s;(c) Ejet1 < 0.995Ebeam;(d) Ejet1 + Ejet2 < 0.95

√s.

(2.3) The invariant massMinv of the two jets mussatisfyMinv > 40 GeV. Typical mass resolutionare about 4 GeV for ee and 10 GeV forµµ. Nomass reconstruction is possible forττ , due tothe undetected neutrinos.

(2.4) Bhabha scattering is rejected by requiring tthe acollinearity angle,φacol, satisfiesφacol >

25. The angleφacol is defined to be 180 minusthe opening angle of the two jets.

(2.5) The polar angle of each jet must satisfy|cosθ | <0.75. The H±± candidate jet polar angles aplotted in Fig. 3(a) and (b) after cuts (2.1)–(2.

(2.6) Each jet associated to the H±± must have eitheone or three charged tracks. The numbercharged tracks is plotted in Fig. 3(c) after cu(2.1)–(2.5).

(2.7) Defining the sum of the track charges witheach jet as the “jet charge”, the product of tcharges of the two jets must be equal to+1. Thisvalue is plotted in Fig. 3(d) after cuts (2.1)–(2.

The requirements for the three-lepton analysis are

(3.1) The preselection is identical to that in cut (2except that exactly three reconstructed jetsrequired. The two jets which have the highreconstructed mass, as described in cut (3have to satisfy|cosθ | < 0.95 and must not beprecisely back-to-back (within 5). There is no|cosθ | requirement for the third jet. Finallythe sum of the energies of the three jets recstructed in the event must be greater than 2of

√s.

direction. The centre of the e+e− collision region defines the originof the coordinate system.


t is appliedndidate jetsted

ckgrounds for agted

Fig. 3. Examples of some of the quantities used in the two-lepton analysis selection shown immediately before the corresponding cu(see Section 3.2). The absolute values of the cosines of the polar angle of the more central and the more forward Higgs boson caare shown in (a) and (b), the number of charged tracks in each of the two H±± candidate jets in (c), and the product of the reconstruccharges of the two H±± candidate jets in (d). The points with error bars indicate the OPAL data and the shaded regions indicate the baexpectation. Note that “hadrons” includes both qq(γ ) and hadronic events from all 4-fermion processes. Two example signal expectation130 GeV doubly-charged Higgs boson are also shown normalised to a cross-section corresponding tohee= 0.1 scaled by a factor 20, assumineither a 100% H±± → ee branching ratio (dashed line) or a 100% H±± → ττ branching ratio (dotted line). The cut requirements are indicaby the arrows.

eir

t

thatini-edongyn-be

Us-n-

(3.2) Ordering the measured jet energies by thmagnitude (Ejet1 > Ejet2 > Ejet3), the followingrequirements are made:(a) Ejet1 > 0.1

√s;

(b) Ejet2 > 0.05√

s;(c) Ejet3 > 0.025

√s or it must contain at leas

one good charged track;(d) Ejet1 < 0.995Ebeam;(e) Ejet1 + Ejet2 + Ejet3 < 0.95

√s.

(3.3) The jet energies are determined assumingthe measured jet direction is the same as thetial lepton direction for each of the reconstructjets and that the missing electron or positris recoiling along the beam axis. Using enerand momentum conservation to give four costraint equations, the four jet energies caninferred (the lepton masses are neglected).ing this improved determination of the jet e


foron-

jetsas

d

enalen-m

strer-

ro-

hat

the

(a)

rofts

inhe

m-afte

mate,-an-

atdi-tors

ral

re-

oftht ofin-re-can-foretheck.heThepar-ari-ec-

ldck-

e aem-

byandftedes

inac-m-

ts ased.

ntsrac-ndiesval-rgeac-ed

bha-of

cer-esand

ergies, the invariant masses are calculatedthe three possible di-jet systems that can be cstructed from the observed jets, and the twohaving the largest di-jet mass are consideredthe H±± candidate jets with a “reconstructeHiggs boson mass”Mrec. The loss due to thisassumption is negligible for H±± masses abov110 GeV, and is taken into account in the sigefficiency calculation. Since this search conctrates on the region above the mass limit fropair creation, it is further required thatMrec sat-isfy Mrec > 80 GeV. Typical mass resolutionare about 1 GeV for ee andµµ modes, and abou4 GeV for ττ decays. Note that in the lattecase, no mass reconstruction from the jet engies would have been possible without this pcedure, due to the undetected neutrinos.

(3.4) Bhabha scattering is rejected by requiring tthe acollinearity angle between the two H±±candidate jets satisfiesφacol> 15.

(3.5) The polar angle of each jet associated toH±± must satisfy |cosθ | < 0.80. The H±±candidate jet polar angles are plotted in Fig. 4and (b) after cuts (3.1)–(3.4).

(3.6) Each jet associated to the H±± must have eitheone or three charged tracks. The numbercharged tracks is plotted in Fig. 4(c) after cu(3.1)–(3.5).

(3.7) Defining the sum of the track charges witheach jet as the “jet charge”, the product of tcharges of the two jets associated with the H±±must be equal to+1. This value is plotted inFig. 4(d) after cuts (3.1)–(3.6).

The results are summarised in Table 2. The nubers of observed and expected events agree welleach cut in both analyses.

3.3. Systematic uncertainties

The largest background in the selection is froprocesses with four charged leptons in the final stparticularly from multi-peripheral “two-photon” processes. Of concern is the fact that, in our stdard Monte Carlo background samples availableall centre-of-mass energies, the multi-peripheralagrams are treated with specialised event generawhich neglect interference with non-multi-periphe

r

diagrams. Special samples of the full set of e+e− →e+e−+− diagrams, including interference, were ppared using grc4f2.2[14] at

√s = 206 GeV to study

this effect. The background using the full sete+e−+− diagrams including interference is in boanalyses about 25% lower than our standard seMonte Carlo generators. While grc4f2.2 includesterference effects, it has other differences withspect to our standard background simulations andnot be used as the primary sample. We theresimply assign a 25% systematic uncertainty one+e−+− background according to this cross-cheMonte Carlo modelling of the variables used in tselection cuts can also induce systematic effects.possible level of mismodelling is assessed by coming data and background Monte Carlo for each vable after the preselection (cut (2.1) and (3.1), resptively) where the contribution from a signal woube negligible. Differences between the data and baground Monte Carlo simulation are used to definpossible shift in each variable, and then the systatic uncertainties are evaluated by varying the cutsthese shifts. Both the final expected backgroundsignal efficiencies are recalculated with these shicuts, and the full differences from the nominal valuare assigned as systematic uncertainties.

The uncertainty of charge identification, usedcuts (2.7/3.7) in Section 3.2 to reject a significant frtion of the background, is estimated from a clean saple of Bhabha events selected by changing the cufollows. The cuts (2.2)(c) and (3.2)(d) are not appliCuts (2.2)(d) and (3.2)(e) are changed fromEjet1 +Ejet2(+Ejet3) < 0.95

√s to Ejet1 + Ejet2(+Ejet3) >

0.95√

s. This sample consists mainly of Bhabha eveand has no overlap with the search sample. The ftion of like-sign electron pairs is 2.0% in data a1.7% in Monte Carlo. The systematic uncertainton the background and signal efficiencies are euated by randomly changing the sign of the chafor 0.15% of the tracks, in order to increase the frtion of fake like-sign events by 0.3%, the observdifference between data and Monte Carlo in Bhasample. No significant cosθ dependence of this difference was observed. An additional cross-checkτpair events from calibration data taken at

√s = mZ

indicates that the charge-confusion systematic untainty is no larger than 0.15%. The full differencbetween the new background and efficiencies


t is appliedndidate jetsted

ckgrounds for agted

Fig. 4. Examples of some of the quantities used in the three-lepton analysis selection shown immediately before the corresponding cu(see Section 3.2). The absolute values of the cosines of the polar angle of the more central and the more forward Higgs boson caare shown in (a) and (b), the number of charged tracks in each of the two H±± candidate jets in (c), and the product of the reconstruccharges of the two H±± candidate jets in (d). The points with error bars indicate the OPAL data and the shaded regions indicate the baexpectation. Note that “hadrons” includes both qq(γ ) and hadronic events from all 4-fermion processes. Two example signal expectation130 GeV doubly-charged Higgs boson are also shown normalised to a cross-section corresponding tohee= 0.1 scaled by a factor 10, assumineither a 100% H±± → ee branching ratio (dashed line) or a 100% H±± → ττ branching ratio (dotted line). The cut requirements are indicaby the arrows.

tain-

inas

thegies

thein

assallandntsved

the nominal ones are taken as systematic uncerties.

The systematic uncertainties are summarisedTable 3. Additional systematic uncertainties, suchon the integrated luminosity, are negligible.

3.4. Direct search results

In the two-lepton analysis the invariant mass oftwo jets is calculated using the measured jet ener

and directions, because it is not possible to use“angle-based” kinematic reconstruction describedSection 3.2 for the three-lepton analysis. The mdistribution is shown in Fig. 5 for events passingcuts except the like-signed charge requirement (a),also with all cuts applied (b). No excess of evewhich could imply the presence of a signal is obserin the data.

In the three-lepton analysis we calculate the H±±candidate reconstructed masses,Mrec, shown in Fig. 5,


o shown ared

te Carlo

Table 2The number of remaining events in the data after each cut, and the number expected from Standard Model background sources. Alsthe efficiencies of expected signal events for a 130 GeV doubly-charged Higgs boson assuming ee,µµ or ττ decays. The number of expectesignal events forhee= 0.1 is shown in brackets assuming 100% branching ratio for the given decay mode. The errors due to Monstatistics are also listed for events surviving the full analysis

Cut Data Total Bkg. +− 4- ‘γ γ ’ ee qq ‘γ γ ’ eeqq Efficiency [%]

ee µµ ττ

Two-lepton analysis

(2.1) 19612 17659.3 13776.9 1249.6 2249.7 173.3 209.9 45.7 45.9 41.5(2.2) 15168 14731.3 11381.3 1118.7 1971.5 158.1 101.8 44.3 39.1 36.4(2.3) 13455 13002.6 10855.6 988.1 1026.5 120.8 11.6 44.3 39.0 35.0(2.4) 6681 6685.9 5025.5 774.0 777.5 100.1 8.7 41.0 36.3 32.6(2.5) 1318 1353.4 890.6 325.9 124.3 12.5 0.1 23.8 24.3 20.3(2.6) 1181 1216.2 792.6 299.5 121.4 2.7 0.0 23.0 23.9 17.9

(2.7) 27 22.1 10.4 2.7 8.5 0.5 0.0 22.9 23.8 17.5±1.7 ±1.3 ±0.2 ±1.1 ±0.1 ±0.0 ±1.9 ±2.0 ±2.0

(64.6) (67.3) (49.1)

Three-lepton analysis

(3.1) 40948 40899.7 7422.7 467.9 27011.1 260.1 5738.0 34.1 36.2 33.3(3.2) 3203 2816.0 1685.9 153.3 778.9 63.1 134.8 22.7 24.0 21.1(3.3) 2031 1912.0 1557.9 100.5 199.4 44.4 9.8 22.7 24.0 20.0(3.4) 1359 1247.1 939.8 83.2 182.2 32.5 9.3 21.8 23.4 19.5(3.5) 572 538.3 427.4 41.4 55.5 13.3 0.7 15.5 17.8 14.1(3.6) 390 361.8 273.4 29.9 52.5 5.8 0.2 14.7 17.3 12.6

(3.7) 28 22.3 4.4 4.0 13.3 0.5 0.1 14.6 17.2 11.9±1.6 ±0.7 ±0.3 ±1.4 ±0.1 ±0.0 ±2.0 ±2.0 ±2.1

(41.0) (48.8) (33.4)

Sum∑

55 44.4 14.8 6.8 21.8 1.0 0.1 37.5 41.0 29.3±2.0 ±1.3 ±0.3 ±1.5 ±0.1 ±0.0 ±2.8 ±2.8 ±2.9

(105.6) (116.1) (82.5)

Table 3Systematic uncertainties on signal and background

2-lepton analysis: 3-lepton analysis:

Quantity Variation Bkg (%) Sig (%) Bkg (%) Sig (%)

Jet cosθ ±0.5 8 1 7 1Jet energy ±1% 1 1 2 1φacol ±0.5 2 1 1 1Charge misidentification 0.15% 14 1 4 1

Background modelling (see text) 25 − 25 −Monte Carlo statistics – 8 10 7 14

Quadratic sum 31 10 27 14

de-bu-cept

ithtovent

using the “angle-based” kinematic reconstructionscribed in item (3.3) in Section 3.2. The mass distritions are shown both for events passing all cuts ex

the like-signed charge requirement (c), and also wall cuts applied (d). Additionally, as a cross-checkensure that no di-jet mass peak present after the e


nd aftersta and the

es.ponding toe

Fig. 5. The reconstructed H±± candidate mass distributions. The invariant di-jet mass is shown for the 2-lepton analysis both before athe like-signed jet requirement (cut (2.7)) in (a) and (b), respectively. For the 3-lepton analysis, the reconstructed H±± mass using the jet angleas discussed in the text, is shown before and after cut (3.7) in (c) and (d), respectively. The points with error bars indicate the OPAL dashaded regions indicate the background expectation. Note that “hadrons” includes both qq(γ ) and hadronic events from all 4-fermion processTwo example signal expectations for a 130 GeV doubly-charged Higgs boson are also shown normalised to a cross-section correshee= 0.1, assuming either a 100% H±± → ee branching ratio (dashed line) or a 100% H±± → ττ branching ratio (dotted line). Note that du

±±
to the undetected neutrinos from the tau-lepton decay there is no peak in the H→ ττ signal sample of the 2-lepton analysis ((a) and (b)).
hod,ck

ed.nce

nsson

theberofthe

ned8],intoe.

reconstruction is reduced by the angle-based metthe largest di-jet mass calculated from only the traand cluster information (Section 3.2) was examinNo excess of events which could imply the preseof a signal is observed in the data.

Limits are set on the H±± Yukawa couplinghee,assuming that the sum of the branching fractioof the H±± to all lepton flavour combinations i100%. The efficiency for an arbitrary Higgs bos

mass is determined by linear interpolation betweensimulated signal Monte Carlo samples. The numof observed events, together with the numberexpected signal and background events from bothtwo-lepton and three-lepton analyses are combiusing the likelihood ratio method described in [2which incorporates the systematic uncertaintiesthe limits using a numerical convolution techniquFor the purpose of extracting the limits, a±10 GeV


gsareheeVuchnts.r

neld,ructson

n-m-inedion

nedveln

he

ism

uld

p-n

let isins the

re

ton

orbly-has

for

ed

rre-ga-ta,rn

ngeiveni--hed.

hes-us-data.dif-

be-woeVhets

c-ofow-ibleesa-

tted

edeV,

rthegedval-e-ons

“sliding mass window” around the hypothetical Higboson mass is used. Events within this windowcounted in data and Monte Carlo simulation. Thypothetical Higgs boson mass is varied in 1 Gsteps. The width of the mass window is chosen sthat it contains most of the expected signal eveA small efficiency correction, typically around 5% foee andµµ and 10% forττ , due to this window isapplied. In the two-lepton analysis for any chancontainingτ leptons no mass window cut is appliebecause in this channel it is not possible to reconstthe correct mass of the doubly-charged Higgs bodue to the undetected neutrinos.

The limits onhee are calculated using the efficiecies determined from the PYTHIA Monte Carlo saples and the production cross-sections are determin a consistent manner using PYTHIA (see discussin Section 3.1). No systematic uncertainty is assigfor theoretical uncertainties. The 95% confidence lelimits onhee from combining both analyses are showin Fig. 6(a)–(c) assuming a branching fraction of tdoubly-charged Higgs boson into ee,µµ, ττ of 100%,respectively. Strictly, due to the production mechaninvolving non-zerohee, exactly 100%µµ or ττ de-cays are not possible, therefore, the latter limits shobe considered for the casehµµ,ττ hee. In Fig. 6(d),for each mass the highest limit from all possible leton flavour combinations is shown. An upper limit ohee< 0.071 is inferred forM(H±±) < 160 GeV at the95% confidence level, which is valid for all possiblepton flavour combinations in the decays. The limidetermined by the pureττ case except for massesexcess of 170 GeV. For the case of pure ee decaylimit is hee< 0.042, and forµµ decayshee< 0.049,both for M(H±±) < 160 GeV. For the mixed flavoudecay modes eµ, eτ , andµτ the limit is between thosfor pure decays of the two involved flavours.

4. Indirect search

Doubly-charged Higgs bosons would contributeBhabha scattering viat-channel exchange as showin Fig. 2. The Born level differential cross-section fBhabha scattering including the exchange of a doucharged Higgs boson with right-handed couplingsbeen calculated in [5]. At high masses,M(H±±) √

s, the cross-section is identical to that derived

four-fermion contact interactions with right-handcurrents [29] (ηRR = 1, ηLL = ηLR = 0), with the re-placement ofg/Λ by hee/M(H±±) wherehee is theHiggs coupling to electrons.26 At values ofM(H±±)

comparable to the centre-of-mass energy, this cospondence is modified by the inclusion of a propator term. For comparison with the experimental daQED radiative corrections are applied to the Bolevel terms for doubly-charged Higgs boson exchaand interference with Standard Model processes gin [5] using the program MIBA [30]. Initial state radation is calculated up toO(α2) in the leading log approximation with soft photon exponentiation, and tO(α) leading log final state QED correction is applieThe BHWIDE [21] program is used to calculate tStandard Model contribution to the differential crossection. The theoretical predictions are calculateding the same acceptance cuts as are applied to the

This analysis uses OPAL measurements of theferential cross-section for e+e− → e+e− at centre-of-mass energies of 183–209 GeV [31,32]. The datatween 203 GeV and 209 GeV are grouped into tsets with mean energies of approximately 205 Gand 207 GeV. The total integrated luminosity of tdata amounts to 688.4 pb−1. These measuremencover the range|cosθ | < 0.9, in 15 bins of cosθ(as defined in [32]), and correspond toθacol < 10where θacol is the acollinearity angle between eletron and positron. It is verified that the effectdoubly-charged Higgs boson exchange on the langle Bhabha scattering cross-section has a negligeffect on the luminosity determination even for valuof hee a few times larger than excluded by this mesurement.

The measured differential cross-sections are fiwith the theoretical prediction using aχ2 fit. The fitis performed for fixed values of the doubly-chargHiggs boson mass between 80 GeV and 2000 Gallowing the square of the coupling,h2

ee, to vary. Al-though onlyh2

ee> 0 is physically meaningful, in ordeto allow for the case where the data fluctuate inopposite direction to that expected for doubly-charHiggs boson exchange, both positive and negativeues ofh2

eeare allowed in the fit. Experimental and thoretical systematic uncertainties and their correlati

26 In [5] hee is denotedgee.


s shouldinceassumingd lines. Intthe OPAL

Fig. 6. Limits at the 95% confidence level on the Yukawa couplinghee assuming a 100% branching fraction of the H±± to (a) ee, (b)µµ

and (c)ττ . The limits are calculated with the combined results of the two-lepton and three-lepton analysis. In (b) and (c), the limitbe regarded as valid in the large branching fraction limit, since non-zerohee implies a non-zero electron branching fraction (see text). Sthe ee andµµ efficiencies and mass resolutions are very similar, figures (a) and (b) are almost identical. The median expected limitsonly Standard Model processes are shown by the dotted lines, while the actual limits inferred from the data are shown by the solifigure (d) the limit for arbitrary lepton flavour combinations (ee, eµ, eτ , µµ, µτ andττ ) is shown. It is determined by the pureττ case excepfor masses in excess of 170 GeV. The shaded regions for masses below 98.5 GeV are excluded in left–right symmetric models bypair production search [6].

hatpre-ted

atioer-ard

fit.nc-od

blyPE-ctThe

are treated as discussed in [32]. The fitted values ofh2ee

are consistent with zero for all masses, indicating tthe data are consistent with the Standard Modeldiction. For example, for a mass of 130 GeV the fitvalue ofh2

ee is 0.003± 0.011, and the fit has aχ2 of97.0 for 119 degrees of freedom. Fig. 7 shows the rof the measured luminosity-weighted average diffential cross-section at 183–207 GeV to the Stand

Model prediction, together with the results of the95% confidence level limits on the coupling as a fution of mass were derived by integrating the likelihofunction obtained fromχ2 over the regionh2

ee > 0,and are shown in Fig. 8. The limits are consideramore stringent than those derived from PEP andTRA data [5]. Fig. 9 shows the limits from the indiresearch together with those from the direct search.


fer-

theou-rre-

s to a

ingtasare

ing

ton

adedight

thegher

ly-ev-

u-

of

ct

uc-re-

Fig. 7. Ratio of the measured luminosity-weighted average difential cross-section for e+e− → e+e− at 183–207 GeV to theStandard Model prediction. The points with error bars showOPAL data, while the curves show theoretical predictions for a dbly-charged Higgs boson mass of 130 GeV. The solid curve cosponds to the best fit to all data, the dashed curve correspondcoupling equal to the 95% confidence level limit.

Fig. 8. Limits at the 95% confidence level on the Yukawa couplhee as a function ofM(H±±) derived from Bhabha scattering da(solid line) for an H±± coupling to right-handed particles. Limitat 90% confidence level derived from PEP and PETRA data [5]shown, as a dashed line, for comparison.

Fig. 9. Limits at the 95% confidence level on the Yukawa couplhee assuming a 100% branching fraction of the H±± → ee. Thedirect limit is calculated with the combined results of the two-lepand three-lepton analyses. The indirect limit onhee obtained fromBhabha scattering described in Section 4 is also shown. The shregions for masses below 98.5 GeV are excluded in left–rsymmetric models by the OPAL pair production search [6].

indirect limits are less restrictive than those fromdirect search at low masses, but extend to much himasses.

5. Conclusion

A direct search for the single production of doubcharged Higgs bosons has been performed. Noidence for the existence of H±± is observed. Up-per limits are determined on the Higgs Yukawa copling to like-signed electron pairs,hee. A 95% con-fidence level upper limit ofhee < 0.071 is inferredfor M(H±±) < 160 GeV assuming that the sumthe branching fractions of the H±± to all leptonflavour combinations is 100%. Additionally, indireconstraints onhee for M(H±±) < 2 TeV are derivedfrom Bhabha scattering where the H±± would con-tribute viat-channel exchange forM(H±±) < 2 TeV.These are the first results on both the single prodtion search and constraints from Bhabha scatteringported from LEP.


ngevendandthe

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Acknowledgements

The authors would like to thank André Schönifor suggesting that we perform this search, StGodfrey and Pat Kalyniak for valuable discussions aassistance during the preparation of this paper,also Emmanuelle Perez for a helpful hint aboutPYTHIA code.

We particularly wish to thank the SL Divisiofor the efficient operation of the LEP acceleratorall energies and for their close cooperation with oexperimental group. In addition to the support stafour own institutions we are pleased to acknowledthe

– Department of Energy, USA,– National Science Foundation, USA,– Particle Physics and Astronomy Research Co

cil, UK,– Natural Sciences and Engineering Research C

cil, Canada,– Israel Science Foundation, administered by

Israel Academy of Science and Humanities,– Benoziyo Center for High Energy Physics,– Japanese Ministry of Education, Culture, Spo

Science and Technology (MEXT) and a graunder the MEXT International Science ReseaProgram,

– Japanese Society for the Promotion of Scie(JSPS),

– German–Israeli Bi-national Science Foundat(GIF),

– Bundesministerium für Bildung und ForschunGermany,

– National Research Council of Canada,– Hungarian Foundation for Scientific Resear

OTKA T-038240, and T-042864,– The NWO/NATO Fund for Scientific Researc

The Netherlands.

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Model and Constraints on New Physics from Measuremeof Fermion-pair Production at 189–209 GeV at LEP,preparation.

b

d



Measurement of charged-particle multiplicity distributions antheirHq moments in hadronicZ decays at LEP

L3 Collaboration

P. Achardt, O. Adrianiq, M. Aguilar-Benitezx, J. Alcarazx,r, G. Alemanniv, J. Allabyr,A. Aloisio ab, M.G. Alviggi ab, H. Anderhubau, V.P. Andreevf,ag, F. Anselmoi,

A. Arefievaa, T. Azemoonc, T. Aziz j,r, P. Bagnaiaal, A. Bajox, G. Baksayp, L. Baksayy,S.V. Baldewb, S. Banerjeej, Sw. Banerjeed, A. Barczykau,as, R. Barillèrer, P. Bartaliniv,

M. Basilei, N. Batalovaar, R. Battistonaf, A. Bayv, F. Becattiniq, U. Beckern,F. Behnerau, L. Bellucciq, R. Berbecoc, J. Berdugox, P. Bergesn, B. Bertucciaf,

B.L. Betevau, M. Biasiniaf, M. Biglietti ab, A. Bilandau, J.J. Blaisingd, S.C. Blythah,G.J. Bobbinkb, A. Böhma, L. Boldizsarm, B. Borgiaal, S. Bottaiq, D. Bourilkovau,M. Bourquint, S. Braccinit, J.G. Bransonan, F. Brochud, A. Buijsaq, J.D. Burgern,

W.J. Burgeraf, X.D. Cain, M. Capelln, G. Cara Romeoi, G. Carlinoab, A. Cartacciq,J. Casausx, F. Cavallarial, N. Cavalloai, C. Cecchiaf, M. Cerradax, M. Chamizot,Y.H. Changaw, M. Chemarinw, A. Chenaw, G. Cheng, G.M. Cheng, H.F. Chenu,

H.S. Cheng, G. Chiefariab, L. Cifarelli am, F. Cindoloi, I. Claren, R. Clareak,G. Coignetd, N. Colinox, S. Costantinial, B. de la Cruzx, S. Cucciarelliaf,

J.A. van Dalenad, R. de Asmundisab, P. Déglont, J. Debreczenim, A. Degréd,K. Deitersas, D. della Volpeab, E. Delmeiret, P. Denesaj, F. DeNotaristefanial,

A. De Salvoau, M. Diemozal, M. Dierckxsensb, D. van Dierendonckb, C. Dionisial,M. Dittmarau,r, A. Doriaab, M.T. Dovak,5, D. Duchesneaud, P. Duinkerb, B. Echenardt,

A. Eliner, H. El Mamouniw, A. Englerah, F.J. Epplingn, A. Ewersa, P. Extermannt,M.A. Falaganx, S. Falcianoal, A. Favaraae, J. Fayw, O. Fedinag, M. Felciniau,

T. Fergusonah, H. Fesefeldta, E. Fiandriniaf, J.H. Fieldt, F. Filthautad, P.H. Fishern,W. Fisheraj, I. Fiskan, G. Forconin, K. Freudenreichau, C. Furettaz, Yu. Galaktionovaa,n,S.N. Gangulij , P. Garcia-Abiae,r, M. Gataullinae, S. Gentileal, S. Giagual, Z.F. Gongu,

G. Grenierw, O. Grimmau, M.W. Gruenewaldh,a, M. Guidaam, R. van Gulikb,V.K. Guptaaj, A. Gurtuj, L.J. Gutayar, D. Haase, D. Hatzifotiadoui, T. Hebbekerh,a,A. Hervér, J. Hirschfelderah, H. Hoferau, M. Hohlmanny, G. Holznerau, S.R. Houaw,

Y. Hu ad, B.N. Jing, L.W. Jonesc, P. de Jongb, I. Josa-Mutuberríax, D. Käfera,M. Kauro, M.N. Kienzle-Focaccit, J.K. Kimap, J. Kirkbyr, W. Kittel ad,



110 L3 Collaboration / Physics Letters B 577 (2003) 109–119

s

A. Klimentovn,aa, A.C. Königad, M. Kopalar, V. Koutsenkon,aa, M. Kräberau,R.W. Kraemerah, W. Krenza, A. Krügerat, A. Kunin n, P. Ladron de Guevarax,I. Laktinehw, G. Landiq, M. Lebeaur, A. Lebedevn, P. Lebrunw, P. Lecomteau,P. Lecoqr, P. Le Coultreau, J.M. Le Goffr, R. Leisteat, P. Levtchenkoag, C. Li u,

S. Likhodedat, C.H. Linaw, W.T. Lin aw, F.L. Lindeb, L. Listaab, Z.A. Liu g,W. Lohmannat, E. Longoal, Y.S. Lug, K. Lübelsmeyera, C. Lucial, L. Luminarial,

W. Lustermannau, W.G. Mau, L. Malgerit, A. Malinin aa, C. Mañax, D. Mangeolad,J. Mansaj, J.P. Martinw, F. Marzanoal, K. Mazumdarj, R.R. McNeilf , S. Meler,ab,

L. Merolaab, M. Meschiniq, W.J. Metzgerad, A. Mihul l, H. Milcentr, G. Mirabellial,J. Mnicha, G.B. Mohantyj, G.S. Muanzaw, A.J.M. Muijsb, B. Musicaran, M. Musyal,

S. Nagyp, S. Natalet, M. Napolitanoab, F. Nessi-Tedaldiau, H. Newmanae, T. Niessena,A. Nisatial, H. Nowakat, R. Ofierzynskiau, G. Organtinial, C. Palomaresr,

D. Pandoulasa, P. Paolucciab, R. Paramattial, G. Passalevaq, S. Patricelliab, T. Paulk,M. Pauluzziaf, C. Pausn, F. Paussau, M. Pedaceal, S. Pensottiz, D. Perret-Gallixd,B. Petersenad, D. Piccoloab, F. Pierellai, M. Pioppiaf, P.A. Pirouéaj, E. Pistolesiz,

V. Plyaskinaa, M. Pohlt, V. Pojidaevq, J. Pothierr, D.O. Prokofievar, D. Prokofievag,J. Quartieriam, G. Rahal-Callotau, M.A. Rahamanj, P. Raicsp, N. Rajaj, R. Ramelliau,

P.G. Rancoitaz, R. Ranieriq, A. Rasperezaat, P. Razisac, D. Renau, M. Rescignoal,S. Reucroftk, S. Riemannat, K. Rilesc, B.P. Roec, L. Romerox, A. Roscah,

S. Rosier-Leesd, S. Rotha, C. Rosenblecka, B. Rouxad, J.A. Rubior, G. Ruggieroq,H. Rykaczewskiau, A. Sakharovau, S. Saremif, S. Sarkaral, J. Salicior, E. Sanchezx,

M.P. Sandersad, C. Schäferr, V. Schegelskyag, S. Schmidt-Kaersta, D. Schmitza,H. Schopperav, D.J. Schotanusad, G. Schweringa, C. Sciaccaab, L. Servoliaf,S. Shevchenkoae, N. Shivarovao, V. Shoutkon, E. Shumilovaa, A. Shvorobae,

T. Siedenburga, D. Sonap, P. Spillantiniq, M. Steuern, D.P. Sticklandaj, B. Stoyanovao,A. Straessnerr, K. Sudhakarj, G. Sultanovao, L.Z. Sunu, S. Sushkovh, H. Suterau,

J.D. Swaink, Z. Szillasiy,3, X.W. Tangg, P. Tarjanp, L. Tauschere, L. Taylork,B. Tellili w, D. Teyssierw, C. Timmermansad, Samuel C.C. Tingn, S.M. Tingn,S.C. Tonwarj,r, J. Tóthm, C. Tully aj, K.L. Tungg, J. Ulbrichtau, E. Valenteal,

R.T. Van de Wallead, V. Veszpremiy, G. Vesztergombim, I. Vetlitskyaa, D. Vicinanzaam,G. Viertelau, S. Villaak, M. Vivargentd, S. Vlachose, I. Vodopianovag, H. Vogelah,

H. Vogtat, I. Vorobievah,aa, A.A. Vorobyovag, M. Wadhwae, W. Wallraff a, X.L. Wangu,Z.M. Wangu, M. Webera, P. Wienemanna, H. Wilkensad, S. Wynhoffaj, L. Xia ae,

Z.Z. Xuu, J. Yamamotoc, B.Z. Yangu, C.G. Yangg, H.J. Yangc, M. Yangg, S.C. Yehax,An. Zaliteag, Yu. Zaliteag, Z.P. Zhangu, J. Zhaou, G.Y. Zhug, R.Y. Zhuae,

H.L. Zhuangg, A. Zichichi i,r,s, G. Zilizi y,3, B. Zimmermannau, M. Zöller a,3

a I. Physikalisches Institut, RWTH, D-52056 Aachen, and III. Physikalisches Institut, RWTH, D-52056 Aachen, Germany1

b National Institute for High Energy Physics, NIKHEF, and University of Amsterdam, NL-1009 DB Amsterdam, The Netherland

L3 Collaboration / Physics Letters B 577 (2003) 109–119 111

ance

c University of Michigan, Ann Arbor, MI 48109, USAd Laboratoire d’Annecy-le-Vieux de Physique des Particules, LAPP, IN2P3-CNRS, BP 110, F-74941 Annecy-le-Vieux cedex, Fr

e Institute of Physics, University of Basel, CH-4056 Basel, Switzerlandf Louisiana State University, Baton Rouge, LA 70803, USA

g Institute of High Energy Physics, IHEP, 100039 Beijing, China6

h Humboldt University, D-10099 Berlin, Germany1

i University of Bologna and INFN, Sezione di Bologna, I-40126 Bologna, Italyj Tata Institute of Fundamental Research, Mumbai (Bombay) 400 005, India

k Northeastern University, Boston, MA 02115, USAl Institute of Atomic Physics and University of Bucharest, R-76900 Bucharest, Romania

m Central Research Institute for Physics of the Hungarian Academy of Sciences, H-1525 Budapest 114, Hungary2

n Massachusetts Institute of Technology, Cambridge, MA 02139, USAo Panjab University, Chandigarh 160 014, Indiap KLTE-ATOMKI, H-4010 Debrecen, Hungary3

q INFN, Sezione di Firenze and University of Florence, I-50125 Florence, Italyr European Laboratory for Particle Physics, CERN, CH-1211 Geneva 23, Switzerland

s World Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerlandt University of Geneva, CH-1211 Geneva 4, Switzerland

u Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China6

v University of Lausanne, CH-1015 Lausanne, Switzerlandw Institut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université Claude Bernard, F-69622 Villeurbanne, France

x Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, CIEMAT, E-28040 Madrid, Spain4

y Florida Institute of Technology, Melbourne, FL 32901, USAz INFN, Sezione di Milano, I-20133 Milan, Italy

aa Institute of Theoretical and Experimental Physics, ITEP, Moscow, Russiaab INFN, Sezione di Napoli and University of Naples, I-80125 Naples, Italy

ac Department of Physics, University of Cyprus, Nicosia, Cyprusad University of Nijmegen and NIKHEF, NL-6525 ED Nijmegen, The Netherlands

aeCalifornia Institute of Technology, Pasadena, CA 91125, USAaf INFN, Sezione di Perugia and Università Degli Studi di Perugia, I-06100 Perugia, Italy

ag Nuclear Physics Institute, St. Petersburg, Russiaah Carnegie Mellon University, Pittsburgh, PA 15213, USA

ai INFN, Sezione di Napoli and University of Potenza, I-85100 Potenza, Italyaj Princeton University, Princeton, NJ 08544, USA

ak University of California, Riverside, CA 92521, USAal INFN, Sezione di Roma and University of Rome, “La Sapienza”, I-00185 Rome, Italy

am University and INFN, Salerno, I-84100 Salerno, Italyan University of California, San Diego, CA 92093, USA

ao Bulgarian Academy of Sciences, Central Laboratory of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgariaap The Center for High Energy Physics, Kyungpook National University, 702-701 Taegu, Republic of Korea

aq Utrecht University and NIKHEF, NL-3584 CB Utrecht, The Netherlandsar Purdue University, West Lafayette, IN 47907, USA

asPaul Scherrer Institut, PSI, CH-5232 Villigen, Switzerlandat DESY, D-15738 Zeuthen, Germany

au Eidgenössische Technische Hochschule, ETH Zürich, CH-8093 Zürich, Switzerlandav University of Hamburg, D-22761 Hamburg, Germanyaw National Central University, Chung-Li, Taiwan, ROC

ax Department of Physics, National Tsing Hua University, Taiwan, ROC


Editor: L. Rolandi


eventseent are

Abstract

The charged-particle multiplicity distribution is measured for all hadronic events as well as for light-quark and b-quarkproduced in e+e− collisions at the Z pole. Moments of the charged-particle multiplicity distributions are calculated. ThHq

moments of the multiplicity distributions are studied, and their quasi-oscillations as a function of the rank of the mominvestigated. 2003 Published by Elsevier B.V.

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1. Introduction

Since quarks and gluons are not observedrectly, the understanding of the hadronization procwhereby a quark–gluon system evolves to hadronof importance and provides a tool for studying tquark–gluon system itself. One of the most basic chacteristics of the resulting hadronic system is thetribution of the number of hadrons produced.

Assuming local parton–hadron duality (LPHD) [1characteristics of the charged-particle multiplicity dtribution are directly related to the characteristicsthe corresponding parton distributions. The partontributions are calculable using perturbative quantchromo-dynamics (pQCD). In particular, the depedence on the center-of-mass energy,

√s, of the mean,

〈n〉, of the charged-particle multiplicity is an impotant test of pQCD. Since these calculations are ovalid for light quarks, a separate measurement for liquarks is of interest.

In this Letter, the charged-particle multiplicity ditributions of hadronic decays of the Z boson are msured for b- and for light-quark (u, d, s and c) eveas well as for all events. From these distributions mments are calculated, which characterize the shapthe distributions.

1 Supported by the German Bundesministerium für BilduWissenschaft, Forschung und Technologie.

2 Supported by the Hungarian OTKA fund under contrNos. T019181, F023259 and T024011.

3 Also supported by the Hungarian OTKA fund under contrNo. T026178.

4 Supported also by the Comisión Interministerial de CienciTecnología.

5 Also supported by CONICET and Universidad Nacional dePlata, CC 67, 1900 La Plata, Argentina.

6 Supported by the National Natural Science FoundationChina.

The shape of the charged-particle multiplicity dtribution is a fundamental tool in the study of parcle production. Independent emission of single pticles leads to a Poissonian multiplicity distributioDeviations from this shape, therefore, reveal corretions [2]. To study the shape, we use the normalifactorial moments. In terms of the multiplicity distribution,P(n), the normalized factorial moment of ranq is defined by

(1)Fq =∑∞

n=q n(n − 1) · · · (n − q + 1)P (n)(∑∞

n=1 nP(n))q .

It reflects correlations in the production of up toqparticles. If the particle distribution is Poissonian,Fq are equal to unity. If the particles are correlatthe distribution is broader and theFq are greaterthan unity. If the particles are anti-correlated, tdistribution is narrower and theFq are less than unity

Normalized factorial cumulants,Kq , obtained fromthe normalized factorial moments by

(2)Kq = Fq −q−1∑

m=1

(q − 1)!m!(q − m − 1)!Kq−mFm,

measure the genuine correlations betweenq particles,i.e., q-particle correlations which are not a consquence of correlations among fewer thanq particles.

Since|Kq | andFq both increase rapidly withq , itis useful to define theHq moments,

(3)Hq = Kq

Fq,

which have the same order of magnitude over a larange ofq .

The shape of the charged-particle multiplicity dtribution analyzed in terms of theHq was found to re-veal quasi-oscillations [3–6], when plotted versusrank q , in e+e−, as well as hadron–hadron, hadroion and ion–ion interactions. In e+e− annihilation,


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Fig. 1. Qualitative behavior ofHq as a function ofq for variousapproximations of perturbative QCD [3,8].

this result was interpreted [5,7] in terms of pQCfrom which the Hq of the parton multiplicity dis-tribution were calculated [3,8]. The expected behior of Hq vs. q is quite sensitive to the approximtion used, as is illustrated qualitatively in Fig. 1 fthe double logarithm approximation (DLA), the moified leading logarithm approximation (MLLA), thnext-to-leading logarithm approximation (NLLA), anthe next-to-next-to-leading logarithm approximati(NNLLA). In the NNLLA a negative first minimum isexpected nearq = 5 and quasi-oscillations about zeare expected for larger values ofq .

According to the LPHD hypothesis, hadronizatidoes not distort the shape of the multiplicity distribtion. If this is valid, the same shape may be expecfor the charged-particle multiplicity distribution as fthe parton multiplicity distribution.

2. Experimental procedures

2.1. Event selection

This analysis is based on 1.5 million hadronevents collected by the L3 detector [9] at LEP in tyears 1994 and 1995 at the Z pole.

Events are selected in a two-step procedure [First, at least 15 calorimetric clusters of at le100 MeV are required in order to reduce backgroufrom the e+e− → τ+τ− process. Hadronic evenfrom the process e+e− → qq are then selected brequiring small energy imbalance both along atransverse to the beam direction.

The second step is the selection of charged trameasured in the central tracker and the silicon micvertex detector. A number of quality cuts are usedselect well-measured tracks. Further, the thrust dition calculated from the charged tracks is requiredlie within the full acceptance of the central trackNo selection specifically rejects or selects tracks frlong-lived neutral particles. The track selection eciency, determined from Monte Carlo, is about 75The resulting data sample corresponds to apprmately one million selected hadronic events, anda purity of about 99.8%.

To correct for detector acceptances and inefficicies, we make use of the JETSET 7.4 [11] parshower Monte Carlo program, tuned using L3 daEvents are generated, passed through the L3 detor simulation program [12], and further subjectedtime-dependent detector effects. Then they are restructed and the events and tracks are selected insame way as the data. For systematic studies weuse events generated by ARIADNE 4.2 [13]. For coparisons with the data we use HERWIG 5.9 [14]well as JETSET.

To select b- and udsc-quark enhanced samplesuse the full three-dimensional information on tracfrom the central tracker to calculate for each trackprobability that it originated at the primary vertex [15We select b- and udsc-quark samples with puritieabout 96% and 93% and efficiencies of about 38%96%, respectively.

2.2. Unfolding

The resulting multiplicity distributions are fullcorrected for detector resolution using an iteratBayesian unfolding method [16]. The detector agenerator level Monte Carlo events are used to cstruct a matrixR(ndet, n) which represents the probbility that ndet tracks would be detected ifn chargedparticles were produced. A distribution,P0(n), is as-sumed forn. For this P0, the distribution expectein the detector isP det

0 (ndet) = ∑n R(ndet, n)P0(n).

This is compared to the actual distribution of the rdata, and, making use of Bayes’ theorem, an impromultiplicity distribution is calculated, which replaceP0(n) in the above expression. This process is repeiteratively until satisfactory agreement between thepected and actual raw data distribution is found.


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practice, this occurs after the second iteration ifJETSET multiplicity distribution is chosen asP0(n).

In addition, corrections are made for efficienand acceptance of the event selection, initial sradiation, and K0S and decays. Furthermore, thdistributions for the b- and udsc-enhanced samplescorrected for the purity of the flavor selection.

The unfolding method gives [16] an estimatethe covariance matrix of the unfolded distributioThis matrix, combined with the uncertainties on tcorrections mentioned above, is used to determthe uncertainties on the moments of the multiplicdistribution for the all- and udsc-flavor cases. Whthe statistics is too small, as in the b-flavor case,uncertainty on the estimate of the covariance matrilarge. In this case we use a Monte Carlo method. MMonte Carlo variations of the raw data multiplicidistribution are made, choosing the number of eveat each multiplicity from a Poisson distribution havias mean the observed number of events. These MCarlo distributions are then analysed in the saway as the data distribution. The uncertainty onmoment is determined from the spread in valuesthe moments of the Monte Carlo distributions. Forhigh-statistics cases, both methods agree.

2.3. Systematic uncertainties

The following sources of systematic uncertaintyinvestigated:

Selection The value of each cut used in the eventlection is varied independently over a resonable range around the default value athe resulting fully corrected distributions, together with their covariance matrices, detmined, and from them the moments of tmultiplicity distribution. For each multiplic-ity, as well as for each multiplicity momenwe assign a systematic uncertainty of hof the maximum difference between the nevalues. The same procedure is followedthe track selection and flavor tagging. For flvor tagging there is an additional contributiodue to an uncertainty of 2.5% in the puritythe resulting sample, which accounts for tdifferent response of the tagging algorithmdata and Monte Carlo.

Monte Carlo uncertaintiesThe analysis is repeateusing ARIADNE instead of JETSET to determine the corrections and the unfolding mtrix. The difference between the two resultstaken as the systematic uncertainty. Furththe c- and b-quark fragmentation parameteεc and εb, are varied. Also, the strangenesuppression parameter is varied by an amoconsistent with the measured K0

S productionrate [17]. In each case, half the difference btween the results using the two parameter vues is taken as the systematic uncertainty.

Unfolding methodThree contributions are detemined: first, ARIADNE is used to derive thinitial distribution. Secondly, the analysisrepeated using a different number of itetions in the unfolding. Finally, the detectolevel multiplicity distribution of events geneated by ARIADNE is unfolded using the response matrix,R(ndet, n), determined usingJETSET events. In each case, the differefrom the default value is taken as the systeatic uncertainty.

BackgroundThe background of about 0.2% is moly from two-photon processes. We take asystematic uncertainty the effect of twice tamount of estimated background.

The contributions from each of these sourcesadded in quadrature. The track selection contributhe dominant part of the total systematic uncertaiwhen all events are used, while the flavor-taggpurity uncertainty dominates that of the udsc sam

Table 1Contribution of the various sources of systematic uncertainty tomeasurement of the mean charged-particle multiplicity,〈n〉Source full udsc b

Event selection 0.005 0.006 0.004Track selection 0.090 0.080 0.116Tagging cuts 0.018 0.021Tagging purity 0.185 0.126MC modeling 0.032 0.031 0.040Unfolding 0.034 0.034 0.043Background 0.024 0.024 0.023γ conversion 0.039 0.039 0.039

Total 0.11 0.21 0.19


SET and
Fig. 2. Charged-particle multiplicity distribution for all, udsc-, and b-quark events compared to the expectations of (a), (c), (e), (g) JET(b), (d), (f), (h) HERWIG. The error bars include both statistical and systematic uncertainties.
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For the b-quark sample, these two contributionsabout equal.

In addition, the accuracy of the simulation of trate of photon conversion is considered. This is fouto be about 15% smaller than in data [10] andassigned as a systematic uncertainty on〈n〉. It is foundto be negligible for the other moments. Breakdowof the systematic uncertainties on〈n〉 are shown inTable 1.

3. Results

3.1. Charged-particle multiplicity distributions

Charged-particle multiplicity distributions are mesured both including and excluding K0

S and decay

products.7 Fig. 2 shows the charged-particle multipliity distribution including K0

S and decay products fothe full, udsc- and b-quark samples. All distributioagree rather well with JETSET, but in all cases HEWIG gives a poor description of the data, as is seeFig. 2(a) and 2(b).

From these distributions various moments ofcharged-particle multiplicity distribution are calclated. The results are summarized in Table 2. Tmean multiplicity including K0S and decay products

7 Note that−, − and − have only one charged particamong their decay products apart from those produced in decay,and0 and0 have none. Thus including or not the decay produof these baryons does not affect the charged multiplicity excthrough the decay.


second
Table 2Moments of the charged-particle multiplicity distribution for all, udsc-, and b-quark events. The first uncertainty is statistical, thesystematic
Moments Without K0S and decay With K0S and decay

All events

〈n〉 18.63± 0.01± 0.11 20.46± 0.01± 0.11

〈n2〉 381.7± 0.3± 4.4 457.7± 0.3± 4.9

〈n3〉 × 10−2 85.2± 0.1± 1.5 111.1± 0.1± 1.8

〈n4〉 × 10−3 205.9± 0.4± 5.1 290.6± 0.5± 6.5

D =√

〈(n − 〈n〉)2〉 5.888± 0.005± 0.051 6.244± 0.005± 0.051

S = 〈(n − 〈n〉)3〉/D3 0.596± 0.004± 0.010 0.600± 0.004± 0.010

K = 〈(n − 〈n〉)4〉/D4 − 3 0.51± 0.01± 0.04 0.49± 0.01± 0.03

〈n〉/D 3.164± 0.002± 0.016 3.277± 0.002± 0.016

F2 = 〈n(n − 1)〉/〈n〉2 1.0461± 0.0002± 0.0040 1.0441± 0.0001± 0.0034

udsc-quark events

〈n〉 18.07± 0.01± 0.21 19.88± 0.01± 0.21

〈n2〉 340.0± 0.3± 8.4 432.4± 0.4± 9.2

〈n3〉 × 10−2 78.3± 0.1± 2.7 102.2± 0.1± 3.3

〈n4〉 × 10−3 184.4± 0.4± 8.6 260.7± 0.5± 11.1

D =√

〈(n − 〈n〉)2〉 5.769± 0.007± 0.071 6.111± 0.007± 0.071

S = 〈(n − 〈n〉)3〉/D3 0.613± 0.005± 0.014 0.617± 0.005± 0.012

K = 〈(n − 〈n〉)4〉/D4 − 3 0.54± 0.02± 0.06 0.53± 0.02± 0.05

〈n〉/D 3.133± 0.003± 0.020 3.252± 0.003± 0.020

F2 = 〈n(n − 1)〉/〈n〉2 1.0464± 0.0002± 0.0045 1.0441± 0.0002± 0.0038

b-quark events

〈n〉 20.51± 0.02± 0.19 22.45± 0.03± 0.19

〈n2〉 453.9± 1.1± 1.8 542.0± 1.2± 3.0

〈n3〉 × 10−2 107.9± 0.4± 0.7 140.1± 0.5± 1.1

〈n4〉 × 10−3 273.9± 1.5± 1.9 385.8± 1.9± 1.7

D =√

〈(n − 〈n〉)2〉 5.78± 0.01± 0.07 6.16± 0.01± 0.07

S = 〈(n − 〈n〉)3〉/D3 0.574± 0.017± 0.008 0.573± 0.017± 0.007

K = 〈(n − 〈n〉)4〉/D4 − 3 0.43± 0.04± 0.04 0.42± 0.04± 0.03

〈n〉/D 3.551± 0.006± 0.055 3.645± 0.005± 0.049

F2 = 〈n(n − 1)〉/〈n〉2 1.0305± 0.0003± 0.0027 1.0307± 0.0002± 0.0023

,19]

e

ges-w-

ean

le

nd

d-

s,

is consistent with our previous measurements [18and about 0.6 below the world average (21.07± 0.11)[17]. The difference in mean multiplicity between thcases of including or not the K0S and decay prod-ucts is consistent with our measurement of the K0 and production rates [20] and with the world avera[17]. All the moments, with the exception of the dipersion,D, show significant flavor dependence. Hoever, the flavor dependence ofF2 is quite small.F2 isalso quite insensitive to the inclusion or not of K0

S and decay products. The difference between the m

charged-particle multiplicity of the b-quark sampand that of the udsc-quark sample is 2.58±0.03±0.08when K0

S and decay products are included a2.43± 0.03± 0.08 otherwise.

3.2. Hq

TheHq are calculated from the unfolded chargeparticle multiplicity distributions. Since theHq aresensitive to low statistics at very high multiplicitiewe truncate the multiplicity distribution. TheHq thus


s of (a),
Fig. 3. TheHq of the truncated (a), (b) and non-truncated (c), (d) charged-particle multiplicity distribution compared to the expectation(c) JETSET and (b), (d) HERWIG. The error bars include both statistical and systematic uncertainties.
geres,d-

un-a-

f thein-ceslla-

, for%the

-ot.bu-the

c-ts,at

r-eened

thontethe

obtained are biased estimators of theHq of the untrun-cated distribution. This bias increases with strontruncation, while the statistical uncertainty decreaswhich allows a more significant comparison with moels. It was suggested [21] that even without this trcation, theHq may be biased since a natural trunction occurs as a consequence of the finiteness osample. The truncation can induce oscillations orcrease their size [21]. The truncation also introducorrelations between theHq , although these are smafor low q [10,21,22]. We choose the point of trunction such that multiplicities with relative error onP(n)

greater than 50% are rejected. This correspondsall multiplicity distributions studied, to about 0.005of events. For all three samples (full, udsc, and b)

truncation is at 53 if K0S and decay products are included in the multiplicity and at 49 when they are nThe Hq presented here are calculated from distritions not including these decay products. However,Hq are insensitive to their inclusion [10].

TheHq of the truncated charged-particle multipliity distribution from all, udsc- and b-quark evenshown in Fig. 3, have a first negative minimumq = 5 and quasi-oscillations for largerq . They are verysimilar for the three samples, with only slight diffeences for the b-quark sample. Similar behavior is sfor JETSET (Fig. 3(c)). Oscillations are also observfor HERWIG (Fig. 3(d)), but they do not agree withose seen in the data. For both data and the MCarlo models, truncation at a lower value increases


m

hethe

i-

ity

essilla-at

ET.

ts,

ofrgee.

ethe0s ofblish

ffor

a--er-teddo,ed

at, by

ib-

-db-se-

s.

in,

7.

Fig. 4. 1-standard deviation bands of expectedHq of thenon-truncated charged-particle multiplicity distribution froPYTHIA for sample sizes of 105, 106 and 107. The insert showsthe meanHq of 100 samples of 105, 106 and 107 PYTHIA events.

depth of the first minimum and the amplitudes of toscillations, while truncation at a larger value hasopposite effect.

We note that ourHq , based on an order of magntude greater statistics, agree with theHq of SLD if wetruncate at a value equal to the maximum multiplicthey observed [5].

No truncation, other than that due to the finitenof the sample, reduces the amplitudes of the osctions to statistical insignificance, but the minimumq = 5 remains, as is shown in Fig. 3. Again, JETSagrees well with the data, while HERWIG does not

To investigate the effect of sample size on theHq ,100 samples of PYTHIA [23] Monte Carlo evenwere generated for sample sizes of 105, 106 and 107

events, and theirHq determined. Their±1 standarddeviation bands are shown in Fig. 4. In the insertFig. 4 the mean of the values is shown. For laq the values of theHq depend on the sample sizHowever, for smallq the values of theHq are stable.In particular,H5 (the first minimum) changes littlwith the sample size, giving us confidence thatmeasuredH5 is robust. Fig. 4 suggests that at least 17

events, an order of magnitude beyond the statisticthe present experiment, would be needed to estathe maximum atq = 8.

4. Conclusions

The charged particle multiplicity distribution ohadronic Z decay and its moments are measuredlight-quark and for b-quark, as well as for all flvor events. TheHq moments of truncated multiplicity distributions, which have smaller statistical unctainties than those of the full distributions, are plotversus the rankq . A negative minimum is observeat q = 5 followed by quasi-oscillations about zerwhich is qualitatively similar to the behavior expectin NNLLA for the Hq moments of the full multiplic-ity distribution. Since Monte Carlo studies show ththese oscillations are magnified, or even createdtruncation of the multiplicity distribution, theHq arealso measured for the untruncated multiplicity distrution. In this case the minimum atq = 5, expected inboth MLLA and NNLLA, is confirmed. But the oscillations at higher values ofq , which are expecteonly in NNLLA, cannot be confirmed. Previous oservations of these oscillations are most likely a conquence of truncation resulting from limited statistic

Acknowledgements

We have benefited from discussions with I. DremW. Ochs, A. Giovannini and R. Ugoccioni.

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[8] I.M. Dremin, Phys. Lett. B 313 (1993) 209;I.M. Dremin, V.A. Nechitaılo, JETP Lett. 58 (1993) 881;I.M. Dremin, R.C. Hwa, Phys. Rev. D 49 (1994) 5805.

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b

riationspowerfulned data.plane ofadoptednces are



Variations on KamLAND: likelihood analysis andfrequentist confidence regions

Thomas Schwetz

Institut für Theoretische Physik, Physik Department, Technische Universität München, James-Franck-Strasse,D-85748 Garching, Germany

Received 7 August 2003; received in revised form 29 September 2003; accepted 8 October 2003

Editor: G.F. Giudice

Abstract

In this Letter the robustness of the first results from the KamLAND reactor neutrino experiment with respect to vain the statistical analysis is considered. It is shown that an event-by-event based likelihood analysis provides a moretool to extract information from the currently available data sample than a least-squares method based on energy binFurthermore, a frequentist analysis of KamLAND data is performed. Confidence regions with correct coverage in thethe oscillation parameters are calculated by means of a Monte Carlo simulation. I find that the results of the usuallyχ2-cut approximation are in reasonable agreement with the exact confidence regions, however, quantitative differedetected. Finally, although the current data is consistent with an energy independent flux suppression, a∼ 2σ indication infavour of oscillations can be stated, implying quantum mechanical interference over distances of the order of 200 km. 2003 Elsevier B.V. All rights reserved.

Keywords: KamLAND reactor neutrino experiment; Neutrino oscillations

c-ntear-theb-,elay

see

datatrinoerlysissededdata.to

lla-ur-fewap-

1. Introduction

The outstanding results from the KamLAND reator neutrino experiment [1] have lead to a significaprogress in neutrino physics. The observed disappance of reactor anti-neutrinos is in agreement withso-called LMA solution of the solar neutrino prolem [2]. Alternative oscillation solutions like LOWVAC or SMA are ruled out with very high confidenclevel [3–12], and non-oscillation mechanisms can p

E-mail address: [email protected] (T. Schwetz).


only a sub-leading role (for a review and referencesRef. [13]).

These important conclusions are based on asample consisting of 54 events above the geo-neuthreshold in KamLAND. The purpose of this Lettis to discuss issues related to the statistical anaof these data. In Section 2 an event-by-event balikelihood analysis is compared to the widely usleast-squares method based on energy binnedIt is shown that the likelihood method allows oneextract more precise information about the oscition parameters from KamLAND data. Since the crently available data sample consists only of ratherevents, one might ask the question whether the

.


T. Schwetz / Physics Letters B 577 (2003) 120–128 121

uales-nceto

4].byntple

me-cil-nd

ofIn

antal.eo-pt54

Alledngthe

aseds

tionthisrgy

in.

plestic,[17,

[15].

otcest-

be

nptergy

sss

mmomheverto

le 3

tory

proximate confidence regions obtained from the usχ2-cut method are reliable. In Section 3 this qution is addressed by calculating frequentist confideregions for the oscillation parameters accordingthe prescription given by Feldman and Cousins [1The explicit construction of the confidence regionsMonte Carlo simulation takes properly into accoustatistical fluctuations of the rather small data samand the non-linear character of the oscillation paraters. In Section 4 the statistical significance of an oslatory signal in the KamLAND data is discussed, aI conclude in Section 5.

2. Comparing likelihood and least-squaresmethods

The current KamLAND data sample consists86 anti-neutrino events in the full energy range.the lower part of the spectrum there is a relevcontribution from geo-neutrino events to the signTo avoid large uncertainties associated with the gneutrino flux an energy cut at 2.6 MeV promenergy is applied for the oscillation analysis, andanti-neutrino events remain in the final sample.analyses of KamLAND data [3–12,15,16] performso far outside the KamLAND Collaboration are usithese data binned into 13 energy intervals abovegeo-neutrino cut, as given in Fig. 5 of Ref. [1].1 InSubsection 2.1 I describe an alternative analysis bon the likelihood function of the data, which allowone to take into account the precise energy informacontained in each single event. The results ofanalysis are compared to the ones from the enebinned least-squares method in Subsection 2.2.

Before exact confidence regions are calculatedSection 3 the usualχ2-cut approximation will be usedOne constructs a statisticX2(sin2 2θ,m2) fromthe data. Under certain assumptions, like large samlimit and linear parameter dependence, this statiwill be distributed as aχ2 with 2 degrees of freedomindependent of the point in the parameter space18]. Then a given point(sin2 2θ,m2) is contained in

1 For an analysis including the geo-neutrino events see Ref.

the allowed region atβ CL if

X2(sin2 2θ,m2) χ2β(2), where

(1)

χ2β (n)∫

0

fχ2(x,n)dx = β.

Here fχ2(x,n) denotes theχ2-distribution with ndegrees of freedom. In the following I will refer tthis procedure as “χ2-cut method”. In this section iwill be applied to calculate approximate confidenregions by using the likelihood as well as the leasquares method.

2.1. Likelihood analysis of KamLAND data

For given oscillation parameters sin2 2θ andm2

the predicted event spectrum in KamLAND cancalculated by

f(Epr;sin2 2θ,m2)

=N∞∫

0

dEν σ(Eν)

(2)

×∑j

φj (Eν)Pj(Eν,sin2 2θ,m2)R(Epr,E

′pr).

Here R(Epr,E′pr) is the energy resolution functio

and Epr,E′pr are the observed and the true prom

energies, respectively, and we use a Gaussian enresolution of 7.5%/

√Epr(MeV) [1]. The neutrino

energy is related to the true prompt energy byEν =E′

pr + ∆ − me, where∆ is the neutron–proton masdifference andme is the positron mass. The crosectionσ(Eν) for the detection processνe + p →e+ + n is taken from Ref. [19]. The neutrino spectruφ(Eν) from nuclear reactors is well known. I ausing the phenomenological parameterisation frRef. [20] and the average fuel composition for tnuclear reactors as given in Ref. [1]. The sum oj in Eq. (2) runs over 16 nuclear plants, taking inaccount the different distances from the detectorLjand the power output of each reactor (see Tabof Ref. [21]). Finally, Pj (Eν,sin2 2θ,m2) is thesurvival probability for neutrinos emitted at the reacj , depending on the distanceLj , the neutrino energ

122 T. Schwetz / Physics Letters B 577 (2003) 120–128

Table 1Prompt energies of the 86 anti-neutrino events in KamLAND

i Eipr [MeV] i Eipr [MeV] i Eipr [MeV] i Eipr [MeV]

1 0.906 23 2.151 45 3.243 67 4.2842 0.978 24 2.280 46 3.328 68 4.3223 1.035 25 2.294 47 3.345 69 4.3534 1.089 26 2.314 48 3.382 70 4.4145 1.198 27 2.524 49 3.416 71 4.4206 1.205 28 2.531 50 3.437 72 4.4557 1.208 29 2.534 51 3.460 73 4.5778 1.262 30 2.565 52 3.484 74 4.6109 1.313 31 2.568 53 3.504 75 4.675

10 1.340 32 2.595 54 3.650 76 4.72611 1.378 33 2.636 55 3.671 77 4.80412 1.408 34 2.721 56 3.671 78 4.99713 1.524 35 2.782 57 3.718 79 5.02114 1.639 36 2.843 58 3.735 80 5.15015 1.683 37 2.850 59 3.864 81 5.16016 1.703 38 2.982 60 3.881 82 5.26917 1.748 39 2.982 61 3.915 83 5.28918 1.812 40 3.040 62 3.969 84 5.48219 1.832 41 3.060 63 4.115 85 5.68920 1.985 41 3.162 64 4.142 86 5.70621 2.029 43 3.226 65 4.26122 2.100 44 3.240 66 4.268

ono

to

b-

y

d in]

ove

pe

edthe

and the two-flavour oscillation parameters sin2 2θ andm2.

The total number of events predicted for oscillatiparameters sin2 2θ andm2 above the geo-neutrincutEcut = 2.6 MeV is given by

Npred(sin2 2θ,m2)

(3)=∞∫

Ecut

dEprf(Epr;sin2 2θ,m2).

The over-all constantN in Eq. (2) is determined bynormalising the number of events for no oscillationsNpred(sin2 2θ = 0,m2 = 0) = 86.8 [1]. The proba-bility distribution of the expected events, i.e., the proability to obtain an event with the prompt energyEprin the interval[Epr,Epr + dEpr], can be obtained bnormalising the spectrum given in Eq. (2):

(4)p(Epr; sin2 2θ,m2) = f (Epr; sin2 2θ,m2)

Npred(sin2 2θ,m2).

The prompt energies of the 86 events observeKamLAND can be extracted from Fig. 3 of Ref. [1and are listed in Table 1. Using the 54 events abthe geo-neutrino cut withEipr > Ecut one obtains

the likelihood function containing the spectral shainformation of the data:

(5)

Lshape(sin2 2θ,m2) =

86∏i=33

p(Eipr;sin2 2θ,m2).

To take into account also the information impliby the total number of observed events I applymodified likelihood method (see, e.g., Ref. [17]):

Ltot(sin2 2θ,m2)

(6)= Lshape(sin2 2θ,m2)Lrate

(sin2 2θ,m2)

with2

Lrate(sin2 2θ,m2)

= 1√2π σrate

(7)

× exp

[−1

2

(Npred(sin2 2θ,m2)−Nobs

σrate

)2].

2 In general a Poisson distribution has to be used forLrate.However, for a mean of orderNobs= 54 the Poisson distributionis very well approximated by the Gaussian distribution.


nd

fce o

e

ento-

ans

g toare

thenesastar,es,

the

anyata

fe

tistic8]:

entof

pthas

cal

onss

iand in

ing

n byodr toased

HereNobs= 54 is the observed number of events, a

σ 2rate

(sin2 2θ,m2)

=Npred(sin2 2θ,m2)

(8)+ σ 2systN

2pred

(sin2 2θ,m2),

with the systematical errorσsyst = 6.42% [1]. Notethat we deriveσrate from the predicted number oevents, which introduces the parameter dependenσrate.

By maximising the likelihood function Eq. (6) thbest fit parametersm2 = 7.05 × 10−5 eV2 andsin2 2θ = 0.98 are obtained, in very good agreemwith the values obtained by the KamLAND Collabration:m2 = 6.9× 10−5 eV2 and sin2 2θ = 1 [1]. Tocalculate allowed regions for the parameters by meof theχ2-cut method one defines [17,18]

X2(sin2 2θ,m2)(9)= 2 lnLtot,max− 2 lnLtot

(sin2 2θ,m2),

where Ltot,max is the maximum of the likelihoodfunction with respect to sin2 2θ andm2. The 95%confidence regions obtained from Eq. (9) accordinEq. (1) are shown in Fig. 1. One finds that they

Fig. 1. Comparison of the 95% CL regions obtained fromlikelihood and the least-squares methods (lines) with the opublished by the KamLAND Collaboration [1] (regions labeled“Rate+ Shape allowed”). The best fit points are marked by a striangle, dot for the likelihood, least-squares, KamLAND analysrespectively.

f

in excellent agreement with the ones published byKamLAND Collaboration.

2.2. Least-squares analysis of KamLAND data

The least-squares analyses performed by mauthors [3–12] are based on the KamLAND dbinned into 13 energy intervals,Ni

obs, i = 1, . . . ,13,as given in Fig. 5 of Ref. [1].3 Since the number oevents in the individual bins is rather small (in sombins even zero) the use of a least-squares stabased on the Poisson distribution is appropriate [1

X2(sin2 2θ,m2)

= 2∑i

αNi

pred−Niobs+Ni

obslnNi

obs

αNipred

(10)+(

1− α

σsyst

)2

,

where the term containing the logarithm is absin bins with no events. The predicted numbereventsNi

pred(sin2 2θ,m2) in bin i is obtained byintegrating the spectrum Eq. (2) over the promenergy interval corresponding to that bin. Eq. (10)to be minimised with respect toα in order to takeinto account the overall uncertainty of the theoretipredictionsσsyst = 6.42% [1]. Although the “least-squares” character of the statisticX2 in Eq. (10) isnot explicitly visible due to the use of the Poissdistribution it is denoted here by this term to strethe analogy to the commonly used “χ2-function”.A comparison of KamLAND analyses using Gaussand Poisson least-squares functions can be founRef. [3].

The best fit parameters obtained by minimisEq. (10) arem2 = 7.24× 10−5 eV2 and sin2 2θ =0.90. Assuming that

(11)

X2(sin2 2θ,m2) =X2(sin2 2θ,m2) −X2min

3 In Ref. [16] a different likelihood analysis of KamLANDdata has been presented, including a goodness of fit evaluatioMonte Carlo methods. Note however, that in Ref. [16] the likelihofunction is also calculated from the energy binned data similathe least-squares method, in contrast to the event-by-event blikelihood discussed in the present work.


mon-

heareod

D4].heodact-

be-sincho-resod.

ail-es-cal-n 2the

r,

torc-nedn-s Iere. Ton

oodeticra-rstpleis-

-ehod

-a

evi-

an

asteyn

the

ntatl

s. 2ods,are

thend,

theCLnfi-sthe

ionslev-atnfi-sti-

e

follows a χ2-distribution with 2 degrees of freedoapproximate confidence regions are obtained by csidering contours of constantX2 according to theχ2-cut method in Eq. (1). From Fig. 1 we find that t95% confidence regions obtained by this methodsignificantly larger than the ones from the likelihoanalysis and the regions published by the KamLANCollaboration. This fact was already noted in Ref. [I conclude that the loss of information implied by tbinning of the data is not negligible, and the likelihoanalysis provides a more powerful method to extrinformation from the current KamLAND data sample. Note, however, that in future the differencestween the two methods are expected to decrease,if more data is available a smaller bin size can be csen, and in the limit of zero bin width the least-squamethod converges to the unbinned likelihood meth

3. Confidence regions with correct coverage

Since the number of events in the currently avable KamLAND data sample is rather small the qution arises, whether the standard procedures toculate confidence regions as described in Sectioare reliable. Especially the assumption concerningdistribution ofX2 might be not justified. Moreovethe parameters of interest,m2 and sin2 2θ , enter theproblem in a highly non-linear way, which leadsmultiple local maxima of the likelihood function (olocal minima of theX2-statistic). In such a case the atual confidence level of the parameter regions obtaifrom Eq. (1) may differ significantly from the canoical valueβ . To check the robustness of the resulthave calculated frequentist confidence regions, whthe correct coverage is guaranteed by constructionthis aim I follow the prescription given by Feldmaand Cousins in Ref. [14].

For both approaches discussed above—likelihas well as least-squares methods—many synthdata sets are simulated for fixed oscillation pameters. In the case of the likelihood method fithe number of events in the synthetic data samNsim(sin2 2θ,m2) is generated from a Gaussian dtribution with meanNpred(sin2 2θ,m2) and standarddeviationσrate given in Eq. (8). Then the prompt energies of theNsim events is thrown according to thdistribution Eq. (4). To test the least-squares met

e

a valueαsim for the parameterα describing the normalisation uncertainty in Eq. (10) is generated fromGaussian distribution with mean 1 and standard dationσsyst. Then the number of events in each bini issimulated from a Poisson distribution with the meαsimN

ipred(sin2 2θ,m2).

Each “data set” generated this way is analyseddescribed in Section 2 in order to calculaX2(sin2 2θ,m2). For each point on a sufficientldense grid in the(sin2 2θ,m2) plane this has beedone 104 times for the likelihood method and 105

times for the least-squares method to map outactual distribution ofX2 in that point:psim(X

2;sin2 2θ,m2). Then, in analogy to Eq. (1), the poi(sin2 2θ,m2) is included in the confidence regionβ CL if X2

data(sin2 2θ,m2) obtained from the readata is smaller than the one of 100β% of the simulateddata sets in that point in the parameter space:

X2data

(sin2 2θ,m2) X2

β, where

(12)

X2β∫

0

psim(x;sin2 2θ,m2)dx = β.

The results of these analyses are shown in Figand 3 for the likelihood and the least-squares methrespectively. The regions with correct coveragecompared to the ones obtained by theχ2-cut approx-imation. In both cases reasonable agreement ofexact and approximate confidence regions is foualthough quantitative differences are visible. Forlikelihood method the regions at 99.73% and 99%are in excellent agreement, whereas for lower codence levels theχ2-cut approximation gives regionsomewhat smaller than the exact ones. Especiallyregion 10−5 eV2 m2 4× 10−5 eV2 does not ap-pear at 90% CL for theχ2-cut approximation. In thecase of the least-squares method the 95% CL regare in excellent agreement. For higher confidenceels theχ2-cut approximation gives regions somewhlarger than the exact ones, whereas for lower codence levels the allowed regions are a bit underemated. E.g., the regionm2 2 × 10−4 eV2 doesnot appear at 68.3% CL for theχ2-cut approxima-tion. In general theχ2-cut approximation works quitwell in the vicinity of the best fit point aroundm2 ≈7× 10−5 eV2.


d

d

Fig. 2. Comparison of confidence regions with correct coverage (lines) with the regions obtained from theχ2-cut approximation (shaderegions) for the likelihood method.

Fig. 3. Comparison of confidence regions with correct coverage (lines) with the regions obtained from theχ2-cut approximation (shaderegions) for the least-squares method.

ob-

rs.-s ofer-

ast-

on-

se

them

ood

ll,

A better understanding of these results can betained by considering howX2

β defined in Eq. (12)varies as a function of the oscillation parameteNote that this quantity doesnot depend on the actually observed data; it characterises the propertiethe statistical method applied to the specific expimental setup. For definiteness I consider the lesquares method,4 for which contours of constantX2

β

4 Similar behaviour is also found for the likelihood method.

are shown in Fig. 4 for 68.3% and 95% CL. In theleft panel of that figure one can see that the ctour for X2

0.95 = 5.99, which corresponds to theχ2-distribution for 95% CL, happens to be rather cloto the 95% CL region from theχ2-cut approxima-tion. This explains the good agreement observed inmiddle panel of Fig. 3. Furthermore, one finds froFig. 4 thatX2

β decreases for small values of sin2 2θ and

m2. The reason for this behaviour can be understas follows: if sin2 2θ becomes 0.2 and/orm2 10−5 eV2 the effect of oscillations gets very sma


e

ulde

toromlso

ex-

ato-os-

bil-ee-

t ishodter

of

e-re oftlya-lo-

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s,thats,ex-fite in

2rom

ns.nceact

ecttheicalhethe

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ay

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os-teseu-ifi-

Fig. 4. Contours of constantX2β as defined in Eq. (12) for th

least-squares method forβ = 0.95 (left panel) andβ = 0.683(right panel). The thick lines correspond to the values which woresult from aχ2-distribution with 2 degrees of freedom. Thshaded regions are the approximate allowed regions from theχ2-cutmethod.

and the signal in KamLAND corresponds roughlythe no-oscillation case. Analysing data generated fparameters in that region leads to best fit points ain the no-oscillation region, with a rather similarX2.Hence, the distribution ofX2 is more peaked at lowvalues, which implies relatively small values ofX2

β .This explains the tendency of more constrainingact confidence regions for small values of sin2 2θ andm2. The physical reason for this behaviour is theven with the present KamLAND data sample ndisappearance can be very well distinguished fromcillations with sin2 2θ 0.2 andm2 10−5 eV2.Moreover, in the region of small sin2 2θ or m2 thefull 2-parameter dependence of the survival probaity is lost, and the effective number of degrees of frdom is reduced, leading to smaller values ofX2

β . Thereason why for the likelihood method the agreemenbetter for higher CL than for the least-squares metcan be partially attributed to the fact that for the latthe approximate regions extend to smaller valuessin2 2θ , which implies smaller values ofX2

β and larger

disagreement with theχ2-approximation.In contrast, for sin2 2θ 0.4 andm2 10−5 eV2

the simulation yields relatively higher values ofX2β .

In that region oscillations are important. However, bcause of the rather small data sample the signatugiven parameters cannot be identified with sufficienhigh significance. This implies that statistical fluctutions can lead easily to best fit points in a different

cal minimum. In other words, when data are generaby given parameters in that region, fluctuations cmimic a signal which is better fitted by quite diffeent parameters. Hence, the best fit points are stroaffected by fluctuations, resulting into a broader disbution ofX2 and larger values ofX2

β . From Fig. 4one observes that the approximate confidence regat 68.3% CL are well inside the highX2

β regime. Thisexplains the weaker constraints from exact allowedgions for low confidence levels in Fig. 3. Note, hoever, that in the region aroundm2 ∼ 7 × 10−5 eV2,where KamLAND is most sensitive to oscillationtheX2

β values decrease again. This shows that inregion KamLAND can well identify the parameterleading already to statistical properties close to thepectedχ2-distribution. Therefore, around the bestpoint exact and approximate confidence regions argood agreement.

The main conclusion to be drawn from Figs.and 3 is that already using the current 54 events fKamLAND the approximateχ2-cut method givesa rather reliable determination of allowed regioThe small quantitative differences to exact confideregions can be understood by considering the impof statistical fluctuations on the fit. One may expthat once more data will have been collecteddifferences will further decrease, because statistfluctuations will be less important. Furthermore, if ttrue oscillation parameters happen to be close topresent best fit region aroundm2 ∼ 7 × 10−5 eV2

and large sin2 2θ a rather clear oscillation signal cabe observed in KamLAND. In that case the impactother local minima will become small and one mexpect thatX2 will follow a distribution rather closeto theχ2-distribution.

4. Have we already observed oscillations inKamLAND?

Because of the limited statistics of the current KaLAND data sample the data is consistent with anergy independent suppression of the reactor neutflux [1]. This is evident, since allowed regions appefor largem2, corresponding to energy averagedcillations. However, even this first data set indicasome spectral distortion which is consistent with ntrino oscillations. In this section the statistical sign


g aoba-ae-lla-

aical

reaergy

the

od.d.

eli-ec-he

av-tion13)tum

at

or-

pa-nifi--ur-m-

fed

il-

orx-ent-oreothodhodon-a-

en-aveionhishelueata

f theromf

solutewithwithCL.

Fig. 5.X2 as a function of the decoherence parameterζ for thelikelihood and the least-squares method.

cance for an oscillatory signal is quantified by usinso-called decoherence parameter. The survival prbility for the electron anti-neutrinos is modified (inrather arbitrary way) by multiplying the quantum mchanical interference term which leads to the oscitory behaviour by a factor(1− ζ ):

(13)P = 1− 1

2sin2 2θ

[1− (1− ζ )cos

m2L

2Eν

].

Restrictingζ to the interval[0,1] one can describe inmodel independent way a loss of quantum mechancoherence due to some unspecified mechanism.ζ = 0corresponds to standard quantum mechanics, wheζ = 1 describes complete decoherence, i.e., an enand baseline independent suppression of the flux.5

Now the data is analysed as a function ofthree parametersm2,sin2 2θ andζ . TheX2 mar-ginalised with respect tom2 and sin2 2θ is shown inFig. 5 for the likelihood and the least-squares methA clear indication in favour of oscillations is observeComplete decoherence is disfavoured withX2 = 4.4using the likelihood method andX2 = 3.2 by theleast-squares method. This confirms that the likhood method is a more powerful tool to extract sptral information from the data, in agreement with t

5 Decoherence might have its origin, e.g., in quantum grity [22]. See also Ref. [23] and references therein, for an applicato atmospheric neutrino oscillations. A method similar to Eq. (has been used in Ref. [24] to investigate the evidence for quanmechanical interference in theB0B 0 andK0 K 0 systems.

s

results of Section 2. Assuming thatX2(ζ ) is distrib-uted as aχ2 with 1 degree of freedom I conclude ththe current KamLAND data provides a∼ 2σ indica-tion in favour of neutrino oscillations,6 implying quan-tum mechanical interference over distances of theder of 200 km.

Depending on the true values of the oscillationrameters one may expect that the statistical sigcance for oscillations in KamLAND will strongly improve by future data. A simple rescaling of the crent data by a factor 5 leads to an exclusion of coplete decoherence at 3.7σ if the true value ofm2

turns out to be 7× 10−5 eV2. On the other hand im2 = 1.5× 10−4 eV2 decoherence can be excludonly at 2.6σ , since for largem2 the baselines inKamLAND are too long to be sensitive to the osclations.

5. Conclusions

In this Letter two different analysis methods fthe first data from the KamLAND reactor neutrino eperiment have been compared. I found that an evby-event based likelihood method provides a mpowerful tool to extract information on two-neutrinoscillation parameters than a least-squares mebased on energy binned data. The likelihood mettakes into account the precise energy information ctained in each single event and avoids the informtion loss due to binning. Furthermore, exact frequtist confidence regions in the parameter space hbeen calculated by means of Monte Carlo simulataccording to the Feldman–Cousins method [14]. Tmethod properly accounts for the non-linearity of toscillation parameters sin2 2θ andm2, and statisticafluctuations in the data, which can be quite large dto the rather small number of events in the current dsample. I have found a reasonable agreement oexact confidence regions with the ones obtained ftheχ2-cut approximation, especially in the vicinity othe best point atm2 ≈ 7 × 10−5 eV2. However, de-

6 Note that here arelative comparison of the fits for oscillationand decoherence is performed; no statement about the absquality of the fit is made. Hence, these results are in agreementRef. [1], where the observed spectrum is found to be consistentan oscillation signal at 93% CL but with flat suppression at 53%


st-iallyfit

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pending on the analysis method (likelihood or leasquares) quantitative differences are visible, especfor lower confidence levels and far from the bestpoint. Finally, although the current data is consistwith an energy independent flux suppression, a∼ 2σindication in favour of oscillations can be stated usthe likelihood method, which is especially sensitivethe spectral shape information. Put in other words,implies a∼ 2σ evidence for quantum mechanical iterference over distances of the order of 200 km.

In summary, the results obtained in this work cofirm that even for the limited statistics of the curreKamLAND data sample theχ2-cut approximation tocalculate confidence regions for the oscillation pameters gives rather reliable results. One expects thfuture the agreement between approximate and econfidence regions will improve due to increase in stistics. Moreover, the differences between likelihoand least-squares methods will become smaller.

Acknowledgements

I thank M. Maltoni and J.W.F. Valle for collaboration on the KamLAND analysis. Furthermore, I woulike to thank M. Lindner, P. Huber and T. Lassefor very useful discussions. This work is supporby the “Sonderforschungsbereich 375-95 für AstTeilchenphysik” der Deutschen Forschungsgemschaft.

References

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[2] SNO Collaboration, Q.R. Ahmad, et al., Phys. Rev. Lett.(2001) 071301;SNO Collaboration, Q.R. Ahmad, et al., Phys. Rev. Lett.(2002) 011301;Super-Kamiokande Collaboration, S. Fukuda, et al., Phys. LB 539 (2002) 179;B.T. Cleveland, et al., Astrophys. J. 496 (1998) 505;J.N. Abdurashitov, et al., J. Exp. Theor. Phys. 95 (2002) 18GALLEX Collaboration, W. Hampel, et al., Phys. Lett. B 44(1999) 127;

t

GNO Collaboration, E. Bellotti, Nucl. Phys. B (ProSuppl.) 91 (2001) 44.

[3] M. Maltoni, T. Schwetz, J.W.F. Valle, Phys. Rev. D 67 (200093003, hep-ph/0212129.

[4] G.L. Fogli, et al., Phys. Rev. D 67 (2003) 073002, heph/0212127.

[5] J.N. Bahcall, M.C. Gonzalez-Garcia, C. Pena-GarJHEP 0302 (2003) 009, hep-ph/0212147.

[6] A. Bandyopadhyay, et al., Phys. Lett. B 559 (2003) 121, hph/0212146.

[7] P.C. de Holanda, A.Y. Smirnov, JCAP 0302 (2003) 001, hph/0212270.

[8] P. Creminelli, G. Signorelli, A. Strumia, hep-ph/0102234.[9] P. Aliani, V. Antonelli, M. Picariello, E. Torrente-Lujan, hep

ph/0212212.[10] V. Barger, D. Marfatia, Phys. Lett. B 555 (2003) 144, he

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B 562 (2003) 28, hep-ph/0212202.[12] A.B. Balantekin, H. Yuksel, J. Phys. G 29 (2003) 665, h

ph/0301072.[13] S. Pakvasa, J.W.F. Valle, hep-ph/0301061.[14] G.J. Feldman, R.D. Cousins, Phys. Rev. D 57 (1998) 38

physics/9711021.[15] G. Fiorentini, T. Lasserre, M. Lissia, B. Ricci, S. Schone

Phys. Lett. B 558 (2003) 15, hep-ph/0301042.[16] A. Ianni, hep-ph/0302230.[17] H. Cramér, Mathematical Methods of Statistics, Prince

Univ. Press, Princeton, NJ, 1946;A.G. Frodesen, O. Skjeggestad, H. Tofte, Probability aStatistics in Particle Physics, Universitatsforlaget, Berg1979.

[18] Particle Data Group, K. Hagiwara, et al., Phys. Rev. D(2002) 010001.

[19] P. Vogel, J.F. Beacom, Phys. Rev. D 60 (1999) 053003, hph/9903554.

[20] P. Vogel, J. Engel, Phys. Rev. D 39 (1989) 3378.[21] J. Busenitz, et al., Proposal for US participation in KamLAN

1999;J. Busenitz, et al., The KamLAND proposal, Stanford-HE98-03, 1999.

[22] J.R. Ellis, J.S. Hagelin, D.V. Nanopoulos, M. Srednicki, NuPhys. B 241 (1984) 381.

[23] E. Lisi, A. Marrone, D. Montanino, Phys. Rev. Lett. 85 (2001166, hep-ph/0002053;G.L. Fogli, E. Lisi, A. Marrone, D. Montanino, Phys. Rev. D 6(2003) 093006, hep-ph/0303064.

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b

l, inflectsh decays



Anomalous decay of pion and eta at finite density

P. Costaa, M.C. Ruivoa, Yu.L. Kalinovskyb

a Departamento de Física da Universidade de Coimbra, P-3004-516 Coimbra, Portugalb Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia


Editor: J.-P. Blaizot

Abstract

We study the anomalous decaysπ0, η → γ γ in the framework of the three-flavor Nambu–Jona-Lasinio [NJL] modethe vacuum and in quark matter inβ-equilibrium. It is found that the behavior of the relevant observables essentially rea manifestation of the partial restoration of chiral symmetry, in nonstrange and strange sectors. The probability of sucdecreases with density, showing that anomalous mesonic interactions are significantly affected by the medium. 2003 Published by Elsevier B.V.

PACS: 11.30.Rd; 11.55.Fv; 14.40.Aq

Keywords: NJL model; Pseudoscalar mesons; Strange quark matter; Finite density; Pion decay width; Eta decay width

assrestin-ori-s orr-

newoc-un

hey

by(Yu.

ther ofveig-tterm-

Dwithn-is

as aoflicit

thatit

byof

of

1. Introduction

The structure of pseudoscalar mesons, its mspectra and decays have attracted a lot of intealong the years, an important motivation for thisterest being certainly related to the fact that thegin of these mesons is related to the spontaneouexplicit breakdown of symmetries of QCD. Furthemore, since at high densities and temperaturesphases with restored symmetries are expected tocur, the study of pseudoscalar meson observablesder those conditions is specially relevant since t

Work supported by grant SFRH/BD/3296/2000 (P. Costa),grant RFBR 03-01-00657, Centro de Física Teórica and GTAEKalinovsky).

E-mail addresses: [email protected] (P. Costa),[email protected] (M.C. Ruivo), [email protected](Yu.L. Kalinovsky).


-

could provide signs for the phase transitions andassociated restoration of symmetries. As a mattefact, major theoretical and experimental efforts habeen dedicated to heavy-ion physics looking for snatures of the quark–gluon plasma, a state of mawith deconfinement of quarks and restoration of symetries [1–3].

In the limit of vanishing quark masses, the QCLagrangian has 8 Goldstone bosons, associatedthe dynamical breaking of chiral symmetry. The noexistence of a ninth Goldstone boson in QCDexplained by assuming that the QCD Lagrangian hUA(1) anomaly. The origin of the physical massesthe different pseudoscalar mesons is due to the expbreaking of symmetries, but it presents differenceswill be analyzed next. While for pions and kaonsis enough to break explicitly the chiral symmetrygiving current masses to the quarks, the breakingthe UA(1) symmetry by instantons has the effect


130 P. Costa et al. / Physics Letters B 577 (2003) 129–136

stherdeing

tectsagere,

ike”m

assthe

cayto

s inthe

gens

theass

odipicis-s

therac-

on-

nicsideher

ryper-ar,els

dein-

er-

iesnse

ark

sionlarthe25],r, it

iraln.saimaysinionWetherese

n-eter-l-

,

n-

bece-

giving a mass toη′ of about 1 GeV. So the masof η′ has a different origin than the masses ofother pseudoscalar mesons and it cannot be regaas the remnant of a Goldstone boson. Concernthe other two neutral mesons,η and π0, they aredegenerated when theUA(1) anomaly and the currenquark masses are turned off, but, when these effare taken into account it turns out that a percentof η mass is due to the anomaly, and, therefothis meson should regarded as less “Goldstone-lthan the pion. Investigating this problem in vacuuand in medium is an important task. Besides mspectrum and meson–quark coupling constants,observables associated with the two photon deof these mesons might provide useful insight inthis problem, and calculations of such observablevacuum and at finite temperature may be found inliterature [4–11].

Understanding the processesπ0(η) → γ γ is spe-cially relevant having in mind that the great percentaof photons in the background of heavy-ion collisiois due to the decay ofπ0 andη [12]. As a matter offact the production of such mesons is indicated byoccurrence of two photon pairs with an invariant mequal to these meson masses. Possible medium mfications of anomalous mesonic interactions is a tothat has attracted lost of interest. As pointed by Parski [7] and Pisarski and Tytgat [8] while for fermionthe axial anomaly is not affected by the medium,opposite is expected for anomalous mesonic intetions. In this concern, the study ofπ0 → γ γ is particu-larly interesting due to its simplicity and its associatiwith restoration of chiral symmetry. Although the lifetime of the neutral pion is much longer than hadrotime scales and it is not expected to be observed inthe fireball, the physics is the same as that of otanomalous decays (ω → πππ,ω → ρπ ) that are rel-evant for experiments in the hot/dense region.

A great deal of knowledge on chiral symmetbreaking and restoration, as well as on meson proties, comes from model calculations [13]. In particulthe Nambu–Jona–Lasinio [NJL] [14,15] type modhave been extensively used over the past years toscribe low energy features of hadrons and also tovestigate restoration of chiral symmetry with tempature or density [16–25].

This work comes in the sequel of previous studon the behavior of neutral mesons in hot and de

d

-

-

matter [23–25]. The study of phase transitions in qumatter simulating neutron matter inβ equilibrium, atzero and finite temperature, as well as the discusof behavior of pseudoscalar mesons (in particuneutral mesons) in such media, in connection withrestoration of symmetries, has been done in [23–by analyzing only the mass spectrum. In particulawas shown that the behavior of the masses ofπ0 andηin this concern reflects mainly the restoration of chSU(2) symmetry and manifests strongly in the pioThis not so evident for theη, due to its strangenescontent and the dependence of the anomaly. Theof this Letter is to investigate the anomalous decof π0 and η in the vacuum and in quark matterβ-equilibrium and discuss our results in connectwith the breaking and restoration of symmetries.also compare our results with those obtained by oauthors who studied the effect of temperature on thanomalous mesonic interactions [5–7,11].

2. Formalism

We consider the three-flavor NJL type model cotaining scalar–pseudoscalar interactions and a dminantal term, the ’t Hooft interaction, with the folowing Lagrangian:

L= q(iγ µ∂µ − m

)q

+ 1

2gS

8∑a=0

[(qλaq

)2 + (qiγ5λ

aq)2]

(1)+ gDdet

[q(1+ γ5)q

] + det[q(1− γ5)q

].

Hereq = (u, d, s) is the quark field with three flavorsNf = 3, and three colors,Nc = 3. m = diag(mu,md,

ms) is the current quark masses matrix andλa are theGell-Mann matrices,a = 0,1, . . . ,8, λ0 = √

2/3I.The last term in (1) is the lowest six-quark dime

sional operator and it has theSUL(3) ⊗ SUR(3) in-variance but breaks theUA(1) symmetry. This term isa reflection of the axial anomaly in QCD and canput in a form suitable to use the bosonization produre ([20,24] and references therein):

LD = 1

6gDDabc

(qλcq

)

(2)× [(

qλaq)(qλbq

) − 3(qiγ5λ

aq)(qiγ5λ

bq)]

P. Costa et al. / Physics Letters B 577 (2003) 129–136 131

d

tiven-

een

ral

lar

set

eansver

me-

t

d as

n-t

e-al

24,

-

avei-er-

ous

with constantsDabc = dabc if a, b, c ∈ 1,2, . . . ,8,where dabc are theSU(3) structure constants, anD000= √

2/3,D0ab = −√1/6δab.

The usual procedure to obtain a four quark effecinteraction from the six quark interaction is to cotract one bilinear(qλaq) making a shift(qλaq) →(qλaq) + 〈qλaq〉 with the vacuum expectation valu〈qλaq〉. Then, an effective Lagrangian can be writtas:

Leff = q(iγ µ∂µ − m)q + Sab[(qλaq

)(qλbq

)](3)+ Pab

[(qiγ5λ

aq)(qiγ5λ

bq)],

where

Sab = gSδab + gDDabc

⟨qλcq

⟩,

(4)Pab = gSδab − gDDabc

⟨qλcq

⟩.

Integration over quark fields in the functional integwith (3) gives the meson effective action

Weff = −i Tr ln(i∂µγµ − m+ σaλ

a + iγ5φaλa)

(5)− 1

2

(σaSab

−1σb + φa Pab−1φb

).

The fieldsσa andφa are the scalar and pseudoscameson nonets.

The first variation of the action (5) leads to theof gap equations for constituent quark massesMi :

(6)Mi =mi − 2gS〈qiqi〉 − 2gD〈qj qj 〉 < qkqk〉with i, j, k = u,d, s cyclic and 〈qiqi〉 = −i TrSi(p)are the quark condensates. Here the symbol Tr mtrace in color and Dirac spaces and integration omomentump with a cut-off parameterΛ to regu-larize the divergent integrals. The pseudoscalarson massesMH (H = π0, η) are obtained from thecondition(1 − PijΠ

ij (P0 = MH,P = 0)) = 0, whereΠij (P0 = MH,P = 0) is the polarization operator athe rest frame

Πij (P0)

(7)

= 4[(I i1 + I

j

1

) − (P 2

0 − (Mi −Mj)2)I ij2 (P0)

],

and integrals are given by

(8)I i1 = Nc

4π2

Λ∫0

p2

Ei

dp,

Iij

2 (P0)= Nc

4π2

Λ∫0

p2dp

EiEj

Ei +Ej

P 20 − (Ei +Ej)2

(9)+ i1

2π

p∗

(E∗i +E∗

j ),

whereEi,j =√p2 +M2

i,j andE∗i,j =

√(p∗)2 +M2

i,j

are the quark energies. The momentump∗ is defined

by p∗ =√(P 2

0 − (Mi −Mj)2)(P20 − (Mi +Mj)2)/

2P0.The quark–meson coupling constant is evaluate

(10)g−2Hqq = − 1

2MH

∂

∂P0

[Πij (P0)

]|P0=MH

,

where the bound state contains quark flavorsi, j .Having the on-shell quark–meson coupling co

stant we can calculate the meson decay constanfHaccording to the definition

fH =NcgHqqPµ

P 2

∫d4p

(2π)4

(11)× tr[(iγ5)Si(p)(γµγ5)Sj (p + P)

].

Our model parameters, the bare quark massesmd =mu,ms , the coupling constants and the cutoff in thremomentum space,Λ, are fitted to the experimentvalues of masses for pseudoscalar mesons (Mπ0 =135.0 MeV,MK = 497.7) andfπ = 92.4 MeV.

Here we use the following parameterization [21,25]: Λ = 602.3 MeV, gSΛ2 = 3.67,gDΛ5 = −12.39,mu =md = 5.5 MeV andms = 140.7 MeV.

We also haveMη = 514.8 MeV, θ(M2η) = −5.8,

gηuu = 2.29,gηss = −3.71.Note, thatθ(M2

η) is the mixing angle which repre

sents the mixing ofλ8 andλ0 components in theη-meson state (for details see [24,25]).

For the quark condensates we have:〈uu〉 = 〈dd〉 =−(241.9 MeV)3, 〈ss〉 = −(257.7 MeV)3, andMu =Md = 367.7 MeV, Ms = 549.5 MeV, for the con-stituent quark masses. In this section we hdescribed the NJL model with the ’t Hooft determnant. The model describes well the vacuum propties related with chiral symmetry and its spontanebreaking including their flavor dependence.


Fig. 1. The quark triangle diagram for theH → γ γ (direct and exchange process).

me-nd-

rtex,

rto

r of

est

als

lyralsenlar

3. The decay H → γ γ

For the description of the decaysH → γ γ we con-sider the triangle diagrams for the electromagneticson decays. They are shown in Fig. 1. The correspoing invariant amplitudes are given by

TH (P,q1, q2)

= i

∫d4p

(2π)4Tr

ΓHS(p − q1)ε1S(p)ε2S(p + q2)

(12)+ exchange.

Here the trace Tr= trc trf trγ , must be performed ovecolor, flavor and spinor indices. The meson verfunction ΓH has theiγ5 form in the Dirac spacecontains the corresponding coupling constantgHqq

(see (10)) and presents itself the 3× 3 matrix form inthe flavor space.S(p) is the quark propagatorS(p) =diag(Su, Sd , Ss), ε1,2 is the photon polarization vectowith momentumq1,2. The trace over flavors leadsdifferent factors for different mesonsH : QHqq . Thisfactor depends on the electric charges and flavoquarks into the mesonH : Qπ = 1/3, Qηu = 5/9 andQηs = −√

2/9.For this evaluation, we move to the meson r

frame and use the kinematicsP = q1 + q2 andP =(MH ,0). Taking the trace in (12) we can obtain

(13)TH (P,q1, q2)= εµναβε

µ1 ε

ν2q

α1 q

β2 TH

(P 2, q2

1, q22

),

where

(14)Tπ0

(P 2 =M2

π0, q21, q

22

) = 32απgπ0uuIuπ0

and

Tη(P 2 =M2

η , q21, q

22

)= 32απ

3√

3

[cosθ

(5gηuuIuη − 2gηssI sη

)(15)− sinθ

√2(5gηuuIuη + gηssI

sη

)],

whereα is the fine structure constant. The integrI iH ≡ I iH (P ) are given by

I iH (P ) = iMi

∫d4p

(2π)41

(p2 −M2i )

(16)

× 1

[(p − q1)2 −M2i ][(p + q2)2 −M2

i ].

In order to introduce finite density effects, we appthe Matsubara technique [6,26], and the integrelevant for our calculation ((8) and (9)) are thmodified in a standard way [23–25]. In particuI iH (P ) (16) takes the form:

I iH (P0,P = 0)

(17)= − Mi

4π2

∞∫λi

dpp

E2i

1

4E2i − P 2

0

ln

(Ei + p

Mi

),

whereλi is the Fermi momentum.Finally, the decay width is obtained from

(18)ΓH→γ γ = M3H

64π|TH→γ γ |2

and the decay coupling constant is

(19)gH→γ γ = TH→γ γ

e2.


we

lcu-

ndraltoere

.

tters is

Weim--lyand

the9,

ra-av-

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4. Discussion and conclusions

We present in Table 1 our results forTH→γ γ ,ΓH→γ γ andgHγγ (H = (π0, η)) in the vacuum, incomparison with experimental results [4,9,27], andcan see that there is a good agreement.

Some comments are in order concerning our calation of the integralI iH (P ) (17). The fermionic ac-tion of NJL model (5) has ultraviolet divergences arequires a regularizing cutoff. However, the integI iH (P ) (17) is not a divergent quantity. We choseregularize the action from the beginning, so that this no need to cut the integralI iH —only the ultravio-

let integralsI i1 (8) andI ij2 (9) are regularized [22]The advantages of usingΛ → ∞ in nondivergent in-tegrals was already shown in [5,6,22], where a beagreement with experiment of several observableobtained with this procedure.

Now let us discuss our results at finite density.consider here the case of asymmetric quark matterposing the condition ofβ equilibrium and charge neutrality through the following constraints, respectiveon the chemical potentials and densities of quarkselectrons:µd = µs = µu+µe and2

3ρu− 13(ρd +ρs)−

ρe = 0, with ρi = 1π2 (µ

2i − M2

i )3/2θ(µ2

i − M2i ) and

ρe = µ3e

3π2 [23–25].As discussed by several authors, this version of

NJL model exhibits a first order phase transition [123,28]. As shown in [28], by using a convenient pameterization [21] the model may be interpreted as hing a mixing phase—droplets of lightu,d quarks at acritical densityρc = 2.25ρ0 (whereρ0 = 0.17 fm−3

Table 1Comparison of the experimental values with numerical resobtained in the NJL model

NJL Exp.

π0 |Tπ0→γ γ | [eV]−1 2.5× 10−11 (2.5± 0.1) × 10−11

Γπ0→γ γ

[eV] 7.65 7.78(56)

gπ0γ γ [GeV]−1 0.273 0.274± 0.010

τπ0→γ γ

[s] 8.71× 10−17 8.57× 10−17

η |Tη→γ γ | [eV]−1 2.54× 10−11 (2.5± 0.06) × 10−11

Γη→γ γ [keV] 0.440 0.465

gηγγ [GeV]−1 0.278 0.260

τη→γ γ [s] 1.52× 10−18 1.43× 10−18

Fig. 2. Mesonic and quark masses (a) and meson–quark–qcoupling constant, (b) as function of the baryonic density.

is the nuclear matter density) surrounded by a ntrivial vacuum—and, above this density, a quark phwith partially restored chiral symmetry [23,28]. An interesting feature of quark matter in weak equilibriuis that at densities aboveρs ∼ 3.8ρ0 the mass of thestrange quark becomes lower than the chemical potial what implies the occurrence of strange quarksthis regime and this fact leads to meaningful effectsthe behavior of meson observables [23–25].

In order to evaluate the transition amplitudethe decayH → γ γ in function of the density, werequire the behavior ofMH and gHqq with density,that are plotted in Fig. 2(a) and (b), respectiveAs we will discuss in the sequel, this behavioressentially a manifestation of the partial restorationchiral symmetry. The difference between the behaat T = 0, ρ = 0 andT = 0, ρ = 0 is that, in the lascase the mesons are no more bound states abovcritical point since they dissociate inqq pairs at theMott temperature. At finite density they continuebe bound states but with a weaker coupling to


y

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cts

erntralnd

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rningity,the

thericales

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inghigh

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-

to aal

-t

heon

me.

s atuethe

eesr

Fig. 3. The decayπ0 → γ γ : (a) transition amplitude; (b) decawidth; (c) coupling constant.

quarks as it can be seen in Fig. 2(b). So, it is naturaexpect that the effect of density onH → γ γ decayobservables be qualitatively similar to the effectfinite temperature.

We discuss now our results for the medium effeon the two photon decay ofπ0: Tπ0→γ γ , Γπ0→γ γ

and gπ0γ γ that are plotted in Fig. 3(a)–(c). In ordto understand this results let us remember the cerole of this meson in connection with the breaking arestoration of chiral symmetry in theSU(2) sector.A sign for the restoration of this symmetry is ththe mass of the pion increases with density andmeson becomes degenerated withσ meson and thepion decay constantfπ goes asymptotically to zeroThe behavior ofπ0 → γ γ observables with density iclosely related with the restoration of chiral symmein the SU(2) sector. The fact thatTπ0→γ γ , as well as

gπ0→γ γ decrease with density reflects the fact thatMu

and gπ0qq decrease with density. As it can be sefrom Fig. 2, the quark mass decreases sharply wgπ0uu decreases more slowly. In the regionρ < ρcthe behavior of the transition amplitude is dictatby a compromise between the behavior of the mand the meson quark coupling. Aboveρc the massdecrease seems to be the dominant effect. ConceΓπ0→γ γ it has a maximum at about the critical denssince there are two competitive effects, on one sidedecrease of the transition amplitude and, on the oside, the increase of the pion mass. Above the critdensity the two photon decay of the pion becomless favorable, what reflects that it turns a weaboundqq pair, as already mentioned before. Thiscompatible with recent experimental results indicatthat pionic degrees of freedom are less relevant atdensities [29].

In order to clarify the connection between the bhavior of the anomalous couplings and the restoraof chiral symmetry one can do the simple exercisecalculating the transition amplitude in the chiral limby setting the external momenta equal to zero. Thsimilarly to [7,8], where such analysis was done w

temperature, we get|Tπ0→γ γ | ∝ Mu2

fπ

1λu

2 , the mass de

creases being the dominant effect, which leadsvanishing of the transition amplitude at the criticdensity.

Concerning theη → γ γ decay, although qualitatively similar toπ0 → γ γ , there are differences thawe will examine in detail and that are related to tevolution of the strange quark content of this mesand the behavior of the strange quark in this regiThe quark content ofη is given by

|η〉 = cosθ1√3|uu+ dd − 2ss〉

(20)− sinθ

√2

3|uu+ dd + ss〉.

It was show in [24] that the mixing angle (θ =−5.8 in the vacuum) decreases with density, haminimum ( −25) at ρ 2.8ρ0, equals to zero aρ 3.5ρ0, then it increases rapidly up to the val∼ 30, when strange valence quarks appear inmedium (ρ 3.8ρ0). gηss (Fig. 1(b)) reflects thisevolution of the strange quark content. So, one sthat at high densities theη is governed by the behavio


y

inn forlf inhectsy,cee

s

o-

s-of

dif-

nsi-es-atby

omed.w

ioncal

in-k of3)

allldra-

r-loust ofac-d.

2)

57

d23–

02;

7)

7)

6)

Fig. 4. The decayη → γ γ : (a) transition amplitude; (b) decawidth; (c) coupling constant.

of the strange quark mass. Since afterρ 3.8ρ0 thereis a tendency to the restoration of chiral symmetrythe strange sector, although less pronounced thenonstrange quarks, this effect should manifest itsethe behavior ofη observables. Therefore, although tη is less “Goldstone like” than the pion, one experesults qualitatively similar for the two photon decawhich are shown in Fig. 4(a)–(c). The main differenis that the widthΓη → γ γ almost vanishes abovρ = 3.8ρ0. This behavior of theη seems to indicatethat the role of theUA(1)anomaly for the mass of thimeson at high densities is less important.

In conclusion, we studied the behavior of two phton decay observables for the neutral mesonsπ0, andη in quark matter in weak equilibrium and we dicussed the results in connection with restorationsymmetries. We have shown that, in spite of the

ferent quark structure of these mesons, at high deties they share a behavior which is mainly a maniftation of restoration of chiral symmetry. We show ththese anomalous decays are significantly affectedthe medium, however the relevance of this results frthe experimental point of view should be discussRecent experimental results from PHENIX [29] shothatπ0 production is suppressed in the central regof Au + Au collisions as compared to the peripheriregion. This means thatπ0 → γ γ decay could only beinteresting for experimental heavy-ion collisions attermediate densities. However, although the peathe π0 width is at a moderate density (see Fig.its life time is here of the order of 2.08 × 10−17 s,much longer than the expected lifetime of the firebin the hadronic phase, 10−22 s, so the decay shouoccur outside of the fireball. The same considetions apply to theη, although its maximum lifetimeis 9.36× 10−19 s. However, since the physics undelying these processes is the same of other anomaprocesses interesting from the experimental poinview, the modification of anomalous mesonic intertions by the medium might, in principle, be observe

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b

structuren the onlyphysical

quantumis BRST



Triviality of higher derivative theories

Victor O. Rivelles1

Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Received 27 June 2003; received in revised form 28 August 2003; accepted 13 October 2003

Editor: M. Cvetic

Abstract

We show that some higher derivative theories have a BRST symmetry. This symmetry is due to the higher derivativeand is not associated to any gauge invariance. If physical states are defined as those in the BRST cohomology thephysical state is the vacuum. All negative norm states, characteristic of higher derivative theories, are removed from thesector. As a consequence, unitarity is recovered but the S-matrix is trivial. We show that a class of higher derivativegravity theories have this BRST symmetry so that they are consistent as quantum field theories. Furthermore, thsymmetry may be present in both relativistic and non-relativistic systems. 2003 Elsevier B.V. All rights reserved.

PACS: 11.10.-z; 11.15.-q; 11.30.Ly; 04.60.-m

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ysis

Higher derivative (HD) theories were introducin quantum field theory in an attempt to get ridultraviolet divergences [1]. It was soon recognizthat they have an energy which is not bounded frbelow [2] and that these negative energy statesbe traded by negative norm states (or ghosts)leading to non-unitary theories. Although inconsisteHD theories have better renormalization properthan conventional ones and a large amount of wwas dedicated to the study of such theories [4].the gravitational context, for instance, it is ableproduce a renormalizable quantum gravity theoryTo overcome the ghost problem many attempts w

E-mail address: [email protected] (V.O. Rivelles).1 On leave from Instituto de Física, Universidade de São Pa

Caixa Postal 66318, 05315-970 São Paulo, SP, Brazil. E-address:[email protected].


done mainly by imposing some superselection rulesome subsidiary condition to remove the undesirastates [4]. However, there is no general schemeremove the ghosts and this is done in a case bybasis.

In this Letter we will show that some HD theoriehave a BRST symmetry after ghost fields are intduced. Usually the BRST symmetry is found in gautheories as a symmetry of the gauge fixed action.2 Itspurpose is to remove the negative norm states asated to the gauge invariance. Physical states aredefined as those which have zero ghost numberare invariant under the BRST symmetry. In the prescase, however, the BRST symmetry is not due to ga

2 The BRST transformations may be written in different wa(even in non-local form) but that is not the case here. Thisdiscussed in [6].

.


mailto:[email protected]

138 V.O. Rivelles / Physics Letters B 577 (2003) 137–142

ureene asi-r andatwe

thezeroy isitymevacin

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ayme.

ofivehostarehatrm

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the

invariance. Rather, it is a feature of the HD structof the action. As it will be shown, it can be found evin the case of a HD real scalar field. Since we havBRST symmetry it is natural to require that the phycal states are those which have zero ghost numbeare left invariant by this symmetry, in analogy to whis done in gauge theories. With these requirementsfind that HD theories have only one physical state,vacuum, since all others physical states appear innorm combinations. Therefore, the resulting theorghost free but it is also empty. In this way the unitarproblem associated to HD theories can be overcobut the resulting theory has no states besides theuum. We will show that this symmetry is presentHD non-Abelian gauge theories and also in HD grity theories, so that they are unitary but have a trivS-matrix.

Even though we work mostly with relativistic sytems, relativistic invariance is not a necessary ingdient. The HD BRST symmetry may also be foundnon-relativistic situations. We will exemplify this fothe case of the HD harmonic oscillator.

Let us first consider a real scalar fieldφ in d

dimensions with an action

(1)S =∫ddx

(1

2OnφOnφ − cOnc

),

whereO = ∏Ni=1( +m2

i ) is a product ofN Klein–Gordon operators with massesmi , c is a ghost,can anti-ghost andn is an integer. This HD action iinvariant under the following BRST transformations

(2)δφ = c, δc= 0, δc=Onφ.These transformations are nilpotent forφ and c andon-shell nilpotent forc. To find out the role of thissymmetry let us introduce an auxiliary fieldb andrewrite the action (1) as

(3)S =∫ddx

(bOnφ − 1

2b2 − cOnc

).

The BRST transformations now read

(4)δφ = c, δc= 0, δc= b, δb= 0,

and are off-shell nilpotent. This action can nowwritten as a total BRST transformation

(5)S =∫ddx δ

[c

(Onφ − 1

2b

)],

-

indicating that theory may be empty. It looks liketopological theory of Witten type [7] but it clearldepends on the local structure of the space–tiIn topological theories there are no local degreesfreedom from the start while here we have positand negative norm states before introducing the gfields. The requirement that the physical statesin the cohomology of the BRST charge means tall of them, except the vacuum, appear in zero nocombinations as we will show.

Interactions can be introduced trough a prepotenU(φ). The action

(6)S =∫ddx δ

[c

(Onφ − 1

2b−U

)],

which is invariant under the BRST transformatio(4), yields, after elimination of the auxiliary field,

S =∫ddx

[1

2

(Onφ

)2 + 1

2U2

(7)+UOnφ − c(Onc+U ′c)].

Assuming that the BRST symmetry has no anomit is enough to examine the free case to find outphysical states.

In order to simplify the analysis we will considefrom now on the casen = 1 and only one factor inO, that isN = 1. The simplest situation is the ondimensional case, that is, quantum mechanics, wO = d2/dt2 +m2. Then the action (1) reduces to thof a HD harmonic oscillator. Canonical quantizatiis straightforward if we keep the auxiliary field anuse the action in the form (3) where only first ordderivatives appear after an integration by partsperformed. We then find that the non-trivial equal timcommutation relations are

(8)[φ, b

] = [b, φ

] = −i,where dots denote time derivatives. The solution tofield equation forφ andb can be expanded as

(9)

φ(t)= 1

2m3/2

[(a + bmt)e−imt + (

a† + b†mt)eimt

],

(10)b(t)= −im1/2(be−imt − b†eimt).

The canonical Hamiltonian yields

(11)H =m(2b†b− ib†a + ia†b

),

V.O. Rivelles / Physics Letters B 577 (2003) 137–142 139

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a-ns

ti-

9),

thes at ofina-theD

but

to

0),onbeyndthethe

Thecased.eoryd

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e

tomethe

ures weev–incengr,

e

al

isld.

rth

and using the transformationa = ia − b/2, b = ia −3b/2 we find

(12)H =m(a†a − b†b

),

so that it is not positive definite at the classiclevel. Upon quantization we find that the non-trivcommutators for the operatorsa andb are given by

(13)[a, a†] = −1,

[a, b†] = i,

wherea andb are annihilation operators anda† andb†

are creation ones. By the transformationa = b − ia,b = −ia, we find

(14)[a, a†] = −[

b, b†] = 1,

so that the Hilbert space is not positive definite.We now consider the ghost fields in (1). Quantiz

tion is straightforward. The solution to the equatioof motion can be expanded as

(15)c(t)= 1

2m3/2

(ce−iωt + c†eiωt

),

(16)c(t)=m1/2(ce−iωt + c†eiωt),

where c and c are annihilation operators andc†

and c† are creation operators. The non-trivial ancommutators are given by

(17)c, c† = −

c, c† = 1.

The BRST transformations (4) for the operators in ((10), (15) and (16) (not for the fields) are

(18)δa = c, δc= 0, δc= −ib, δb = 0.

This means that the these operators belong toquartet representation of the BRST algebra [8]. Aconsequence, the BRST invariant states, build outhese operators, appear only in zero norm combtions through the quartet mechanism. Thereforeonly physical state is the vacuum. In this way the Hharmonic oscillator is free of negative norm statesthe only state left is the vacuum.

The situation for the scalar field is analogousthe quantum mechanical case. NowO = + m2

and the fields have expansions similar to (9), (1(15) and (16) with the creation and annihilatioperators depending on the momenta. They ocommutation relations similar to (13) and (17) athe Hamiltonian has the same form as (11). HenceBRST transformations are the same as in (18) and

quartet mechanism is also operational in this case.only physical state is the vacuum. The masslessneeds some care but again the same result is foun

At this point it is worth to remind that to removthe negative norm states for the HD scalar field thethe conditionb = 0 is often employed [9]. It is arguethat there is a “gauge symmetry”δφ = Λ with Λsatisfying ( + m2)Λ = 0. The “gauge conditionb = 0 is then imposed to remove the ghost staHowever, the Hamiltonian analysis reveals that therno true gauge symmetry since there are no constraat all. Amazingly, a “BRST symmetry” associatedthis “gauge symmetry” can be found3 and it agreeswith (18). Now its origin is clear; it is completely duto the HD structure as we have shown.

We can now easily generalize this constructionother types of fields. Since we want to keep the saBRST transformations (4) then the ghosts andauxiliary field b must have the same tensor structas the field under consideration. For gauge theorieshould also take into account the ordinary FaddePopov ghosts associated to the gauge symmetry sthey have a different origin from the ghosts comifrom the HD structure [11]. We will argue, howevethat only one set of ghost fields is needed.

For a theory with a non-Abelian vector field wstart with

(19)S =∫ddx Tr δ

[cµ

(Eµ − 1

2bµ

)],

whereEµ depends only on the vector fieldAµ. TheBRST transformations are given by

δAµ = cµ, δcµ = 0,

(20)δcµ = bµ, δbµ = 0.

This structure is similar to that found in topologicfield theories [12]. There,E, b and c are two formsinstead of vectors so that a topological invariantgenerated after the elimination of the auxiliary fieHere the tensor structure is quite different andEµ ischosen so that it gives rise to a HD theory. For a fouorder gauge theory we can choose

(21)Eµ =DνFνµ + 1

2ξ∂µ∂

νAν.

3 In fact, it was found in the singleton field theory in [10].


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The first term in (21) will produce a gauge invariaterm in the action if the second term is absent. Tsecond term breaks gauge invariance and canregarded as a gauge fixing term since it allows ufind the propagator forAµ. At this point we shoulddecide whether we introduce the gauge fixing tein Eµ, as in (21), or if we consider the ordinaFaddeev–Popov procedure for gauge fixing. If wenot add the gauge fixing term in (21) thenEµ willgive rise to an action forcµ andcµ which has a gaugsymmetryδcµ =DµΣ , δcµ =DµΣ , whereΣ andΣare Grassmannian functions. This would requireintroduction of ghosts for ghosts besides the ordinFaddeev–Popov ghosts forAµ. We then choose tointroduce the gauge fixing term directly inEµ to avoidthe proliferation of ghost fields.

With the choice (21) we find that (19) yields thfollowing action

S = 1

2

∫ddx

(22)

× Tr

(DνFνµDρF

ρµ + 1

4ξ2∂µ∂A∂µ∂A

+ 1

ξDνFνµ∂

µ∂A+ FµνFµν

− 2icµ, cν

Fµν + 1

ξ∂µcµ∂

νcν

),

where Fµν and Fµν are the field strengths forcµ

andcµ, respectively. Canonical quantization is easperformed keeping the auxiliary fieldbµ since it givesrise to a first order Lagrangian. No constraintsfound and the Hamiltonian is not positive definiQuantization simplifies in the Feynman gaugeξ = 1and we find that the quartet mechanism applies to ecomponent of the vector field. Again, the only physistate is the vacuum. Coupling to ordinary or Hmatter is straightforward. However, only non-minimcouplings arise. Details will be given elsewhere.

Other choices forEµ are possible. For instance,

(23)Eµ = 1

mDνFνµ + m

2Aµ,

gives rise to a fourth order massive vector thewhich includes the standard Maxwell term. Howevthere is no gauge invariance in this case.

For gravity the ghosts and the auxiliary field asecond order symmetric tensors. The action is

(24)S =∫ddx δ

[cµν

(Eµν − 1

2bµν

)],

and the BRST transformations are given by

δgµν = cµν, δcµν = 0,

(25)δcµν = bµν, δbµν = 0.

For a generic fourth order gravity theory we cchoose

(26)Eµν = g1/4(c1Rµν + c2gµνR + c3gµν + · · ·),where gµν is the metric, g its determinant,Rµνthe Ricci tensor,R the curvature scalar and dodenote the gauge fixing terms. After the eliminatof the auxiliary field we find that the action for thgravitational sector can be written as

(27)

Sgr =∫ddx

√−g[γR −Λ+ αR2 + βRµνRµν],

with γ 2 = −4Λ(dα + β)/d . Gauge fixing terms weromitted. Notice that we cannot get the EinsteHilbert action since settingα = β = 0 to get rid ofthe HD contributions also eliminates the term inR.However, we can chooseΛ= 0 in order to get a purelyHD gravity theory. Alternatively we can chooseβ =−dα, which corresponds to a traceless Ricci tenThis case is distinguished by energy considerati[13]. The conformal case has no special featuNotice also that (26) does not allow us to generatesquare of the Riemann tensor thus precluding GauBonnet terms which arise in string theory. Details wbe presented elsewhere.

Some final remarks are in order. Could a BRsymmetry be found for ordinary second order thries? Covariance requires that the operatorO be atleast quadratic in the derivatives. However, in lowdimensions, this requirement can be relaxed. Chbosons in two dimensions have a BRST symmewhich allows the vacuum as the only physical st[14]. In higher dimensions we could consider thetion (6) without the termOnφ and U as a func-tion of φ and its derivatives. Then we can takeU =√φ( +m2)φ. The termU2 in (7) yields the La-

grangian for the ordinary scalar field but we get nolocal interactions with the ghosts due to the termU ′cc.

V.O. Rivelles / Physics Letters B 577 (2003) 137–142 141

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2)

;3,

Even though there is a BRST symmetry, a detaanalysis shows that on-shellc= b= 0 so that the quartet mechanism cannot be applied. It is imperativehave non-trivial solutions to the field equation for tquartet mechanism to work. Sincec = 0 all contri-butions from the ghost sector to the physical Hilbspace vanish because they must be functions ofcc.Then we end up with the usual scalar theory andBRST symmetry is trivial in this case.

A more radical possibility would be to considnon-local expression forO, for instance O =√

+m2. The action (1) withn= 1 would be the or-dinary one for a scalar field but for the ghosts we finnon-local action. Quantization of such non-local theries has been done [15] but it not clear how the quamechanism can be applied with non-local ghosts. Tdeserves further understanding.

Returning to the quantum mechanical case,action (7) resembles that of supersymmetric quanmechanics ifO = d/dt and the ghosts are regardedfermions. The BRST transformations (4) are identito the supersymmetry transformations but the aBRST transformation (obtained by replacing ghoby anti-ghosts and vice versa)δφ = c, δc = 0, δc =−(O + V ), are not. The anti-commutator of thBRST and anti-BRST transformations vanishesexpected while in the supersymmetric case it wobe proportional to the Hamiltonian. There are crucsigns in the action and in the transformation ruwhich, when changed, produces the supersymmmodel. Hence the supersymmetric model is obtaiby twisting the BRST symmetry.

We should also remark that the BRST symmecannot be found in any HD theory. For instance, insimple case of non-degenerated masses

S =∫ddx

[1

2

( +m2

1

)φ( +m2

2

)φ

(28)− c( +m21

)c

],

there is a symmetry of the action given byδφ = c,δc = 0, δc = ( +m2

2)φ. However, this symmetry isnot nilpotent since on-shellδ2c = (m2

2 − m21)c = 0.

It is nilpotent only when both masses are equal timplying in (1) withn= 1 andO = +m2, wheremis the common mass.

As a last remark it must be stressed that a trivtopology for the space (or space–time) was assuthroughout the Letter. If a non-trivial topologypresent then topological excitations may arise as tdo in topological field theories of Witten type. Finstance, in the case of non-Abelian gauge fields (there are instanton solutions which may give ntrivial contributions to correlation functions. Thispresently under investigation and will be reportelsewhere.

Acknowledgements

I would like to thank A.J. Accioly, S. DeseR. Jackiw, I. Shapiro and S. Sorella for useful discsions. This work was partially supported by CAPECNPQ and PRONEX under contract CNPq 66.201998-99.

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b



Cumulative author index to volumes 571–577

Abazov, V.M.,574, 169Abbiendi, G.,572, 8; 577, 18, 93Abbott, B.,574, 169Abdallah, J.,576, 29Abdesselam, A.,574, 169Abdullah, M.N.A.,571, 45Abe, K.,577, 10Abe, T.,573, 46Abe, Y.,573, 248Abolins, M.,574, 169Abramo, L.R.,575, 165Abramov, V.,574, 169Abramowicz, H.,573, 46Abreu, P.,576, 29Abu-Ibrahim, B.,576, 273Achard, P.,571, 11;572, 133;575, 208;576, 18;577, 109Acharya, B.S.,574, 169Adam, W.,576, 29Adamczyk, L.,573, 46Adams, D.L.,574, 169Adams, M.,574, 169Adamus, M.,573, 46Adhikari, S.,571, 21Adler, V., 573, 46Adriani, O.,571, 11;572, 133;575, 208;576, 18;577, 109Adzic, P.,576, 29Afonin, S.S.,576, 122Aghuzumtsyan, G.,573, 46Agostino, L.,571, 139;572, 21;575, 190Aguilar-Benitez, M.,571, 11;572, 133;575, 208;576, 18;577, 109Ahmed, S.N.,574, 169Ainsley, C.,572, 8; 577, 18, 93Airapetian, A.,577, 37Ajinenko, I.V.,574, 14Åkesson, P.F.,572, 8; 577, 18, 93Akhoury, R.,572, 37Akimenko, S.A.,574, 14Akopov, N.,577, 37Akopov, Z.,577, 37Akulov, V.P.,575, 137Alberghi, G.L.,571, 245

0370-2693/2003 Published by Elsevier B.V.doi:10.1016/S0370-2693(03)01666-6

Albrecht, T.,576, 29Alcaraz, J.,571, 11;572, 133;575, 208;576, 18;577, 109Alderweireld, T.,576, 29Alekseev, A.,574, 296Alemanni, G.,571, 11;572, 133;575, 208;576, 18;577, 109Alemany-Fernandez, R.,576, 29Alexander, G.,572, 8; 577, 18, 93Alexeev, G.D.,574, 169Ali, S., 571, 45Alimonti, G., 571, 139;572, 21;575, 190Allaby, J.,571, 11;572, 133;575, 208;576, 18;577, 109Allison, J.,572, 8; 577, 18, 93Allmendinger, T.,576, 29Allport, P.P.,576, 29Aloisio, A., 571, 11;572, 133;575, 208;576, 18;577, 109Alton, A., 574, 169Alves, G.A.,574, 169Alviggi, M.G., 571, 11;572, 133;575, 208;576, 18;577, 109Amaldi, U.,576, 29Amapane, N.,576, 29Amaral, P.,572, 8; 577, 18, 93Amarian, M.,577, 37Amato, S.,576, 29Amghar, A.,574, 201Ammosov, V.V.,577, 37Anabalon, A.,572, 202Anagnostou, G.,572, 8; 577, 18, 93Ananias Neto, J.,571, 105Anashkin, E.,576, 29Anderhub, H.,571, 11;572, 133;575, 208;576, 18;577, 109Anderson, E.W.,574, 169Anderson, K.J.,572, 8; 577, 18, 93Andreazza, A.,576, 29Andreev, V.P.,571, 11;572, 133;575, 208;576, 18;577, 109Andringa, S.,576, 29Andronic, A.,571, 36Andrus, A.,577, 37Anishetty, R.,574, 47Anjos, J.C.,571, 139;572, 21;575, 190Anjos, N.,576, 29Anraku, K.,577, 10


144 Cumulative author index to volumes 571–577 (2003) 143–170

Anselmo, F.,571, 11;572, 133;575, 208;576, 18;577, 109Antilogus, P.,576, 29Antonioli, P.,573, 46Antonov, A.,573, 46Anzivino, G.,576, 43Aoki, S.,575, 198Aoyama, S.,576, 281Apel, W.-D.,576, 29Araki, T., 573, 209Arcelli, S.,572, 8; 577, 18, 93Arcidiacono, R.,576, 43Arefiev, A.,571, 11;572, 133;575, 208;576, 18;577, 109Arena, V.,571, 139;572, 21;575, 190Arik, E., 575, 198Arneodo, M.,573, 46Arnoud, Y.,574, 169;576, 29Artamonov, A.,575, 198Asai, S.,572, 8, 117;577, 18, 93Aschenauer, E.C.,577, 37Ask, S.,576, 29Asman, B.,576, 29Attallah, F.,573, 80Augustin, J.E.,576, 29Augustinus, A.,576, 29Augustyniak, W.,577, 37Aulchenko, V.M.,573, 63Avakian, R.,577, 37Avetissian, A.,577, 37Avetissian, E.,577, 37Avila, C., 574, 169Avramidi, I.G.,576, 195Axen, D.,572, 8; 577, 18, 93Azemoon, T.,571, 11;572, 133;575, 208;576, 18;577, 109Aziz, T., 571, 11;572, 133;575, 208;576, 18;577, 109Azuelos, G.,572, 8; 577, 18, 93

Babichenko, A.,573, 239Babintsev, V.V.,574, 169Babujian, H.,575, 144Babukhadia, L.,574, 169Bacchetta, A.,574, 225Bacon, T.C.,574, 169Baden, A.,574, 169Baffioni, S.,574, 169Bagnaia, P.,571, 11;572, 133;575, 208;576, 18;577, 109Bailey, D.S.,573, 46Bailey, I.,572, 8; 577, 18, 93Bailey, P.,577, 37Baillon, P.,576, 29Bajo, A.,571, 11;572, 133;575, 208;576, 18;577, 109Baksay, G.,571, 11;572, 133;575, 208;576, 18;577, 109Baksay, L.,571, 11;572, 133;575, 208;576, 18;577, 109Balashov, S.A.,573, 63Baldew, S.V.,571, 11;572, 133;575, 208;576, 18;577, 109Baldin, B.,574, 169

Baldin, E.M.,573, 63Baldini, W.,576, 43Ballesteros, A.,574, 276Ballestrero, A.,576, 29Balm, P.W.,574, 169Bambade, P.,576, 29Bamberger, A.,573, 46Banerjee, H.,573, 109Banerjee, R.,573, 248;576, 237Banerjee, S.,571, 11;572, 133;574, 169;575, 208;576, 18;

577, 109Banerjee, Sw.,571, 11;572, 133;575, 208;576, 18;577, 109Barakbaev, A.N.,573, 46Barbagli, G.,573, 46Barberio, E.,572, 8; 577, 18, 93Barberis, E.,574, 169Barberis, S.,571, 139;572, 21;575, 190Barbi, M.,573, 46Barbier, R.,576, 29Barbuto, E.,575, 198Barczyk, A.,571, 11;572, 133;575, 208;576, 18;577, 109Bardin, D.,576, 29Barger, V.,576, 303Bari, G.,573, 46Barillère, R.,571, 11;572, 133;575, 208;576, 18;577, 109Baringer, P.,574, 169Barker, G.,576, 29Barlow, R.J.,572, 8; 577, 18, 93Barnyakov, M.Yu.,573, 63Baroncelli, A.,576, 29Barone, V.,571, 50Barreiro, F.,573, 46Barreto, J.,574, 169Barrett, R.C.,574, 197Bartalini, P.,571, 11;572, 133;575, 208;576, 18;577, 109Barth, J.,572, 127Bartl, A., 573, 153Bartlett, J.F.,574, 169Bartsch, D.,573, 46Baru, S.E.,573, 63Barvinsky, A.O.,571, 229;572, 109Basak, A.K.,571, 45Basile, M.,571, 11;572, 133;573, 46;575, 208;576, 18;577, 109Bassler, U.,574, 169Batalova, N.,571, 11;572, 133;575, 208;576, 18;577, 109Batley, J.R.,576, 43Batley, R.J.,572, 8; 577, 18, 93Battacharyya, P.,571, 155Battaglia, M.,576, 29Battiston, R.,571, 11;572, 133;575, 208;576, 18;577, 109Baturin, V.,577, 37Baubillier, M.,576, 29Bauer, D.,574, 169Bauerdick, L.A.T.,573, 46Bäumer, C.,576, 253Baumgarten, C.,577, 37

Cumulative author index to volumes 571–577 (2003) 343–170 145

Bay, A.,571, 11;572, 133;575, 208;576, 18;577, 109Bean, A.,574, 169Beaudette, F.,574, 169Becattini, F.,571, 11;572, 133;575, 208;576, 18;577, 109Bechtle, P.,572, 8; 577, 18, 93Becker, U.,571, 11;572, 133;575, 208;576, 18;577, 109Beckert, K.,573, 80Beckmann, M.,577, 37Becks, K.-H.,576, 29Bediaga, I.,571, 139;572, 21;575, 190Bedny, I.V.,573, 63Begalli, M.,576, 29Begel, M.,574, 169Behler, M.,576, 43Behner, F.,571, 11;572, 133;575, 208;576, 18;577, 109Behnke, T.,572, 8; 577, 18, 93Behrens, U.,573, 46Behrmann, A.,576, 29Bélanger, G.,571, 163;576, 152Bell, K.W., 572, 8; 577, 18, 93Bell, M., 573, 46Bell, N.F.,573, 86Bell, P.J.,572, 8; 577, 18, 93Bella, G.,572, 8; 577, 18, 93Bellagamba, L.,573, 46Bellerive, A.,572, 8; 577, 18, 93Bellucci, L.,571, 11;572, 133;575, 208;576, 18;577, 109Bellucci, S.,571, 92;574, 121Beloborodova, O.L.,573, 63Belostotski, S.,577, 37Belous, K.S.,574, 14Belyaev, A.,574, 169Ben-Haim, E.,576, 29Beneke, M.,576, 173Benekos, N.,576, 29Benelli, G.,572, 8; 577, 18, 93Benen, A.,573, 46Bento, M.C.,575, 172Benussi, L.,571, 139;572, 21;575, 190Benvenuti, A.,576, 29Berat, C.,576, 29Berbeco, R.,571, 11;572, 133;575, 208;576, 18;577, 109Berdugo, J.,571, 11;572, 133;575, 208;576, 18;577, 109Berezinsky, V.,571, 209Berges, P.,571, 11;572, 133;575, 208;576, 18;577, 109Berggren, M.,576, 29Bergmann, U.C.,576, 55Beri, S.B.,574, 169Berman, D.S.,572, 101Bernardi, G.,574, 169Bernreuther, S.,577, 37Berntzon, L.,576, 29Bertani, L.,572, 21Bertani, M.,571, 139;575, 190Bertolami, O.,575, 172

Bertolin, A.,573, 46Bertram, I.,574, 169Bertrand, D.,576, 29Bertucci, B.,571, 11;572, 133;575, 208;576, 18;577, 109Besancon, M.,576, 29Besson, A.,574, 169Besson, N.,576, 29Betev, B.L.,571, 11;572, 133;575, 208;576, 18;577, 109Bethke, S.,572, 8; 577, 18, 93Beuselinck, R.,574, 169Bezrukov, F.,574, 75Bezzubov, V.A.,574, 169Bhadra, S.,573, 46Bhat, P.C.,574, 169Bhatnagar, V.,574, 169Bhattacharjee, M.,574, 169Bialas, A.,575, 30Bianchi, N.,577, 37Bianco, S.,571, 139;572, 21;575, 190Biasini, M.,571, 11;572, 133;575, 208;576, 18;577, 109Bicudo, P.J.A.,573, 131Biebel, O.,572, 8; 577, 18, 93Biglietti, M., 571, 11;572, 133;575, 208;576, 18;577, 109Biino, C.,576, 43Biland, A.,571, 11;572, 133;575, 208;576, 18;577, 109Bizzeti, A.,576, 43Blaising, J.J.,571, 11;572, 133;575, 208;576, 18;577, 109Blasi, N.,576, 253Blazey, G.,574, 169Bleicher, M.,575, 85Blekman, F.,574, 169Blessing, S.,574, 169Blinov, A.E.,573, 63Blinov, V.E.,573, 63Bloch, D.,576, 29Bloch, I.,573, 46Blok, H.P.,577, 37Blom, M., 576, 29Bluj, M., 576, 29Blyth, S.C.,571, 11;572, 133;575, 208;576, 18;577, 109Bobbink, G.J.,571, 11;572, 133;575, 208;576, 18;577, 109Boca, G.,571, 139;572, 21;575, 190Bock, P.,572, 8; 577, 18, 93Bocquet, G.,576, 43Bodmann, B.,573, 46Boehnlein, A.,574, 169Boeriu, O.,572, 8; 577, 18, 93Bogner, S.K.,576, 265Bogomyagkov, A.V.,573, 63Böhm, A.,571, 11;572, 133;575, 208;576, 18;577, 109Bojko, N.I.,574, 169Bołd, T.,573, 46Boldizsar, L.,571, 11;572, 133;575, 208;576, 18;577, 109Bolotov, V.N.,574, 14Bolton, T.A.,574, 169


Bonciani, R.,575, 268Bondar, A.E.,573, 63Bondarev, D.V.,573, 63Bondorf, J.P.,575, 229Bonesini, M.,576, 29Bonomi, G.,571, 139;572, 21;575, 190Boonekamp, M.,576, 29Boos, E.G.,573, 46Booth, P.S.L.,576, 29Borcherding, F.,574, 169Borge, M.J.G.,576, 55Borgia, B.,571, 11;572, 133;575, 208;576, 18;577, 109Borisov, G.,576, 29Borissov, A.,577, 37Borras, K.,573, 46Borysenko, A.,577, 37Bos, K.,574, 169Bosch, F.,573, 80;574, 180Boscherini, D.,573, 46Boschini, M.,571, 139;572, 21;575, 190Bose, T.,574, 169Botner, O.,576, 29Bottai, S.,571, 11;572, 133;575, 208;576, 18;577, 109Böttcher, H.,577, 37Boucaud, Ph.,575, 256Boudjema, F.,571, 163;576, 152Bouquet, B.,576, 29Bourilkov, D.,571, 11;572, 133;575, 208;576, 18;577, 109Bourquin, M.,571, 11;572, 133;575, 208;576, 18;577, 109Boutaleb-J, H.,574, 89Boutemeur, M.,572, 8; 577, 18, 93Boutin, D.,573, 80Bouwhuis, M.,577, 37Bowcock, T.J.V.,576, 29Boyko, I.,576, 29Bozza, C.,575, 198Braccini, S.,571, 11;572, 133;575, 208;576, 18;577, 109Brack, J.,577, 37Bracko, M.,576, 29Braibant, S.,572, 8; 577, 18, 93Brambilla, N.,576, 314Branchina, V.,574, 319Brandenberger, R.,574, 141Brandt, A.,574, 169Branson, J.G.,571, 11;572, 133;575, 208;576, 18;577, 109Braun, M.A.,576, 115Braun, W.,572, 127Braun-Munzinger, P.,571, 36Brax, Ph.,575, 115Brenner, R.,576, 29Brigliadori, L., 572, 8; 577, 18, 93Briskin, G.,574, 169Britvich, G.I.,574, 14Britvich, I.G.,574, 14Brochu, F.,571, 11;572, 133;575, 208;576, 18;577, 109

Brock, I.,573, 46Brock, R.,574, 169Brodet, E.,576, 29Broniowski, W.,574, 57Brooijmans, G.,574, 169Brook, N.H.,573, 46Bross, A.,574, 169Brown, R.M.,572, 8; 577, 18, 93Bruckman, P.,576, 29Brugnera, R.,573, 46Brüll, A., 577, 37Brümmer, N.,573, 46Brunet, J.M.,576, 29Bruni, A., 573, 46Bruni, G.,573, 46Bruno, N.R.,574, 276Bruski, N.,575, 198Bryzgalov, V.,577, 37Buchalla, G.,576, 173Buchholz, D.,574, 169Buchmüller, W.,574, 156Buehler, M.,574, 169Buescher, V.,574, 169Buesser, K.,572, 8; 577, 18, 93Bugg, D.V.,572, 1Bugge, L.,576, 29Buijs, A., 577, 109Bülte, A.,575, 198Buniy, R.V.,576, 127Buontempo, S.,575, 198Burckhart, H.J.,572, 8; 577, 18, 93Burger, J.D.,571, 11;572, 133;575, 208;576, 18;577, 109Burger, W.J.,571, 11;572, 133;575, 208;576, 18;577, 109Burtovoi, V.S.,574, 169Buschmann, P.,576, 29Bussey, P.J.,573, 46Butler, J.M.,574, 169Butler, J.N.,571, 139;572, 21;575, 190Butterworth, J.M.,573, 46Buzykaev, A.R.,573, 63Bylsma, B.,573, 46

Caggiano, J.,571, 155Cai, R.-G.,572, 75;576, 12Cai, X.D.,571, 11;572, 133;575, 208;576, 18;577, 109Calarco, T.,571, 50Caldwell, A.,573, 46Calvetti, M.,576, 43Calvi, M., 576, 29Campana, S.,572, 8; 577, 18, 93Camporesi, T.,576, 29Campos, A.H.,575, 151Canale, V.,576, 29Canelli, F.,574, 169Cano, F.,571, 260


Capell, M.,571, 11;572, 133;575, 208;576, 18;577, 109Capitani, G.P.,577, 37Capua, M.,573, 46Cara Romeo, G.,571, 11;572, 133;573, 46;575, 208;576, 18;

577, 109Carena, F.,576, 29Carli, T.,573, 46Carlin, R.,573, 46Carlino, G.,571, 11;572, 133;575, 208;576, 18;577, 109Carlson, C.E.,573, 101Carnegie, R.K.,572, 8; 577, 18, 93Caron, B.,572, 8; 577, 18, 93Carone, C.D.,573, 101Carpenter, M.P.,571, 155Carrillo, S.,571, 139;572, 21;575, 190Cartacci, A.,571, 11;572, 133;575, 208;576, 18;577, 109Carter, A.A.,572, 8; 577, 18, 93Carter, J.R.,572, 8; 577, 18, 93Cartiglia, N.,576, 43Carvalho, W.,574, 169Casadio, R.,571, 245Casalbuoni, R.,575, 181Casaus, J.,571, 11;572, 133;575, 208;576, 18;577, 109Casey, D.,574, 169Casimiro, E.,571, 139;572, 21;575, 190Casteill, P.-Y.,574, 121Castilla-Valdez, H.,574, 169Castro, N.,576, 29Catanesi, M.G.,575, 198Catani, S.,575, 268Catterall, C.D.,573, 46Catto, S.,575, 137Cavallari, F.,571, 11;572, 133;575, 208;576, 18;577, 109Cavallo, F.,576, 29Cavallo, N.,571, 11;572, 133;575, 208;576, 18;577, 109Cawlfield, C.,571, 139;572, 21;575, 190Cebecioglu, O.,575, 137Cecchi, C.,571, 11;572, 133;575, 208;576, 18;577, 109Ceccucci, A.,576, 43Cederkäll, J.,576, 55Cenci, P.,576, 43Cerrada, M.,571, 11;572, 133;575, 208;576, 18;577, 109Cerri, C.,576, 43Cerutti, A.,571, 139;572, 21;575, 190Chafik, A.,574, 89Chakraborty, D.,574, 169Chamizo, M.,571, 11;572, 133;575, 208;576, 18;577, 109Chan, K.M.,574, 169Chang, C.H.,575, 190Chang, C.Y.,572, 8; 577, 18, 93Chang, Y.H.,571, 11;572, 133;575, 208;576, 18;577, 109Chapkin, M.,576, 29Charlton, D.G.,572, 8; 577, 18, 93Charpentier, Ph.,576, 29Chasman, R.R.,577, 47Chatterjee, D.,573, 109

Checchia, P.,576, 29Chekanov, S.,573, 46Chekulaev, S.V.,574, 169Chemarin, M.,571, 11;572, 133;575, 208;576, 18;577, 109Chen, A.,571, 11;572, 133;575, 208;576, 18;577, 109Chen, G.,571, 11;572, 133;575, 208;576, 18;577, 109Chen, G.M.,571, 11;572, 133;575, 208;576, 18;577, 109Chen, H.,571, 85Chen, H.F.,571, 11;572, 133;575, 208;576, 18;577, 109Chen, H.S.,571, 11;572, 133;575, 208;576, 18;577, 109Chen, W.,576, 289Chen, X.,575, 55Cheshkov, C.,576, 43Cheung, H.W.K.,571, 139;572, 21;575, 190Cheze, J.B.,576, 43Chiang, H.C.,577, 37Chiba, M.,571, 21Chiba, T.,575, 1Chiefari, G.,571, 11;572, 133;575, 208;576, 18;577, 109Chierici, R.,576, 29Chikawa, M.,575, 198Chiochia, V.,573, 46Chiodini, G.,571, 139;572, 21;575, 190Chizhov, M.,575, 198Chliapnikov, P.,576, 29Cho, D.K.,574, 169Cho, K.,571, 139;572, 21;575, 190Choi, K.-Y., 575, 309Choi, S.,574, 169Chopra, S.,574, 169CHORUS Collaboration,575, 198Chudoba, J.,576, 29Chung, S.U.,576, 29Chung, Y.S.,571, 139;572, 21;575, 190Chwastowski, J.,573, 46Ciafaloni, M.,576, 143Ciborowski, J.,573, 46Ciesielski, R.,573, 46Cieslik, K.,576, 29Cifarelli, L., 571, 11;572, 133;573, 46;575, 208;576, 18;

577, 109Cindolo, F.,571, 11;572, 133;573, 46;575, 208;576, 18;577, 109Cinquini, L.,571, 139;572, 21;575, 190Ciullo, G.,577, 37Claes, D.,574, 169Clare, I.,571, 11;572, 133;575, 208;576, 18;577, 109Clare, R.,571, 11;572, 133;575, 208;576, 18;577, 109Clark, A.R.,574, 169Clavelli, L., 576, 184Clemencic, M.,576, 43Close, F.E.,574, 210Cloth, P.,573, 46Cocco, A.G.,575, 198Coignet, G.,571, 11;572, 133;575, 208;576, 18;577, 109Cole, J.E.,573, 46Colferai, D.,576, 143


Colino, N.,571, 11;572, 133;575, 208;576, 18;577, 109Collazuol, G.,576, 43Collins, P.,576, 29Collins-Tooth, C.,573, 46Comelli, D.,571, 115Coney, L.,574, 169Connolly, B.,574, 169Contalbrigo, M.,577, 37Contin, A.,573, 46Contri, R.,576, 29Cooper, W.E.,574, 169Cooper-Sarkar, A.M.,573, 46Coppage, D.,574, 169Coppola, N.,573, 46, 46Cormack, C.,573, 46Corradi, M.,573, 46Corriveau, F.,573, 46Cosme, G.,576, 29Cossutti, F.,576, 29Costa, M.J.,576, 29Costa, P.,577, 129Costantini, F.,576, 43Costantini, S.,571, 11;572, 133;575, 208;576, 18;577, 109Cottrell, A.,573, 46Crawley, B.,576, 29Crennell, D.,576, 29Crépé-Renaudin, S.,574, 169Cristofano, G.,571, 250Csatlós, M.,576, 253Csige, L.,576, 253Csilling, A., 572, 8; 577, 18, 93Cuautle, E.,571, 139;572, 21;575, 190Cucciarelli, S.,571, 11;572, 133;575, 208;576, 18;577, 109Cuevas, J.,576, 29Cuffiani, M.,572, 8; 577, 18, 93Cumalat, J.P.,571, 139;572, 21;575, 190Cummings, M.A.C.,574, 169Cundy, D.,576, 43Cutts, D.,574, 169Cvitan, M.,571, 217Czakon, N.G.,574, 8

Dabrowski, A.,576, 43Dado, S.,572, 8; 577, 18, 93D’Agostini, G.,573, 46Dai, J.,576, 209Dal Corso, F.,573, 46Dalmau, J.,576, 29Dalpiaz, P.,576, 43Dalpiaz, P.F.,577, 37D’Ambrosio, G.,575, 75D’Ambrosio, N.,575, 198Da Motta, H.,574, 169Dange, S.P.,576, 260D’Angelo, P.,571, 139;572, 21;575, 190

Danilov, P.,573, 46Dannheim, D.,573, 46Das, A.,577, 76Das, S.K.,571, 45Da Silva, A.J.,577, 83Da Silva, T.,576, 29Da Silva, W.,576, 29Datsko, K.V.,574, 14Datta, A.,572, 164Davenport III, T.F.,571, 139;572, 21;575, 190Davids, B.,576, 253Davis, G.A.,574, 169De, K.,574, 169De Angelis, A.,576, 29De Asmundis, R.,571, 11;572, 133;575, 208;576, 18;577, 109De Beer, M.,576, 43De Boer, J.,574, 98De Boer, W.,576, 29Debreczeni, J.,571, 11;572, 133;575, 208;576, 18;577, 109Debu, P.,576, 43De Clercq, C.,576, 29Déglon, P.,571, 11;572, 133;575, 208;576, 18;577, 109De Gouvêa, A.,573, 94Degré, A.,571, 11;572, 133;575, 208;576, 18;577, 109Dehmelt, K.,571, 11;572, 133;575, 208;576, 18De Huu, M.A.,576, 253Deiters, K.,571, 11;572, 133;575, 208;576, 18;577, 109De Jong, M.,575, 198De Jong, P.,571, 11;572, 133;575, 208;576, 18;577, 109De Jong, S.J.,574, 169De la Cruz, B.,571, 11;572, 133;575, 208;576, 18;577, 109Delbar, T.,575, 198De Lellis, G.,575, 198De Leo, R.,577, 37Della Ricca, G.,576, 29Della Volpe, D.,571, 11;572, 133;575, 208;576, 18;577, 109Delmeire, E.,571, 11;572, 133;575, 208;576, 18;577, 109De Lotto, B.,576, 29Del Peso, J.,573, 46DELPHI Collaboration,576, 29De Maria, N.,576, 29Demarteau, M.,574, 169Dementiev, R.K.,573, 46De Min, A., 576, 29Demina, R.,574, 169Demine, P.,574, 169Demir, D.A.,571, 193De Miranda, J.M.,571, 139;572, 21;575, 190De Nardo, L.,577, 37Denes, P.,571, 11;572, 133;575, 208;576, 18;577, 109Deng, W.,575, 55Denisov, D.,574, 169Denisov, S.P.,574, 169Denner, A.,575, 290DeNotaristefani, F.,571, 11;572, 133;575, 208;576, 18;577, 109


De Pasquale, S.,573, 46De Paula, L.,576, 29De Roeck, A.,572, 8; 577, 18, 93De Rosa, G.,575, 198Derrick, M.,573, 46Desai, S.,574, 169De Salvo, A.,571, 11;572, 133;575, 208;576, 18;577, 109De Sanctis, E.,577, 37Desch, K.,572, 8; 577, 18, 93De Serio, M.,575, 198Deshpande, A.,573, 46De Soto, F.,575, 256Desplanques, B.,574, 201Devenish, R.C.E.,573, 46Devitsin, E.,577, 37Devlin, M., 571, 155;575, 221De Wolf, E.,573, 46De Wolf, E.A.,572, 8; 577, 18, 93Dhawan, S.,573, 46D’Hondt, J.,576, 29Dibon, H.,576, 43Di Capua, E.,575, 198Di Capua, F.,575, 198Di Ciaccio, L.,576, 29DiCorato, M.,571, 139;572, 21;575, 190Diehl, H.T.,574, 169Diemoz, M.,571, 11;572, 133;575, 208;576, 18;577, 109Dienes, B.,572, 8; 577, 18, 93Dierckxsens, M.,571, 11;572, 133;575, 208;576, 18;577, 109Diesburg, M.,574, 169Diget, C.Aa.,576, 55Dijkgraaf, R.,573, 138Dimopoulos, S.,573, 13Di Nezza, P.,577, 37Dini, P.,571, 139;572, 21;575, 190Dionisi, C.,571, 11;572, 133;575, 208;576, 18;577, 109Di Simone, A.,576, 29Dittmaier, S.,575, 290Dittmar, M.,571, 11;572, 133;575, 208;576, 18;577, 109Doble, N.,576, 43DØ Collaboration,574, 169Dolgoshein, B.A.,573, 46Dolgov, A.D.,573, 1Domienik, J.,574, 253Donkers, M.,572, 8; 577, 18, 93Dore, U.,575, 198Doria, A.,571, 11;572, 133;575, 208;576, 18;577, 109Doroba, K.,576, 29Dosch, H.G.,576, 83Dos Reis, A.C.,571, 139;572, 21;575, 190Doucet, M.,575, 198Doulas, S.,574, 169Dova, M.T.,571, 11;572, 133;575, 208;576, 18;577, 109Doyle, A.T.,573, 46Draayer, J.P.,576, 297

Drago, A.,571, 50Drees, J.,576, 29Drews, G.,573, 46Dris, M., 576, 29Drosg, R.,575, 221Dubbert, J.,572, 8; 577, 18, 93Duchesneau, D.,571, 11;572, 133;575, 208;576, 18;577, 109Duchovni, E.,572, 8; 577, 18, 93Duckeck, G.,572, 8; 577, 18, 93Duda, M.,571, 11;572, 133;575, 208;576, 18Dudal, D.,574, 325Dudko, L.V.,574, 169Duensing, S.,574, 169Duerdoth, I.P.,572, 8; 577, 18, 93Duflot, L., 574, 169Dugad, S.R.,574, 169Duinker, P.,577, 109Duperrin, A.,574, 169Düren, M.,577, 37Durkin, L.S.,573, 46Dusini, S.,573, 46Dyshkant, A.,574, 169

Eberl, H.,572, 56Echenard, B.,571, 11;572, 133;575, 208;576, 18;577, 109Edera, L.,571, 139;572, 21;575, 190Edmunds, D.,574, 169Ehrenfried, M.,577, 37Eidelman, S.I.,573, 63Eigen, G.,576, 29Eisenberg, Y.,573, 46Ekelof, T.,576, 29Elalaoui-Moulay, A.,577, 37Elbakian, G.,577, 37El Hage, A.,571, 11;572, 133;575, 208;576, 18Eline, A.,571, 11;572, 133;575, 208;576, 18;577, 109Elizalde, E.,574, 1Ellert, M., 576, 29Ellinghaus, F.,577, 37Ellis, J.,573, 162Ellison, J.,574, 169El Mamouni, H.,571, 11;572, 133;575, 208;576, 18;577, 109Elschenbroich, U.,577, 37Elsing, M.,576, 29Eltzroth, J.T.,574, 169Elvira, V.D., 574, 169Ely, J.,577, 37Engelmann, R.,574, 169Engh, D.,571, 139;572, 21;575, 190Engler, A.,571, 11;572, 133;575, 208;576, 18;577, 109Eno, S.,574, 169Entem, D.R.,576, 265Eppard, K.,576, 43Eppard, M.,576, 43Eppley, G.,574, 169


Eppling, F.J.,571, 11;572, 133;575, 208;576, 18;577, 109Erba, S.,571, 139;572, 21;575, 190Ereditato, A.,575, 198Ermolov, P.,574, 169Ermolov, P.F.,573, 46Ernst, J.,572, 127Eroshin, O.V.,574, 169Eskreys, A.,573, 46España-Bonet, C.,574, 149Espirito Santo, M.C.,576, 29Estrada, J.,574, 169Ethvignot, T.,575, 221Etzion, E.,572, 8; 577, 18, 93Evans, H.,574, 169Evdokimov, V.N.,574, 169Ewers, A.,577, 109Extermann, P.,571, 11;572, 133;575, 208;576, 18;577, 109

Fabbri, A.,574, 309Fabbri, F.,572, 8; 577, 18, 93Fabbri, F.L.,571, 139;572, 21;575, 190Fabbri, R.,577, 37Falagan, M.A.,571, 11;572, 133;575, 208;576, 18;577, 109Falaleev, V.,576, 43Falch, M.,573, 80Falciano, S.,571, 11;572, 133;575, 208;576, 18;577, 109Falcone, D.,572, 50Fang, D.,571, 21Fanourakis, G.,576, 29Fantechi, R.,576, 43Fantoni, A.,577, 37Farese, S.,574, 309Farrar, G.R.,575, 358Fassouliotis, D.,576, 29Favara, A.,571, 11;572, 133;575, 208;576, 18;577, 109Favart, D.,575, 198Fay, J.,571, 11;572, 133;575, 208;576, 18;577, 109Fechtchenko, A.,577, 37Fedin, O.,571, 11;572, 133;575, 208;576, 18;577, 109Fein, D.,574, 169Feindt, M.,576, 29Felawka, L.,577, 37Felcini, M.,571, 11;572, 133;575, 208;576, 18;577, 109Feld, L.,572, 8; 577, 18, 93Feng, B.,572, 68Ferbel, T.,574, 169Ferguson, T.,571, 11;572, 133;575, 208;576, 18;577, 109Fernandez, J.,576, 29Ferrando, J.,573, 46Ferrari, A.F.,577, 83Ferrari, P.,572, 8; 577, 18, 93Ferreira, E.,576, 83Ferrer, A.,576, 29Ferrero, M.I.,573, 46Ferro, F.,576, 29

Fesefeldt, H.,571, 11;572, 133;575, 208;576, 18;577, 109Fiandrini, E.,571, 11;572, 133;575, 208;576, 18;577, 109Fiedler, F.,572, 8; 577, 18, 93Field, J.H.,571, 11;572, 133;575, 208;576, 18;577, 109Figiel, J.,573, 46Filges, D.,573, 46Filin, A.P.,574, 14Filthaut, F.,571, 11;572, 133;574, 169;575, 208;576, 18;

577, 109Finelli, F.,575, 165Fiorillo, G., 575, 198Fiorini, L., 576, 43Fisher, P.H.,571, 11;572, 133;575, 208;576, 18;577, 109Fisher, W.,571, 11;572, 133;575, 208;576, 18;577, 109Fisk, H.E.,574, 169Fisk, I.,571, 11;572, 133;575, 208;576, 18;577, 109Flagmeyer, U.,576, 29Fleck, I.,572, 8; 577, 18, 93Fleuret, F.,574, 169FOCUS Collaboration,571, 139;572, 21;575, 190Foeth, H.,576, 29Fokitis, E.,576, 29Fonseca Martin, T.,576, 43Forconi, G.,571, 11;572, 133;575, 208;576, 18;577, 109Ford, M.,572, 8; 577, 18, 93Fornengo, N.,576, 189Fortner, M.,574, 169Foster, B.,573, 46Foudas, C.,573, 46Fourletov, S.,573, 46Fourletova, J.,573, 46Fox, B.,577, 37Fox, H.,574, 169Frabetti, P.L.,576, 43Fraile, L.M.,576, 55Franz, J.,577, 37Franzke, B.,573, 80Frekers, D.,575, 198Frenkel, J.,577, 76Freudenreich, K.,571, 11;572, 133;575, 208;576, 18;577, 109Frey, A.,572, 8; 577, 18, 93Fricke, U.,573, 46Frullani, S.,577, 37Fu, S.,574, 169Fuchs, T.,575, 11Fuess, S.,574, 169Fujii, Y., 573, 39Fujikawa, M.,577, 10Fujimoto, J.,571, 163;576, 152Fuke, H.,577, 10Fulda-Quenzer, F.,576, 29Furetta, C.,571, 11;572, 133;575, 208;576, 18;577, 109Fürtjes, A.,572, 8; 577, 18, 93Fusayasu, T.,573, 46Fuster, J.,576, 29Fynbo, H.O.U.,576, 55


Gabareen, A.,573, 46Gagnon, P.,572, 8; 577, 18, 93Gaines, I.,571, 139;572, 21;575, 190Gaiotto, D.,575, 111Galaktionov, Yu.,571, 11;572, 133;575, 208;576, 18;577, 109Gallas, E.,574, 169Gallo, E.,573, 46Galyaev, A.N.,574, 169Gandelman, M.,576, 29Ganguli, S.N.,571, 11;572, 133;575, 208;576, 18;577, 109Gao, M.,574, 169Gapienko, G.,577, 37Gapienko, V.,577, 37Garbincius, P.H.,571, 139;572, 21;575, 190Garcia, C.,576, 29Garcia-Abia, P.,571, 11;572, 133;575, 208;576, 18;577, 109Gardner, R.,571, 139;572, 21;575, 190Garfagnini, A.,573, 46Garg, U.,576, 253Garibaldi, F.,577, 37Garren, L.A.,571, 139;572, 21;575, 190Garrow, K.,577, 37Garutti, E.,577, 37Gary, J.W.,572, 8; 577, 18, 93Gaskell, D.,577, 37Gataullin, M.,571, 11;572, 133;575, 208;576, 18;577, 109Gates Jr., S.J.,576, 97Gatignon, L.,576, 43Gatto, R.,575, 181Gavillet, Ph.,576, 29Gavrilov, G.,577, 37Gavrilov, V.,574, 169Gaycken, G.,572, 8; 577, 18, 93Gazis, E.,576, 29Gegelia, J.,575, 11Geich-Gimbel, C.,572, 8; 577, 18, 93Geiser, A.,573, 46Geissel, H.,573, 80Gemein, N.,571, 29Genik II, R.J.,574, 169Genser, K.,574, 169Genta, C.,573, 46Gentile, S.,571, 11;572, 133;575, 208;576, 18;577, 109Gerber, C.E.,574, 169Gerber, J.,571, 29Gershtein, Y.,574, 169Geyer, B.,575, 349Gharibyan, V.,577, 37Ghoroku, K.,571, 223Ghosh, S.,571, 97Giacomelli, G.,572, 8; 577, 18, 93Giacomelli, P.,572, 8; 577, 18, 93Giagu, S.,571, 11;572, 133;575, 208;576, 18;577, 109Gialas, I.,573, 46Giammarchi, M.,571, 139;572, 21;575, 190Gianini, G.,571, 139;572, 21;575, 190

Gianoli, A.,576, 43Ginther, G.,574, 169Girotti, H.O.,577, 83Gitman, D.M.,576, 227Giudice, G.F.,575, 75Giudici, S.,576, 43Giunta, M.,572, 8; 577, 18, 93Giusti, P.,573, 46Gladilin, L.K., 573, 46Gladkov, D.,573, 46Glander, K.-H.,572, 127Glasman, C.,573, 46Gliga, S.,573, 46Glozman, L.Ya.,575, 18Göbel, C.,571, 139;572, 21;575, 190Godbole, R.M.,571, 184Godfrey, S.,574, 210Goers, S.,573, 46Gogohia, V.,576, 243Gogoladze, I.,575, 66Gokieli, R.,576, 29Goldberg, J.,572, 8; 575, 198;577, 18, 93Golob, B.,576, 29Golubkov, Yu.A.,573, 46Gomes, M.,577, 83Gómez, B.,574, 169Gomez-Ceballos, G.,576, 29Gonçalo, R.,573, 46Goncalves, P.,576, 29Goncharov, P.I.,574, 169Gong, Z.F.,571, 11;572, 133;575, 208;576, 18;577, 109Gonidec, A.,576, 43González, O.,573, 46Gorbunov, P.,575, 198Gordon, H.,574, 169Göttlicher, P.,573, 46Gottschalk, E.,571, 139;572, 21;575, 190Goudzovski, E.,576, 43Gouge, G.,576, 43Gounder, K.,574, 169Goussiou, A.,574, 169Goy Lopez, S.,576, 43Grabowska-Bołd, I.,573, 46Gracey, J.A.,574, 325Graf, N.,574, 169Grafström, P.,576, 43Graham, N.,572, 196Granier, T.,575, 221Grannis, P.D.,574, 169Grassi, P.A.,574, 98Graw, G.,577, 37Graziani, E.,576, 29Graziani, G.,576, 43Grebeniouk, O.,577, 37Greco, F.,576, 18


Green, J.A.,574, 169Greeniaus, L.G.,577, 37Greenlee, H.,574, 169Greenwood, Z.D.,574, 169Grégoire, G.,575, 198Gregor, I.M.,577, 37Grella, G.,575, 198Grenier, G.,571, 11;572, 133;575, 208;576, 18;577, 109Grijpink, S.,573, 46Grimm, O.,571, 11;572, 133;575, 208;576, 18;577, 109Grimus, W.,572, 189Grinstein, S.,574, 169Grisaru, M.T.,573, 138Groer, L.,574, 169Groll, M., 577, 93Gromes, D.,576, 314Gronau, M.,572, 43Grosdidier, G.,576, 29Groshev, V.R.,573, 63Gross, D.H.E.,574, 186Gross, E.,572, 8; 577, 18, 93Gruenewald, M.W.,571, 11;572, 133;575, 208;576, 18;577, 109Grünendahl, S.,574, 169Grunhaus, J.,572, 8; 577, 18, 93Gruwé, M.,572, 8; 577, 18, 93Grzelak, G.,573, 46Grzelak, K.,576, 29Gubarev, F.V.,574, 136Guchait, M.,571, 184Guida, M.,571, 11;572, 133;575, 208;576, 18;577, 109Güler, M.,575, 198Gulyás, J.,576, 253Günther, P.O.,572, 8; 577, 18, 93Guo, Z.-K.,576, 12Gupta, A.,572, 8; 577, 18, 93Gupta, K.S.,574, 93Gupta, V.K.,571, 11;572, 133;575, 208;576, 18;577, 109Gurev, D.,576, 43Gurtu, A.,571, 11;572, 133;575, 208;576, 18;577, 109Gurzhiev, S.N.,574, 169Gutay, L.J.,571, 11;572, 133;575, 208;576, 18;577, 109Gutierrez, G.,574, 169Gutierrez, P.,574, 169Gutsche, O.,573, 46Guy, J.,576, 29Gwenlan, C.,573, 46

Haag, C.,576, 29Haas, D.,571, 11;572, 133;575, 208;576, 18;577, 109Haas, T.,573, 46Hadasz, L.,574, 129Haddou, M.A.B.,575, 100Hadley, N.J.,574, 169Hafidi, K., 577, 37Haggerty, H.,574, 169

Hagopian, S.,574, 169Hagopian, V.,574, 169Haight, R.C.,575, 221Hain, W.,573, 46Haino, S.,577, 10Hajdu, C.,572, 8; 577, 18, 93Hakobyan, R.Sh.,571, 11Hall, R.E.,574, 169Hall-Wilton, R.,573, 46Hallgren, A.,576, 29Hamacher, K.,576, 29Hamaguchi, K.,574, 156Hamann, M.,572, 8; 577, 18, 93Hamatsu, R.,573, 46Hamilton, J.,573, 46Hamilton, K.,576, 29Han, C.,574, 169Handler, T.,571, 139;572, 21;575, 190Hanlon, S.,573, 46Hannappel, J.,572, 127Hansen, S.,574, 169Hanson, G.G.,572, 8; 577, 18, 93Hara, T.,575, 198Harakeh, M.N.,576, 253Harder, K.,572, 8; 577, 18, 93Harel, A.,572, 8; 577, 18, 93Harin-Dirac, M.,572, 8; 577, 18, 93Harlander, R.V.,574, 258Hart, J.C.,573, 46Hartig, M.,577, 37Hartmann, H.,573, 46Hartner, G.,573, 46Hartner, G.F.,573, 46Hasch, D.,577, 37Hatzifotiadou, D.,571, 11;572, 133;575, 208;576, 18;577, 109Haug, S.,576, 29Hauler, F.,576, 29Hauptman, J.M.,574, 169Hauschild, M.,572, 8; 577, 18, 93Hausmann, M.,573, 80Hawkes, C.M.,572, 8; 577, 18, 93Hawkings, R.,572, 8; 577, 18, 93Heaphy, E.A.,573, 46Heath, G.P.,573, 46Heath, H.F.,573, 46Hebbeker, T.,571, 11;572, 133;575, 208;576, 18;577, 109Hebecker, A.,574, 269Hebert, C.,574, 169Hedberg, V.,576, 29Hedin, D.,574, 169Heesbeen, D.,577, 37Heinmiller, J.M.,574, 169Heinson, A.P.,574, 169Heintz, U.,574, 169Heinz, A.,571, 155


Helbich, M.,573, 46Hemingway, R.J.,572, 8; 577, 18, 93Hennecke, M.,576, 29Henoch, M.,577, 37Hensel, C.,572, 8; 577, 18, 93HERMES Collaboration,577, 37Hernandez, H.,571, 139;572, 21;575, 190Herr, H.,576, 29Herranz, F.J.,574, 276Herten, G.,572, 8; 577, 18, 93Hertenberger, R.,577, 37Hervé, A.,571, 11;572, 133;575, 208;576, 18;577, 109Hesselbach, S.,573, 153Hesselink, W.H.A.,577, 37Heuer, R.D.,572, 8; 577, 18, 93Heusch, C.,573, 46Hidaka, K.,573, 153Hikami, K., 575, 343Hildreth, M.D.,574, 169Hilger, E.,573, 46Hill, J.C., 572, 8; 577, 18, 93Hillenbrand, A.,577, 37Hillert, S.,573, 46Hirose, T.,573, 46Hirosky, R.,574, 169Hirschfelder, J.,571, 11;572, 133;575, 208;576, 18;577, 109Hirstius, A.,576, 43Hobbs, J.D.,574, 169Hochman, D.,573, 46Hoek, M.,577, 37Hoeneisen, B.,574, 169Hofer, H.,571, 11;572, 133;575, 208;576, 18;577, 109Hoffman, J.,576, 29Hoffman, K.,572, 8; 577, 18, 93Hofmann, S.,575, 85Hohlmann, M.,571, 11;572, 133;575, 208;576, 18;577, 109Hohn, D.,571, 29Holder, M.,576, 43Holler, Y., 577, 37Holm, U.,573, 46Holmgren, S.-O.,576, 29Holt, P.J.,576, 29Holzner, G.,571, 11;572, 133;575, 208;576, 18;577, 109Hommez, B.,577, 37Horváth, D.,572, 8; 577, 18, 93Hosack, M.,571, 139;572, 21;575, 190Hosaka, A.,571, 55Hoshino, K.,575, 198Hossain, S.,571, 45Hossenfelder, S.,575, 85Hou, H.-S.,571, 85Hou, S.R.,571, 11;572, 133;575, 208;576, 18;577, 109Houlden, M.A.,576, 29Howell, C.R.,574, 8Hristov, P.,576, 43

Hristova, I.R.,575, 198Hu, Y., 571, 11;572, 133;575, 208;576, 18;577, 109Huang, J.,574, 169Huang, Y.,574, 169Hultqvist, K.,576, 29Hunyadi, M.,576, 253Hutcheson, A.,574, 8

Iacobucci, G.,573, 46Iacopini, E.,576, 43Iarygin, G.,577, 37Iashvili, I., 574, 169Ibarra, A.,575, 279Ieva, M.,575, 198Iga, Y.,573, 46Igo-Kemenes, P.,572, 8; 577, 18, 93Iida, K., 576, 273Ikeda, K.,576, 281Illingworth, R.,574, 169Imbergamo, E.,576, 43Imori, M., 577, 10Inoue, Y.,571, 132;572, 145Inuzuka, M.,573, 46Inyakin, A.V.,574, 14Inzani, P.,571, 139;572, 21;575, 190Irrgang, P.,573, 46Ishii, K., 572, 8; 577, 18, 93Ishikawa, T.,571, 163;576, 152ISOLDE Collaboration,576, 55Ito, A.S.,574, 169Ito, K., 573, 209Itoyama, H.,573, 227Itzhaki, N.,575, 111Ivanilov, A., 577, 37Iwasa, N.,571, 21Iwazaki, A.,571, 61Izaurieta, F.,574, 283Izawa, K.-I.,576, 1Izotov, A.,577, 37Izumi, K., 577, 10

Jackson, H.E.,577, 37Jackson, J.N.,576, 29Jaffe, R.L.,572, 196Jaffré, M.,574, 169Jain, S.,574, 169Jakob, H.-P.,573, 46Jalilian-Marian, J.,577, 54Janik, R.A.,576, 90Janssens, R.V.F.,571, 155Jarlskog, G.,576, 29Jarry, P.,576, 29Jaskólski, Z.,574, 129Jeans, D.,576, 29Jeitler, M.,576, 43


Jeppesen, H.,576, 55Jeremie, H.,572, 8; 577, 18, 93Jesik, R.,574, 169Jgoun, A.,577, 37Jin, B.N.,571, 11;572, 133;575, 208;576, 18;577, 109Jinnouchi, O.,572, 117Johansson, E.K.,576, 29Johansson, P.D.,576, 29Johns, K.,574, 169Johns, W.E.,571, 139;572, 21;575, 190Johnson, M.,574, 169Jonckheere, A.,574, 169Jones, L.W.,571, 11;572, 133;575, 208;576, 18;577, 109Jones, T.W.,573, 46Jonson, B.,576, 55Jonsson, P.,576, 29Jöpen, N.,572, 127Joram, C.,576, 29Josa-Mutuberría, I.,571, 11;572, 133;575, 208;576, 18;577, 109Jöstlein, H.,574, 169Jovanovic, P.,572, 8; 577, 18, 93Jungermann, L.,576, 29Junk, B.C.,576, 253Junk, T.R.,572, 8; 577, 18, 93Juste, A.,574, 169

Kachelrieß, M.,577, 1Käfer, D.,571, 11;572, 133;575, 208;576, 18;577, 109Kagawa, S.,573, 46Kahl, W.,574, 169Kahle, B.,573, 46Kahn, S.,574, 169Kaiser, R.,577, 37Kajfasz, E.,574, 169Kakizaki, M.,573, 123Kalinin, A.M., 574, 169Kalinin, S.,575, 198Kalinovsky, Yu.L.,577, 129Kalinowsky, H.,572, 127Kalmus, G.E.,576, 43Kamenshchik, A.Yu.,571, 229Kananov, S.,573, 46Kanaya, N.,572, 8; 577, 18, 93Kaneko, T.,571, 163;576, 152Kang, J.S.,571, 139;572, 21;575, 190Kanno, H.,573, 227Kanungo, R.,571, 21Kanzaki, J.,572, 8; 577, 18, 93Kappes, A.,573, 46Kapusta, F.,576, 29Karapetian, G.,572, 8; 577, 18, 93Karlen, D.,572, 8; 577, 18, 93Karliner, M.,575, 249Karmanov, D.,574, 169Karmgard, D.,574, 169

Karnaev, S.E.,573, 63Karowski, M.,575, 144Karsch, F.,571, 67Karshon, U.,573, 46Kasper, P.H.,571, 139;572, 21;575, 190Katkov, I.I.,573, 46Kato, K., 576, 281Kato, K.,571, 163;576, 152Katsanevas, S.,576, 29Katsoufis, E.,576, 29Katz, U.F.,573, 46Kaur, M.,571, 11;572, 133;575, 208;576, 18;577, 109Kawada, J.,575, 198Kawagoe, K.,572, 8; 577, 18, 93Kawamoto, T.,572, 8; 577, 18, 93Kawamura, T.,575, 198Kawasaki, M.,573, 1Kayis-Topaksu, A.,575, 198Kçira, D.,573, 46KEDR Collaboration,573, 63Keeler, R.K.,572, 8; 577, 18, 93Kehoe, R.,574, 169Kekelidze, V.,576, 43Kelley, J.H.,574, 8Kellogg, R.G.,572, 8; 577, 18, 93Kenn, O.,571, 29Kennedy, B.W.,572, 8; 577, 18, 93Kephart, T.W.,576, 127Keränen, P.,574, 162Kerimo, J.,576, 219Kernel, G.,576, 29Kernreiter, T.,573, 153Kerscher, Th.,573, 80Kersevan, B.P.,576, 29Kerzel, U.,576, 29Khalil, S.,576, 107Khanov, A.,574, 169Kharchilava, A.,574, 169Khein, L.A.,573, 46Khemani, V.,572, 196Khmelnikov, V.A.,574, 14Khodjamirian, A.,571, 75;572, 171Khovansky, V.,575, 198Kiefer, C.,571, 229Kienzle-Focacci, M.N.,571, 11;572, 133;575, 208;576, 18;

577, 109Kiiskinen, A.,576, 29Kim, C.S.,576, 165Kim, D.H., 572, 8; 577, 18, 93Kim, D.Y., 571, 139;572, 21;575, 190Kim, H.-C., 572, 181Kim, J.K.,571, 11;572, 133;575, 208;576, 18;577, 109Kim, J.Y., 573, 46Kim, Y., 572, 81Kim, Y.K., 573, 46Kimura, K.,571, 21


Kind, O.,573, 46King, B.T., 576, 29King, S.F.,574, 239Kinney, E.,577, 37Kirillov, A.N., 575, 343Kirkby, J.,571, 11;572, 133;575, 208;576, 18;577, 109Kiselev, V.A.,573, 63Kisielewska, D.,573, 46Kiskis, J.,574, 65Kisselev, A.,577, 37Kitamura, S.,573, 46Kitano, R.,575, 300Kittel, W., 571, 11;572, 133;575, 208;576, 18;577, 109Kjaer, N.J.,576, 29Klein, F.,572, 127Klein, K., 572, 8; 577, 18, 93Kleinknecht, K.,576, 43Klempt, E.,572, 127Klepper, O.,573, 80Klier, A., 572, 8; 577, 18, 93Klima, B., 574, 169Klimek, K., 573, 46Klimentov, A.,571, 11;572, 133;575, 208;576, 18;577, 109Kluge, Gy.,576, 243Kluge, H.-J.,573, 80Kluit, P., 576, 29Kluth, S.,572, 8; 577, 18, 93Ko, B.R.,571, 139;572, 21;575, 190Kobayashi, T.,572, 8, 117;577, 18, 93Kobel, M.,572, 8; 577, 18, 93Koch, U.,576, 43Kodama, K.,575, 198Koffeman, E.,573, 46Kohli, J.M.,574, 169Kohno, T.,573, 46Koide, Y.,574, 82Koike, M., 575, 300Kokkinias, P.,576, 29Kolev, D.,575, 198Komamiya, S.,572, 8; 577, 18, 93Komatsu, M.,575, 198Komine, S.,575, 300Kondev, F.,571, 155Kondo, K.-I.,572, 210König, A.C.,571, 11;572, 133;575, 208;576, 18;577, 109Königsmann, K.,577, 37Kononov, S.A.,573, 63Konstantinov, A.S.,574, 14Konstantinov, V.F.,574, 14Kooijman, P.,573, 46Koop, T.,573, 46Kopal, M.,571, 11;572, 133;575, 208;576, 18;577, 109Kopytin, M., 577, 37Kormos, L.,572, 8; 577, 18, 93Korolkov, I.Y., 574, 14

Korotkov, V.,577, 37Korzhavina, I.A.,573, 46Köse, U.,575, 198Kosinski, P.,574, 253Kostritskiy, A.V.,574, 169Kotanski, A.,573, 46Kotcher, J.,574, 169Kothari, B.,574, 169Kotov, K.A., 573, 63Kötz, U.,573, 46Kourkoumelis, C.,576, 29Koutsenko, V.,571, 11;572, 133;575, 208;576, 18;577, 109Kouznetsov, O.,576, 29Kovalenko, A.V.,574, 136Kowal, A.M., 573, 46Kowal, M., 573, 46Kowalski, H.,573, 46Kowalski, T.,573, 46Kozelov, A.V.,574, 169Kozhuharov, C.,573, 80Kozlov, V., 577, 37Kozlovsky, E.A.,574, 169Kräber, M.,571, 11;572, 133;575, 208;576, 18;577, 109Kraemer, R.W.,571, 11;572, 133;575, 208;576, 18;577, 109Krakauer, D.,573, 46Kramberger, G.,573, 46Krämer, T.,572, 8; 577, 18, 93Krane, J.,574, 169Krasznahorkay, A.,576, 253Krauss, B.,577, 37Krauss, F.,576, 135Kravchenko, E.A.,573, 63Kreisel, A.,573, 46Kremyanskaya, E.V.,573, 63Krenz, W.,577, 109Kreymer, A.E.,571, 139;572, 21;575, 190Krieger, P.,572, 8; 577, 18, 93Krishnaswamy, M.R.,574, 169Krivkova, P.,574, 169Krivokhijine, V.G.,577, 37Krüger, A.,571, 11;572, 133;575, 208;576, 18;577, 109Kruger, K.,572, 8; 577, 18, 93Krumnack, N.,573, 46Krumstein, Z.,576, 29Kryemadhi, A.,571, 139;572, 21;575, 190Krzywdzinski, S.,574, 169Kubantsev, M.,574, 169Kubischta, W.,576, 43Kucharczyk, M.,576, 29Kudtarkar, S.K.,574, 47Kuhl, T., 572, 8; 577, 18, 93Kuleshov, S.,574, 169Kulik, Y., 574, 169Kunin, A., 571, 11;572, 133;575, 208;576, 18;577, 109Kunori, S.,574, 169


Kuo, T.T.S.,576, 68, 265Kupco, A.,574, 169Kupper, M.,572, 8; 577, 18, 93Kurihara, Y.,576, 152Kutschke, R.,571, 139;572, 21;575, 190Kuze, M.,573, 46Kuzenko, S.M.,576, 97Kuzmin, V.A.,573, 46Kuznetsov, V.E.,574, 169Kwak, J.W.,571, 139;572, 21;575, 190Kwee, H.J.,573, 101

L3 Collaboration,571, 11;572, 133;575, 208;576, 18;577, 109Labarga, L.,573, 46Labes, H.,573, 46Labzowsky, L.,574, 180La Camera, M.,573, 27Ladron de Guevara, P.,571, 11;572, 133;575, 208;576, 18;

577, 109Lafferty, G.D.,572, 8; 577, 18, 93Lagamba, L.,577, 37Laget, J.-M.,571, 260Lainesse, J.,573, 46Laktineh, I.,571, 11;572, 133;575, 208;576, 18;577, 109Lam, C.S.,573, 138Lamanna, G.,576, 43Lammers, S.,573, 46Lamsa, J.,576, 29Landi, G.,571, 11;572, 133;575, 208;576, 18;577, 109Landsberg, G.,574, 169Landsman, H.,572, 8; 577, 18, 93Lanske, D.,572, 8; 577, 18, 93Lapikás, L.,577, 37Laptev, S.V.,574, 14Lauritsen, T.,571, 155Lavoura, L.,572, 189Lawall, R.,572, 127Layter, J.G.,572, 8; 577, 18, 93Laziev, A.,577, 37Lazzeroni, C.,576, 43Lebeau, M.,571, 11;572, 133;575, 208;576, 18;577, 109Lebedev, A.,571, 11;572, 133;575, 208;576, 18;577, 109Lebrun, P.,571, 11;572, 133;575, 208;576, 18;577, 109Lecomte, P.,571, 11;572, 133;575, 208;576, 18;577, 109Lecoq, P.,571, 11;572, 133;575, 208;576, 18;577, 109Le Coultre, P.,571, 11;572, 133;575, 208;576, 18;577, 109Leder, G.,576, 29Ledroit, F.,576, 29Lee, H.M.,575, 309Lee, J.H.,573, 46Lee, K.B.,571, 139;572, 21;575, 190Lee, S.W.,573, 46Lee, W.M.,574, 169Leflat, A.,574, 169Le Goff, J.M.,571, 11;572, 133;575, 208;576, 18;577, 109

Lehner, F.,574, 169Leinonen, L.,576, 29Leins, A.,572, 8; 577, 18, 93Leiste, R.,571, 11;572, 133;575, 208;576, 18;577, 109Leitner, R.,576, 29Lelas, D.,573, 46Lellouch, D.,572, 8; 577, 18, 93Lemes, V.E.R.,574, 325Lemonne, J.,576, 29Lenisa, P.,577, 37Lenti, M., 576, 43Lenz, A.,576, 173Leonidopoulos, C.,574, 169Leontiev, V.M.,574, 14Lepeltier, V.,576, 29Leroy, J.P.,575, 256Lesiak, T.,576, 29Leske, J.,571, 29Letts, J.,572, 8; 577, 18, 93Levchenko, B.B.,573, 46Leveraro, F.,571, 139;572, 21;575, 190Levichev, E.B.,573, 63Levinson, L.,572, 8; 577, 18, 93Levkov, D.,574, 75Levman, G.M.,573, 46Levtchenko, M.,571, 11;572, 133;575, 208;576, 18Levtchenko, P.,571, 11;572, 133;575, 208;576, 18;577, 109Levy, A., 573, 46Le Yaouanc, A.,575, 256Li, C., 571, 11;572, 133;575, 208;576, 18;577, 109Li, J., 574, 169Li, L., 573, 46Li, M., 573, 20Li, Q.Z., 574, 169Li, T., 573, 193Lidsey, J.E.,574, 1; 575, 157Liebig, W.,576, 29Liebing, P.,577, 37Liesen, D.,574, 180Lightwood, M.S.,573, 46Liguori, G.,571, 139;572, 21;575, 190Likhoded, S.,571, 11;572, 133;575, 208;576, 18;577, 109Liko, D., 576, 29Lillich, J., 572, 8; 577, 18, 93Lim, H., 573, 46Lim, I.T., 573, 46Lima, J.G.R.,574, 169Limentani, S.,573, 46Lin, C.H., 571, 11;572, 133;575, 208;576, 18;577, 109Lin, W.T., 571, 11;572, 133;575, 208;576, 18;577, 109Lincoln, D.,574, 169Linde, F.L.,571, 11;572, 133;575, 208;576, 18;577, 109Lindemann, T.,577, 37Ling, T.Y., 573, 46Link, J.,572, 127


Link, J.M.,571, 139;572, 21;575, 190Linn, S.L.,574, 169Linnemann, J.,574, 169Lipka, K., 577, 37Lipkin, H.J.,575, 249Lipniacka, A.,576, 29Lipton, R.,574, 169Lista, L.,571, 11;572, 133;575, 208;576, 18;577, 109Litov, L., 576, 43Litvinenko, V.N.,574, 8Litvinov, Yu.A., 573, 80Liu, T., 573, 193Liu, X., 573, 46Liu, Y., 575, 55Liu, Z.A., 571, 11;572, 133;575, 208;576, 18;577, 109Lloyd, S.L.,572, 8; 577, 18, 93Löbner, K.E.G.,573, 80Loebinger, F.K.,572, 8; 577, 18, 93Lohmann, W.,571, 11;572, 133;575, 208;576, 18;577, 109Löhr, B.,573, 46Lohrmann, E.,573, 46Loizides, J.H.,573, 46Long, K.R.,573, 46Longhin, A.,573, 46Longo, E.,571, 11;572, 133;575, 208;576, 18;577, 109Lopes, J.H.,576, 29Lopes Pegna, D.,571, 139;572, 21;575, 190Lopez, A.M.,571, 139;572, 21;575, 190Lopez, J.M.,576, 29Lorenzon, W.,577, 37Loukas, D.,576, 29Loverre, P.F.,575, 198Lu, D., 575, 55Lü, H., 576, 219Lu, J.,572, 8; 577, 18, 37, 93Lu, Y.S.,571, 11;572, 133;575, 208;576, 18;577, 109Lübelsmeyer, K.,577, 109Lubrano, P.,576, 43Luci, C.,571, 11;572, 133;575, 208;576, 18;577, 109Lucotte, A.,574, 169Ludovici, L., 575, 198Ludwig, J.,572, 8; 577, 18, 93Lueking, L.,574, 169Luiggi, E.,571, 139;572, 21;575, 190Lukina, O.Yu.,573, 46Luminari, L.,571, 11;572, 133;575, 208;576, 18;577, 109Lundstedt, C.,574, 169Luo, C.,574, 169Luo, Y., 576, 297Lupi, A., 573, 46Lustermann, W.,571, 11;572, 133;575, 208;576, 18;577, 109Lutz, P.,576, 29Lyons, L.,576, 29

Ma, B.-Q.,574, 35, 217Ma, W.-G.,571, 85

Ma, W.G.,571, 11;572, 133;575, 208;576, 18;577, 109Maalampi, J.,574, 162Maartens, R.,574, 141Machado, A.A.,575, 190Machleidt, R.,576, 265Maciel, A.K.A.,574, 169MacNaughton, J.,576, 29Macpherson, A.,572, 8; 577, 18, 93Madaras, R.J.,574, 169Maddox, E.,573, 46Mader, W.,572, 8; 577, 18, 93Madigozhin, D.,576, 43Maeda, K.,571, 21Maeno, T.,577, 10Magill, S.,573, 46Magnin, J.,571, 139;572, 21;575, 190Maier, A.,576, 43Maier-Komor, P.,571, 29Maiheu, B.,577, 37Majerotto, W.,572, 56Makida, Y.,577, 10Makins, N.C.R.,577, 37Maklioueva, I.,575, 198Malek, A.,576, 29Malgeri, L.,571, 11;572, 133;575, 208;576, 18;577, 109Malik, F.B.,571, 45Malinin, A., 571, 11;572, 133;575, 208;576, 18;577, 109Maltezos, S.,576, 29Malvezzi, S.,571, 139;572, 21;575, 190Malyshev, V.L.,574, 169Malyshev, V.M.,573, 63Maña, C.,571, 11;572, 133;575, 208;576, 18;577, 109Manankov, V.,574, 169Mandl, F.,576, 29Mangano, M.L.,575, 268Mangeol, D.,577, 109Mankel, R.,573, 46Mannarelli, M.,575, 181Mannel, Th.,571, 75;572, 171Mannelli, I.,576, 43Mans, J.,571, 11;572, 133;575, 208;576, 18;577, 109Mao, H.S.,574, 169Marcellini, S.,572, 8; 577, 18, 93Marchesini, G.,575, 37Marchetto, F.,576, 43Marco, J.,576, 29Marco, R.,576, 29Marechal, B.,576, 29Marel, G.,576, 43Marfatia, D.,576, 303Margoni, M.,576, 29Margotti, A.,573, 46Marianski, B.,577, 37Marin, J.-C.,576, 29Marini, G.,573, 46


Mariotti, C.,576, 29Markou, A.,576, 29Markytan, M.,576, 43Marotta, A.,575, 198Marotta, V.,571, 250Marouelli, P.,576, 43Marrakchi, A.L.,574, 89Marshall, T.,574, 169Martelli, F.,576, 43Martin, A.J.,572, 8; 577, 18, 93Martin, J.F.,573, 46Martin, J.P.,571, 11;572, 133;575, 208;576, 18;577, 109Martin, M.I., 574, 169Martinez-Rivero, C.,576, 29Martini, M., 576, 43Marukyan, H.,577, 37Marzano, F.,571, 11;572, 133;575, 208;576, 18;577, 109Masetti, G.,572, 8; 577, 18, 93Masetti, L.,576, 43Mashimo, T.,572, 8; 577, 18, 93Masik, J.,576, 29Maslennikov, A.L.,573, 63Masoli, F.,577, 37Massafferri, A.,571, 139;572, 21;575, 190Mastroberardino, A.,573, 46Mastroyiannopoulos, N.,576, 29Matorras, F.,576, 29Matsui, N.,577, 10Matsumoto, H.,577, 10Matsunaga, H.,577, 10Matsuzawa, K.,573, 46Matteuzzi, C.,576, 29Mättig, P.,572, 8; 577, 18, 93Mattingly, M.C.K.,573, 46Mauritz, K.,574, 169Mayorov, A.A.,574, 169Mazumdar, A.,573, 5Mazumdar, K.,571, 11, 184;572, 133;575, 208;576, 18;577, 109Mazzucato, E.,576, 43Mazzucato, F.,576, 29Mazzucato, M.,576, 29McCarthy, R.,574, 169McCubbin, N.A.,573, 46McDonald, W.J.,572, 8; 577, 18, 93McKenna, J.,572, 8; 577, 18, 93McMahon, T.,574, 169McMahon, T.J.,572, 8; 577, 18, 93McNeil, R.R.,571, 11;572, 133;575, 208;576, 18;577, 109Mc Nulty, R.,576, 29McPherson, R.A.,572, 8; 577, 18, 93Meijers, F.,572, 8; 577, 18, 93Meinhard, H.,575, 198Meissner, K.A.,574, 319Meister, M.,576, 55Melanson, H.L.,574, 169

Mele, S.,571, 11;572, 133;575, 208;576, 18;577, 109Melic, B.,571, 75;572, 171Meljanac, S.,573, 202Mellado, B.,573, 46Melzer, O.,575, 198Melzer-Pellmann, I.-A.,573, 46Menary, S.,573, 46Menasce, D.,571, 139;572, 21;575, 190Mendez, H.,571, 139;572, 21;575, 190Menges, W.,572, 8; 577, 18, 93Menichetti, E.,576, 43Menze, D.,572, 127Merkin, M., 574, 169Merlo, M.M., 571, 139;572, 21;575, 190Merola, L.,571, 11;572, 133;575, 208;576, 18;577, 109Meroni, C.,576, 29Merritt, F.S.,572, 8; 577, 18, 93Merritt, K.W., 574, 169Mes, H.,572, 8; 577, 18, 93Meschini, M.,571, 11;572, 133;575, 208;576, 18;577, 109Meshkov, O.I.,573, 63Messina, M.,575, 198Metlica, F.,573, 46Metz, A.,574, 225Metzger, W.J.,571, 11;572, 133;575, 208;576, 18;577, 109Mexner, V.,577, 37Meyer, U.,573, 46Meyer, W.T.,576, 29Meyners, N.,577, 37Mezzadri, M.,571, 139;572, 21;575, 190Miao, C.,574, 169Micheli, J.,575, 256Michelini, A., 572, 8; 577, 18, 93Michetti, A., 576, 43Miettinen, H.,574, 169Migliore, E.,576, 29Migliozzi, P.,575, 198Mihalcea, D.,574, 169Mihara, S.,572, 8; 577, 18, 93Mihul, A., 571, 11;572, 133;575, 208;576, 18;577, 109Mikenberg, G.,572, 8; 577, 18, 93Mikhailov, S.F.,574, 8Mikloukho, O.,577, 37Mikulec, I., 576, 43Milcent, H.,571, 11;572, 133;575, 208;576, 18;577, 109Milekovic, M., 573, 202Milite, M., 573, 46Miller, C.A., 577, 37Miller, D.J.,572, 8; 577, 18, 93Mimura, Y.,575, 66Minowa, M.,571, 132;572, 145Mirabelli, G.,571, 11;572, 133;575, 208;576, 18;577, 109Mirea, A.,573, 46Mishnev, S.E.,573, 63Mishustin, I.N.,575, 229


Mitaroff, W., 576, 29Mitchell, R.,571, 139;572, 21;575, 190Mitra, P.,573, 109Miuchi, K., 572, 145Miyachi, Y., 577, 37Miyanishi, M.,575, 198Mjoernmark, U.,576, 29Mnich, J.,571, 11;572, 133;575, 208;576, 18;577, 109Mo, X.H., 574, 41Moa, T.,576, 29Moch, M.,576, 29Moed, S.,572, 8; 577, 18, 93Moenig, K.,576, 29Mohanty, G.B.,571, 11;572, 133;575, 208;576, 18;577, 109Mohr, W.,572, 8; 577, 18, 93Mokhov, N.,574, 169Molokanova, N.,576, 43Monaco, V.,573, 46Mondal, A.S.,571, 45Mondal, N.K.,574, 169Monge, R.,576, 29Monnier, E.,576, 43Montenegro, J.,576, 29Montgomery, H.E.,574, 169Moore, R.W.,574, 169Moosbrugger, U.,576, 43Moraes, D.,576, 29Morales Morales, C.,576, 43Moreno, S.,576, 29Moretti, S.,571, 184Morettini, P.,576, 29Mori, T., 572, 8; 577, 18, 93Morillon, B., 575, 221Morimatsu, O.,571, 61Moritz, M., 573, 46Moroni, L., 571, 139;572, 21;575, 190Moshin, P.Yu.,576, 227Moss, I.G.,577, 71Mourad, J.,575, 115Moutarde, H.,575, 256Muanza, G.S.,571, 11;572, 133;575, 208;576, 18;577, 109Muccifora, V.,577, 37Muchnoi, N.Yu.,573, 63Muciaccia, M.T.,575, 198Mueller, A.H.,575, 37Mueller, U.,576, 29Muenich, K.,576, 29Muijs, A.J.M.,571, 11;572, 133;575, 208;576, 18;577, 109Mulders, M.,576, 29Mülsch, D.,575, 349Munday, D.J.,576, 43Mundim, L.,576, 29Münzenberg, G.,573, 80Murayama, H.,573, 94Murray, W.,576, 29

Muryn, B.,576, 29Musakhanov, M.M.,572, 181Musgrave, B.,573, 46Musicar, B.,571, 11;572, 133;575, 208;576, 18;577, 109Musiri, S.,576, 309Musy, M.,571, 11;572, 133;575, 208;576, 18;577, 109Mutaf, Y.D., 574, 169Müther, H.,576, 68Mutter, A.,572, 8; 577, 18, 93Myatt, G.,576, 29Myklebust, T.,576, 29Myo, T., 576, 281Myung, Y.S.,574, 289Myyryläinen, M.,574, 162

Naddeo, A.,571, 250Nagai, K.,572, 8; 577, 18, 93Nagaitsev, A.,577, 37Nagano, K.,573, 46Nagy, E.,574, 169Nagy, S.,571, 11;572, 133;575, 208;576, 18;577, 109Naik, H.,576, 260Nakamura, A.,571, 223Nakamura, I.,572, 8; 577, 18, 93Nakamura, K.,575, 198Nakamura, M.,575, 198Nakano, T.,575, 198Nandi, S.,575, 66Nang, F.,574, 169Nania, R.,573, 46Nanjo, H.,572, 8; 577, 18, 93Napolitano, M.,571, 11;572, 133;575, 208;576, 18;577, 109Nappi, A.,576, 43Nappi, E.,577, 37Nara, Y.,577, 54Narain, M.,574, 169Narasimham, V.S.,574, 169Narayan, M.,571, 209Narayanan, R.,574, 65Nardulli, G.,575, 181Narita, K.,575, 198Naryshkin, Y.,577, 37Nason, P.,575, 268Nass, A.,577, 37Nassiakou, M.,576, 29Natale, S.,571, 11;572, 133;575, 208;576, 18;577, 109Naumann, N.A.,574, 169Naumenkov, A.I.,573, 63Navarria, F.,576, 29Navarro-Salas, J.,574, 309Nawrocki, K.,576, 29Nayak, R.R.,575, 325Nazaryan, V.,573, 101Neal, H.A.,572, 8; 574, 169;577, 18, 93Nedel, D.L.,573, 217


Neergaard, G.,575, 229Neergård, K.,572, 159Nefediev, A.V.,573, 131Negodaev, M.,577, 37Negret, J.P.,574, 169Nehring, M.,571, 139;572, 21;575, 190Nelson, R.O.,575, 221Nersessian, A.,574, 121Nessi-Tedaldi, F.,571, 11;572, 133;575, 208;576, 18;577, 109Neuberger, H.,574, 65Neuerburg, W.,572, 127Neuhofer, G.,576, 43Newman, H.,571, 11;572, 133;575, 208;576, 18;577, 109Nguyen, C.N.,573, 46Nicolaidou, R.,576, 29Nierste, U.,576, 173Niessen, T.,577, 109Nigro, A., 573, 46Nikitin, S.A., 573, 63Nikolaev, I.B.,573, 63Nikolenko, M.,576, 29Nilsson, T.,576, 55Ning, Y., 573, 46Nisati, A.,571, 11;572, 133;575, 208;576, 18;577, 109Nishimura, J.,577, 10Nishimura, S.,571, 21Nishimura, T.,573, 46Nishino, H.,572, 91Nisius, R.,572, 8; 577, 18, 93Niu, K., 575, 198Niwa, K., 575, 198Nojiri, S., 571, 1; 574, 1; 576, 5Nolden, F.,573, 80Nomerotski, A.,574, 169Nonaka, N.,575, 198Norton, A.,576, 43Notz, D.,573, 46Novak, T.,572, 133;575, 208;576, 18Novikov, V.P.,574, 14Novikov, Yu.N.,573, 80Nowak, H.,571, 11;572, 133;575, 208;576, 18;577, 109Nowak, R.J.,573, 46Nowak, W.-D.,577, 37Nozaki, M.,577, 10Nunnemann, T.,574, 169Nyman, G.,576, 55

Oblakowska-Mucha, A.,576, 29Obraztsov, V.,576, 29Obraztsov, V.F.,574, 14Oda, I.,571, 235Odintsov, S.D.,571, 1; 574, 1; 576, 5O’Donnell, J.M.,575, 221O’Donnell, P.J.,572, 164Oeckl, R.,575, 318

Offer, M., 571, 29Ofierzynski, R.,571, 11;572, 133;575, 208;576, 18;577, 109Oganessyan, K.,577, 37Ogawa, S.,575, 198Ogawa, Y.,571, 21Oguri, V.,574, 169Oh, A.,572, 8; 577, 18, 93Oh, B.Y.,573, 46Oh, S.,576, 165Ohnishi, T.,571, 21Ohsuga, H.,577, 37Ohtsuka, A.,573, 209Oi, M., 576, 75Okada, Y.,575, 300Okpara, A.,572, 8; 577, 18, 93Okusawa, T.,575, 198Oldeman, R.G.C.,575, 198Olive, K.A., 573, 162Olivier, B., 574, 169Olkiewicz, K.,573, 46Olshevski, A.,576, 29O’Neale, S.W.,572, 8; 577, 18, 93O’Neil, D., 574, 169Onengüt, G.,575, 198Onofre, A.,576, 29Onuchin, A.P.,573, 63Ootani, W.,572, 145Ootuka, Y.,572, 145OPAL Collaboration,572, 8; 577, 18, 93Orava, R.,576, 29Oreglia, M.J.,572, 8; 577, 18, 93O’Reilly, B., 571, 139;572, 21;575, 190Oreshkin, S.B.,573, 63Organtini, G.,571, 11;572, 133;575, 208;576, 18;577, 109Orito, S.,572, 8; 577, 10, 18, 93Oshima, N.,574, 169Osterberg, K.,576, 29Ostrick, M.,572, 127Ouraou, A.,576, 29Owen, D.A.,574, 197Oyamatsu, K.,576, 273Oyanguren, A.,576, 29Ozawa, A.,571, 21

Pac, M.Y.,573, 46Padhi, S.,573, 46Padley, P.,574, 169Paganis, S.,573, 46Paganoni, M.,576, 29Pahl, C.,572, 8; 577, 18, 93Paiano, S.,576, 29Pakhotin, Yu.A.,573, 63Pal, I.,571, 11;572, 133;575, 208;576, 18Pal, P.B.,573, 147Pal, S.,574, 21


Palacios, J.P.,576, 29Palka, H.,576, 29Pallua, S.,571, 217Palmonari, F.,573, 46Palomares, C.,571, 11;572, 133;575, 208;576, 18;577, 109Pan, F.,576, 297Pandoulas, D.,577, 109Panigrahi, K.L.,575, 325Panman, J.,575, 198Pantea, D.,571, 139;572, 21;575, 190Panzer-Steindel, B.,576, 43Paolucci, P.,571, 11;572, 133;575, 208;576, 18;577, 109Papadopoulos, I.M.,575, 198Papadopoulou, Th.D.,576, 29Papageorgiou, K.,574, 169Pape, L.,576, 29Paramatti, R.,571, 11;572, 133;575, 208;576, 18;577, 109Parashar, N.,574, 169Parenti, A.,573, 46Paris, A.,571, 139;572, 21;575, 190Park, H.,571, 139;572, 21;575, 190Park, I.H.,573, 46Park, J.,572, 81Parkes, C.,576, 29Parodi, F.,576, 29Partridge, R.,574, 169Parua, N.,574, 169Parzefall, U.,576, 29Paschos, E.A.,574, 232Pashnev, A.,575, 137Passaleva, G.,571, 11;572, 133;575, 208;576, 18;577, 109Passeri, A.,576, 29Passon, O.,576, 29Pastrone, N.,576, 43Pastsjak, A.R.,574, 14Pásztor, G.,572, 8; 577, 18, 93Patel, M.,576, 43Patel, S.,573, 46Pater, J.R.,572, 8; 577, 18, 93Patricelli, S.,571, 11;572, 133;575, 208;576, 18;577, 109Patrick, G.N.,572, 8; 577, 18, 93Patwa, A.,574, 169Patyk, Z.,573, 80Paul, E.,572, 127;573, 46Paul, T.,571, 11;572, 133;575, 208;576, 18;577, 109Pauluzzi, M.,571, 11;572, 133;575, 208;576, 18;577, 109Paus, C.,571, 11;572, 133;575, 208;576, 18;577, 109Pauss, F.,571, 11;572, 133;575, 208;576, 18;577, 109Pavel, N.,573, 46Pawlak, J.M.,573, 46Pedace, M.,571, 11;572, 133;575, 208;576, 18;577, 109Pedrini, D.,571, 139;572, 21;575, 190Peleganchuk, S.V.,573, 63Pelfer, P.G.,573, 46Pellegrino, A.,573, 46

Pène, O.,575, 256Pensotti, S.,571, 11;572, 133;575, 208;576, 18;577, 109Pepe, I.M.,571, 139;572, 21;575, 190Pepe, M.,576, 43Peralta, L.,576, 29Pereira, S.H.,577, 76Perepelitsa, V.,576, 29Perret-Gallix, D.,571, 11;572, 133;575, 208;576, 18;577, 109Perrotta, A.,576, 29Peschanski, R.,575, 30;576, 90Pesci, A.,573, 46Pesen, E.,575, 198Peters, A.,576, 43Peters, O.,574, 169Petersen, B.,571, 11;572, 133;575, 208;576, 18;577, 109Pétroff, P.,574, 169Petrolini, A.,576, 29Petrosyan, S.S.,573, 63Petrov, A.Yu.,577, 83Petrov, V.V.,573, 63Petrucci, F.,576, 43Petrucci, M.C.,573, 46;576, 43Peyaud, B.,576, 43Phillips, J.,576, 97Piao, Y.-S.,576, 12Piccini, M.,576, 43Piccolo, D.,571, 11;572, 133;575, 208;576, 18;577, 109Pickert, N.,577, 37Piedra, J.,576, 29Piegaia, R.,574, 169Pierazzini, G.,576, 43Pierella, F.,571, 11;572, 133;575, 208;576, 18;577, 109Pieri, L.,576, 29Pierre, F.,576, 29Pietroni, M.,571, 115Pilcher, J.E.,572, 8; 577, 18, 93Pimenta, M.,576, 29Pinayev, I.V.,574, 8Pinfold, J.,572, 8; 577, 18, 93Pioppi, M.,571, 11;572, 133;575, 208;576, 18;577, 109Piotrzkowski, K.,573, 46Piotto, E.,576, 29Piroué, P.A.,571, 11;572, 133;575, 208;576, 18;577, 109Pistillo, C.,575, 198Pistolesi, E.,571, 11;572, 133;575, 208;576, 18;577, 109Pittoni, G.L.,575, 198Plane, D.E.,572, 8; 577, 18, 93Plucinski, P.,573, 46Plyaskin, V.,571, 11;572, 133;575, 208;576, 18;577, 109Plyushchay, M.S.,572, 202Podobnik, T.,576, 29Pohl, M.,571, 11;572, 133;575, 208;576, 18;577, 109Poireau, V.,576, 29Pojidaev, V.,571, 11;572, 133;575, 208;576, 18;577, 109Pokrovskiy, N.S.,573, 46


Pol, M.E.,576, 29Poli, B.,572, 8; 577, 18, 93Polikarpov, M.I.,574, 136Polini, A., 573, 46Polok, G.,576, 29Polok, J.,572, 8; 577, 18, 93Poluektov, A.O.,573, 63Polunin, A.A.,573, 63Polyakov, V.A.,574, 14Polyarush, A.Yu.,574, 14Polycarpo, E.,571, 139;572, 21;575, 190Polychronakos, A.P.,574, 296Ponsot, B.,575, 131Pontoglio, C.,571, 139;572, 21;575, 190Pooth, O.,572, 8; 577, 18, 93Pope, B.G.,574, 169Porod, W.,573, 153Poropat, P.,576, 29Posocco, M.,573, 46Pospelov, G.E.,573, 63Postma, M.,573, 5Potashov, S.,577, 37Pothier, J.,571, 11;572, 133;575, 208;576, 18;577, 109Potrebenikov, Yu.,576, 43Potterveld, D.H.,577, 37Pozdniakov, V.,576, 29Praszałowicz, M.,575, 234Pratt, S.,574, 21Prelz, F.,571, 139;572, 21;575, 190Prester, P.,571, 217Prezado, Y.,576, 55Prokofiev, D.,571, 11;572, 133;575, 208;576, 18;577, 109Prokofiev, D.O.,577, 109Proskuryakov, A.S.,573, 46Prosper, H.B.,574, 169Protopopescu, S.,574, 169Protopopov, I.Ya.,573, 63Prozorov, A.,574, 180Przybycien, M., 572, 8; 573, 46;577, 18, 93Przybycien, M.B.,574, 169Pukhaeva, N.,576, 29Pullia, A.,576, 29

Qi, S.,576, 289Qian, J.,574, 169Quadt, A.,572, 8; 577, 18, 93Quandt, M.,572, 196Quartieri, J.,571, 11;572, 133;575, 208;576, 18;577, 109Quinones, J.,571, 139;572, 21;575, 190

Rabbertz, K.,572, 8; 577, 18, 93Radicioni, E.,575, 198Radon, T.,573, 80Rahal-Callot, G.,571, 11;572, 133;575, 208;576, 18;577, 109Rahaman, M.A.,571, 11;572, 133;575, 208;576, 18;577, 109

Rahimi, A.,571, 139;572, 21;575, 190Raics, P.,571, 11;572, 133;575, 208;576, 18;577, 109Raidal, M.,575, 75Raithel, M.,577, 37Raja, N.,571, 11;572, 133;575, 208;576, 18;577, 109Raja, R.,574, 169Rajagopalan, S.,574, 169Rajpoot, S.,572, 91Rakers, S.,576, 253Ramelli, R.,571, 11;572, 133;575, 208;576, 18;577, 109Rames, J.,576, 29Ramirez, J.E.,571, 139;572, 21;575, 190Ramler, L.,576, 29Rancoita, P.G.,571, 11;572, 133;575, 208;576, 18;577, 109Ranieri, R.,571, 11;572, 133;575, 208;576, 18;577, 109Rapidis, P.A.,574, 169Raspereza, A.,571, 11;572, 133;575, 208;576, 18;577, 109Rastelli, L.,575, 111Rathke, A.,571, 229Ratti, S.P.,571, 139;572, 21;575, 190Ratz, M.,574, 156Rautenberg, J.,573, 46Raval, A.,573, 46Rawlinson, A.A.,573, 86Razis, P.,571, 11;572, 133;575, 208;576, 18;577, 109Read, A.,576, 29Reay, N.W.,574, 169Rebbi, C.,574, 75Rebecchi, P.,576, 29Redlich, K.,571, 36, 67Reeder, D.D.,573, 46Reggiani, D.,577, 37Rehn, J.,576, 29Reid, D.,576, 29Reimer, P.E.,577, 37Reinhardt, R.,576, 29Reis, H.C.,575, 151Reischl, A.,577, 37Rembser, C.,572, 8; 577, 18, 93Ren, D.,571, 11;572, 133;575, 208;576, 18;577, 109Ren, Z.,573, 46Renkel, P.,572, 8; 577, 18, 93Renner, R.,573, 46Renton, P.,576, 29Reolon, A.R.,577, 37Repond, J.,573, 46Rescigno, M.,571, 11;572, 133;575, 208;576, 18;577, 109Reucroft, S.,571, 11;572, 133;574, 169;575, 208;576, 18;

577, 109Reyes, M.,571, 139;572, 21;575, 190Ribeiro, A.A.,577, 83Riccardi, C.,571, 139;572, 21;575, 190Ricciardi, S.,575, 198Richard, F.,576, 29Ridel, M.,574, 169Ridky, J.,576, 29


Riedl, C.,577, 37Riemann, S.,571, 11;572, 133;575, 208;576, 18;577, 109Righini, P.,575, 198Riisager, K.,576, 55Riittinen, J.,574, 162Rijssenbeek, M.,574, 169Riles, K.,571, 11;572, 133;575, 208;576, 18;577, 109Rim, C.,574, 111Riotto, A.,571, 115Riska, D.O.,575, 242Rith, K., 577, 37Riveline, M.,573, 46Rivelles, V.O.,577, 137Rivero, M.,576, 29Rizatdinova, F.,574, 169Robins, S.,573, 46Rochman, D.,575, 221Rockwell, T.,574, 169Rodrigo, G.,576, 135Rodrigues, E.,573, 46Rodriguez, D.,576, 29Rodriguez, E.,574, 283Rodríguez-Quintero, J.,575, 256Roe, B.P.,571, 11;572, 133;575, 208;576, 18;577, 109Rolke, W.A.,572, 21Romano, G.,575, 198Romanovsky, V.I.,574, 14Romero, A.,576, 29Romero, L.,571, 11;572, 133;575, 208;576, 18;577, 109Ronchese, P.,576, 29Roney, J.M.,572, 8; 577, 18, 93Ronjin, V.M., 574, 14Rosa, G.,575, 198Rosati, S.,572, 8; 577, 18, 93Rosca, A.,571, 11;572, 133;575, 208;576, 18;577, 109Rosenberg, E.,576, 29Rosenbleck, C.,571, 11;572, 133;575, 208;576, 18;577, 109Rosenfeld, R.,575, 151Rosier-Lees, S.,571, 11;572, 133;575, 208;576, 18;577, 109Rosner, G.,577, 37Rosner, J.L.,572, 43Ross, G.G.,574, 239;575, 279Rostomyan, A.,577, 37Roth, M.,575, 290Roth, S.,571, 11;572, 133;575, 208;576, 18;577, 109Roudeau, P.,576, 29Roux, B.,572, 133;577, 109Rovelli, T.,576, 29Rovere, M.,571, 139;572, 21;575, 190Roy, D.P.,571, 184;574, 232Roy, S.,576, 199Royon, C.,574, 169Rozanov, A.,575, 198Rozen, Y.,572, 8; 577, 18, 93Rubacek, L.,577, 37

Rubakov, V.,574, 75Rubin, P.,576, 43Rubinov, P.,574, 169Rubio, J.A.,571, 11;572, 133;575, 208;576, 18;577, 109Ruchti, R.,574, 169Ruffini, R.,573, 33Ruggieri, M.,575, 181Ruggiero, G.,571, 11;572, 133;575, 208;576, 18, 43;577, 109Ruhlmann-Kleider, V.,576, 29Ruivo, M.C.,577, 129Ruiz-Lapuente, P.,574, 149Ruiz Arriola, E.,574, 57Runge, K.,572, 8; 577, 18, 93Ruppert, J.,575, 85Ruspa, M.,573, 46Ryabtchikov, D.,576, 29Ryckbosch, D.,577, 37Rykaczewski, H.,571, 11;572, 133;575, 208;576, 18;577, 109

Sabirov, B.M.,574, 169Sacchi, R.,573, 46Sacco, R.,576, 43Sachs, K.,572, 8; 577, 18, 93Sadovsky, A.,576, 29Saeki, T.,572, 8; 577, 18, 93Saidi, E.H.,575, 100Saito, K.,575, 4Saitta, B.,575, 198Sajot, G.,574, 169Sakharov, A.,571, 11;572, 133;575, 208;576, 18;577, 109Sala, S.,571, 139;572, 21;575, 190Salam, G.P.,576, 143Salati, P.,571, 121Salehi, H.,573, 46Salgado, P.,574, 283Salicio, J.,571, 11;572, 133;575, 208;576, 18;577, 109Salmi, L.,576, 29Salomatin, Y.,577, 37Salt, J.,576, 29Samanta, C.,571, 21Samsarov, A.,573, 202Sanchez, E.,571, 11;572, 133;575, 208;576, 18;577, 109Sánchez-Hernández, A.,571, 139;572, 21;575, 190Sanders, M.P.,577, 109Sanjiev, I.,577, 37Santacesaria, R.,575, 198Santoro, A.,574, 169Santoso, Y.,573, 162Sanuki, T.,577, 10Sanz, V.,576, 107SAPHIR Collaboration,572, 127Sarandy, M.S.,574, 325Sarangi, S.,573, 181Sarantites, D.G.,571, 155Saremi, S.,571, 11;572, 133;575, 208;576, 18;577, 109


Sarkar, S.,571, 11;572, 133;575, 208;576, 18;577, 109Sarkar, U.,573, 147Sarker, M.S.I.,571, 45Sarkisyan, E.K.G.,572, 8; 577, 18, 93Sartorelli, G.,573, 46Sasaki, M.,577, 10Sato, M.,575, 126Sato, O.,575, 198Sato, Y.,575, 198Satta, A.,575, 198Satuła, W.,572, 152Saull, P.R.B.,573, 46Savin, A.A.,573, 46Savin, I.,577, 37Savinov, G.A.,573, 63Savoy-Navarro, A.,576, 29Savrié, M.,576, 43Sawyer, L.,574, 169Sawyer, R.F.,573, 86Saxon, D.H.,573, 46Scandurra, M.,572, 196Scarlett, C.,577, 37Scarpa, M.,576, 43Schäfer, A.,577, 37Schäfer, C.,571, 11;572, 133;575, 208;576, 18;577, 109Schagen, S.,573, 46Schaile, A.D.,572, 8; 577, 18, 93Schaile, O.,572, 8; 577, 18, 93Schamberger, R.D.,574, 169Scharff-Hansen, P.,572, 8; 577, 18, 93Schegelsky, V.,571, 11;572, 133;575, 208;576, 18;577, 109Scheidenberger, C.,573, 80Schellman, H.,574, 169Scherer, S.,575, 11, 85Schieck, J.,572, 8; 577, 18, 93Schielke, S.,571, 29Schienbein, I.,574, 232Schill, C.,577, 37Schindler, M.R.,575, 11Schioppa, M.,573, 46Schlenstedt, S.,573, 46Schmidke, W.B.,573, 46Schmidt, I.,574, 35Schmidt-Kaerst, S.,577, 109Schmitz, D.,577, 109Schneekloth, U.,573, 46Schnell, G.,577, 37Schopper, H.,571, 11;572, 133;575, 208;576, 18;577, 109Schörner-Sadenius, T.,572, 8; 577, 18, 93Schotanus, D.J.,571, 11;572, 133;575, 208;576, 18;577, 109Schröder, M.,572, 8; 577, 18, 93Schuck, P.,576, 68Schulday, I.,572, 127Schüler, K.P.,577, 37Schumacher, M.,572, 8; 577, 18, 93

Schwartzman, A.,574, 169Schwenk, A.,576, 265Schwering, G.,577, 109Schwetz, T.,577, 120Schwick, C.,572, 8; 577, 18, 93Schwickerath, U.,576, 29Schwille, W.J.,572, 127Schwind, A.,577, 37Sciacca, C.,571, 11;572, 133;575, 208;576, 18;577, 109Sciulli, F.,573, 46Scopel, S.,576, 189Scott, J.,573, 46Scott, W.G.,572, 8; 577, 18, 93Scotto Lavina, L.,575, 198Sedrakian, A.,576, 68Seele, J.,577, 37Segar, A.,576, 29Segoni, I.,571, 139;572, 21;575, 190Seidl, R.,577, 37Seitz, B.,577, 37Sekiya, H.,571, 132;572, 145Sekulin, R.,576, 29Selonke, F.,573, 46Semikoz, D.V.,577, 1Sen, A.A.,575, 172Sen, S.,574, 93Sen Gupta, H.M.,571, 45Serin-Zeyrek, M.,575, 198Servoli, L.,571, 11;572, 133;575, 208;576, 18;577, 109Setare, M.R.,573, 173Seuster, R.,572, 8; 577, 18, 93Sever, R.,575, 198Shabalina, E.,574, 169Shamanov, V.,575, 198Shamov, A.G.,573, 63Shanidze, R.,577, 37Shapiro, I.L.,574, 149Sharon, Y.Y.,571, 29Shatilov, D.N.,573, 63Shcheglova, L.M.,573, 46Sheaff, M.,571, 139;572, 21;575, 190Shearer, C.,577, 37Shears, T.G.,572, 8; 577, 18, 93Sheldon, P.D.,571, 139;572, 21;575, 190Shelikhov, V.I.,574, 14Shen, B.C.,572, 8; 577, 18, 93Sherwood, P.,572, 8; 577, 18, 93Shevchenko, S.,571, 11;572, 133;575, 208;576, 18;577, 109Shibata, T.-A.,577, 37Shibuya, H.,575, 198Shikaze, Y.,577, 10Shimizu, Y.,571, 132, 163;572, 145;576, 152Shivarov, N.,571, 11;572, 133;575, 208;576, 18;577, 109Shivpuri, R.K.,574, 169Shoutko, V.,571, 11;572, 133;575, 208;576, 18;577, 109


Shpakov, D.,574, 169Shumilov, E.,571, 11;572, 133;575, 208;576, 18;577, 109Shupe, M.,574, 169Shusharo, A.I.,573, 63Shutov, V.,577, 37Shvorob, A.,571, 11;572, 133;575, 208;576, 18;577, 109Shwartz, B.A.,573, 63Sick, I.,576, 62Sidorov, V.A.,573, 63Sidwell, R.A.,574, 169Siebel, M.,576, 29Siedenburg, T.,577, 109Simak, V.,574, 169Simani, M.C.,571, 50;577, 37Simone, S.,575, 198Simonov, E.A.,573, 63Simula, S.,574, 189Sinram, K.,577, 37Siopsis, G.,576, 309Sirignano, C.,575, 198Sirodeev, R.Kh.,574, 14Siroli, G.,572, 8; 577, 18, 93Sirotenko, V.,574, 169Sisakian, A.,576, 29Skillicorn, I.O.,573, 46Skovpen, Yu.I.,573, 63Skrinsky, A.N.,573, 63Skuja, A.,572, 8; 577, 18, 93Slater, M.W.,576, 43Slattery, P.,574, 169Słominski, W.,573, 46Smadja, G.,576, 29Smedbäck, M.,574, 296Smirnov, N.E.,574, 14Smirnova, O.,576, 29Smith, A.M.,572, 8; 577, 18, 93Smith, R.P.,574, 169Smith, W.H.,573, 46Snow, G.R.,574, 169Snow, J.,574, 169Snyder, S.,574, 169Soares, M.,573, 46Sobie, R.,572, 8; 577, 18, 93Sobotka, L.G.,571, 155Sobreiro, R.F.,574, 325Sochichiu, C.,571, 92;574, 105Sohler, D.,576, 253Sokolov, A.,576, 29Sokolov, A.A.,574, 14Solà, J.,574, 149Solano, A.,573, 46Söldner-Rembold, S.,572, 8; 577, 18, 93Solomon, J.,574, 169Son, D.,571, 11;572, 133;573, 46;575, 208;576, 18;577, 109Song, J.S.,575, 198

Song, Y.,574, 169Sopczak, A.,576, 29Sorella, S.P.,574, 325Sorín, V.,574, 169Sorrentino, S.,575, 198Sosebee, M.,574, 169Sosnovtsev, V.,573, 46Sosnowski, R.,576, 29Sotnikova, N.,574, 169Souga, C.,571, 11;572, 133;575, 208;576, 18Soukharev, A.M.,573, 63Soustruznik, K.,574, 169Souza, M.,574, 169Sozzi, M.,576, 43Spada, F.R.,575, 198Spano, F.,572, 8; 577, 18, 93Spanos, V.C.,573, 162Spassov, T.,576, 29Speidel, K.-H.,571, 29Spillantini, P.,571, 11;572, 133;575, 208;576, 18;577, 109Stachel, J.,571, 36Stadlmann, J.,573, 80Stahl, A.,572, 8; 577, 18, 93Stairs, D.G.,573, 46Stancari, M.,577, 37Stanco, L.,573, 46Stancu, Fl.,575, 242Standage, J.,573, 46Stanitzki, M.,576, 29Stanton, N.R.,574, 169Stasto, A.M.,576, 143Statera, M.,577, 37Steck, M.,573, 80Steer, D.A.,575, 115Steffens, E.,577, 37Steijger, J.J.M.,577, 37Steinbrück, G.,574, 169Steinhauser, M.,574, 258Stenson, K.,571, 139;572, 21;575, 190Stenzel, H.,577, 37Stephens, K.,572, 8; 577, 18, 93Steuer, M.,571, 11;572, 133;575, 208;576, 18;577, 109Stewart, J.,577, 37Stickland, D.P.,571, 11;572, 133;575, 208;576, 18;577, 109Stifutkin, A., 573, 46Stocchi, A.,576, 29Stöcker, H.,575, 85Stoesslein, U.,573, 46Stoker, D.,574, 169Stolin, V.,574, 169Stone, A.,574, 169Stonjek, S.,573, 46Stopa, P.,573, 46Stösslein, U.,577, 37Stoyanov, B.,571, 11;572, 133;575, 208;576, 18;577, 109


Stoyanova, D.A.,574, 169Stoynev, S.,576, 43Straessner, A.,571, 11;572, 133;575, 208;576, 18;577, 109Stramaglia, S.,575, 181Strang, M.A.,574, 169Straub, P.B.,573, 46Strauss, J.,576, 29Strauss, M.,574, 169Stremnitzer, H.,576, 184Ströhmer, R.,572, 8; 577, 18, 93Strolin, P.,575, 198Strom, D.,572, 8; 577, 18, 93Strovink, M.,574, 169Stugu, B.,576, 29Stutte, L.,574, 169Su, J.,574, 217Suchkov, S.,573, 46Suda, T.,571, 21Sudhakar, K.,571, 11;572, 133;575, 208;576, 18;577, 109Suganuma, W.,571, 132Sultanov, G.,571, 11;572, 133;575, 208;576, 18;577, 109Sumino, Y.,571, 173Sun, L.Z.,571, 11;572, 133;575, 208;576, 18;577, 109Sun, W.-M.,576, 289Sun, W.M.,573, 115Sun, Y.-B.,571, 85Sushkov, S.,571, 11;572, 133;575, 208;576, 18;577, 109Susinno, G.,573, 46Suszycki, L.,573, 46Suter, H.,571, 11;572, 133;575, 208;576, 18;577, 109Sutton, M.R.,573, 46Suzuki, J.,577, 10Suzuki, T.,571, 21Swain, J.D.,571, 11;572, 133;575, 208;576, 18;577, 109Swallow, E.,576, 43Swanson, E.S.,577, 61Syritsyn, S.N.,574, 136Szczekowski, M.,576, 29Szczepaniak, A.P.,577, 61Szeptycka, M.,576, 29Szillasi, Z.,571, 11;572, 133;575, 208;576, 18;577, 109Sznajder, A.,574, 169Sztuk, J.,573, 46Szuba, D.,573, 46Szuba, J.,573, 46Szumlak, T.,576, 29

Tabarelli, T.,576, 29Tachikawa, Y.,573, 235Taffard, A.C.,576, 29Tait, P.,577, 37Takeda, A.,572, 145Talby, M.,574, 169Talyshev, A.A.,573, 63Tanaka, H.,577, 37

Tanaka, K.,577, 10Tandler, J.,573, 46Tang, X.W.,571, 11;572, 133;575, 208;576, 18;577, 109Tanihata, I.,571, 21Tapper, A.D.,573, 46Tapper, R.J.,573, 46Tarem, S.,572, 8; 577, 18, 93Tariq, A.S.B.,571, 45Tarjan, P.,571, 11;572, 133;575, 208;576, 18;577, 109Taroian, S.,577, 37Tasevsky, M.,572, 8; 577, 18, 93Tassi, E.,573, 46Tateo, R.,573, 239Tauscher, L.,571, 11;572, 133;575, 208;576, 18;577, 109Tavakol, R.,575, 157Tawara, T.,573, 46Tawfik, A., 571, 67Taylor, J.C.,577, 76Taylor, L.,571, 11;572, 133;575, 208;576, 18;577, 109Taylor, R.J.,572, 8; 577, 18, 93Taylor, W.,574, 169Tayursky, V.A.,573, 63Tchikilev, O.G.,574, 14Tchuiko, B.,577, 37Tegenfeldt, F.,576, 29Tellili, B., 571, 11;572, 133;575, 208;576, 18;577, 109Telnov, V.I.,573, 63Tengblad, O.,576, 55Tentindo-Repond, S.,574, 169Terkulov, A.,577, 37Terrón, J.,573, 46Teuscher, R.,572, 8; 577, 18, 93Teyssier, D.,571, 11;572, 133;575, 208;576, 18;577, 109Tezuka, I.,575, 198Theußl, L.,574, 201Thomas, S.,573, 13Thomson, M.A.,572, 8; 577, 18, 93Tiecke, H.,573, 46Tikhonov, Yu.A.,573, 63Timmermans, C.,571, 11;572, 133;575, 208;576, 18;577, 109Timmermans, J.,576, 29Ting, S.C.C.,571, 11;572, 133;575, 208;576, 18;577, 109Ting, S.M.,571, 11;572, 133;575, 208;576, 18;577, 109Tinyakov, P.,574, 75Tioukov, V.,575, 198Tkabladze, A.,577, 37Tkatchev, L.,576, 29Tobe, K.,575, 66Tobin, M.,576, 29Todorovova, S.,576, 29Todyshev, K.Yu.,573, 63Tokushuku, K.,573, 46Tolun, P.,575, 198Tome, B.,576, 29Tonazzo, A.,576, 29


Tonwar, S.C.,571, 11;572, 133;575, 208;576, 18;577, 109Toothacker, W.S.,573, 46Tornow, W.,574, 8Torrence, E.,572, 8; 577, 18, 93Tortosa, P.,576, 29Toshito, T.,575, 198Tóth, J.,571, 11;572, 133;575, 208;576, 18;577, 109Toya, D.,572, 8; 577, 18, 93Tran, P.,572, 8; 577, 18, 93Travnicek, P.,576, 29Treille, D.,576, 29Trigger, I.,572, 8; 577, 18, 93Tripathi, S.M.,574, 169Trippe, T.G.,574, 169Tristram, G.,576, 29Trochimczuk, M.,576, 29Trócsányi, Z.,572, 8; 577, 18, 93Troncon, C.,576, 29Troost, J.,574, 301Trzcinski, A.,577, 37Trzhaskovskaya, M.B.,573, 80Tsenov, R.,575, 198Tsuchiya, A.,574, 301Tsujikawa, S.,574, 141Tsukerman, I.,575, 198Tsur, E.,572, 8; 577, 18, 93Tsurugai, T.,573, 46Tsushima, K.,575, 4Tsutsui, I.,573, 248Tully, C., 571, 11;572, 133;575, 208;576, 18;577, 109Tumaikin, G.M.,573, 63Tung, K.L.,571, 11;572, 133;575, 208;576, 18;577, 109Turcato, M.,573, 46Turcot, A.S.,574, 169Turluer, M.-L.,576, 29Turner-Watson, M.F.,572, 8; 577, 18, 93Tuts, P.M.,574, 169Tyapkin, I.A.,576, 29Tyapkin, P.,576, 29Tye, S.-H.H.,573, 181Tymieniecka, T.,573, 46Tytgat, M.,577, 37Tzamarias, S.,576, 29

Uddin, M.A.,571, 45Ueda, I.,572, 8; 577, 18, 93Uiterwijk, J.W.E.,575, 198Ujvári, B., 572, 8; 577, 18, 93Ukleja, A.,573, 46Ukleja, J.,573, 46Ulbricht, J.,571, 11;572, 133;575, 208;576, 18;577, 109Uribe, C.,571, 139;572, 21;575, 190Ushida, N.,575, 198Usov, Yu.V.,573, 63

Uvarov, V.,576, 29Uvarov, V.A.,574, 14

Vaandering, E.W.,571, 139;572, 21;575, 190Vafa, C.,573, 138Vairo, A., 576, 314Valdata, M.,576, 43Valente, E.,571, 11;572, 133;575, 208;576, 18;577, 109Valenti, G.,576, 29Vallage, B.,576, 43Van Dalen, J.A.,571, 11;572, 133;575, 208;576, 18;577, 109Van Dam, P.,576, 29Van Dantzig, R.,575, 198Van den Berg, A.M.,576, 253Vandenbroucke, A.,577, 37Van der Nat, P.,577, 37Van der Steenhoven, G.,577, 37Van de Vyver, B.,575, 198Van de Walle, R.T.,571, 11;572, 133;575, 208;576, 18;577, 109Van Dierendonck, D.,577, 109Van Eldik, J.,576, 29Van Gulik, R.,571, 11;572, 133;575, 208;576, 18;577, 109Vaniev, V.,574, 169Van Kooten, R.,574, 169Van Lysebetten, A.,576, 29Vannerem, P.,572, 8; 577, 18, 93Van Nieuwenhuizen, P.,574, 98Van Pee, H.,572, 127Van Remortel, N.,576, 29Van Vulpen, I.,576, 29Varelas, N.,574, 169Vargas de Usera, I.,576, 243Vasquez, R.,571, 11;572, 133;575, 208;576, 18Vázquez, F.,571, 139;572, 21;575, 190Vázquez, M.,573, 46Vegni, G.,576, 29Velasco, M.,576, 43Veloso, F.,576, 29Velthuis, J.J.,573, 46Veltri, M., 576, 43Veneziano, G.,574, 319Venugopalan, R.,577, 54Venus, W.,576, 29Verdier, P.,576, 29Verschelde, H.,574, 325Vértesi, R.,572, 8; 577, 18, 93Verzi, V., 576, 29Verzocchi, M.,572, 8; 577, 18, 93Veszpremi, V.,571, 11;572, 133;575, 208;576, 18;577, 109Vesztergombi, G.,571, 11;572, 133;575, 208;576, 18;577, 109Vetlitsky, I., 571, 11;572, 133;575, 208;576, 18;577, 109Vetterli, M.C.,577, 37Vicinanza, D.,571, 11;572, 133;575, 208;576, 18;577, 109Viertel, G.,571, 11;572, 133;575, 208;576, 18;577, 109Vikhrov, V., 577, 37


Vilain, P.,575, 198Vilanova, D.,576, 29Villa, S., 571, 11;572, 133;575, 208;576, 18;577, 109Villeneuve-Seguier, F.,574, 169Vincter, M.G.,577, 37Vissani, F.,571, 209Visschers, J.L.,575, 198Vitagliano, L.,573, 33Vitale, L., 576, 29Vitulo, P.,571, 139;572, 21;575, 190Vivargent, M.,571, 11;572, 133;575, 208;576, 18;577, 109Vlachos, S.,571, 11;572, 133;575, 208;576, 18;577, 109Vlasov, N.N.,573, 46Vodopianov, I.,571, 11;572, 133;575, 208;576, 18;577, 109Vogel, C.,577, 37Vogel, H.,571, 11;572, 133;575, 208;576, 18;577, 109Vogt, H.,571, 11;572, 133;575, 208;576, 18;577, 109Vogt, M., 577, 37Volkov, A.A., 574, 169Vollmer, C.F.,572, 8; 577, 18, 93Volmer, J.,577, 37Volya, A., 574, 27Von Krogh, J.,572, 8; 577, 18, 93Vorobiev, A.P.,574, 169Vorobiev, I.,571, 11;572, 133;575, 208;576, 18;577, 109Vorobiov, A.I.,573, 63Vorobyov, A.A.,571, 11;572, 133;575, 208;576, 18;577, 109Voss, H.,572, 8; 577, 18, 93Voss, K.C.,573, 46Vossebeld, J.,572, 8; 577, 18, 93Vrba, V.,576, 29

Wadhwa, M.,571, 11;572, 133;575, 208;576, 18;577, 109Wahl, H.,576, 43Wahl, H.D.,574, 169Wahl, M.,571, 139;572, 21;575, 190Wahlen, H.,576, 29Walczak, R.,573, 46Walker, A.,576, 43Walker, P.M.,576, 75Waller, D.,572, 8; 577, 18, 93Wallraff, W., 577, 109Wang, M.,571, 139;572, 21;573, 46;575, 190Wang, P.,574, 41Wang, Q.,571, 11, 21;572, 133;575, 208;576, 18Wang, S.,575, 25Wang, X.L.,571, 11;572, 133;575, 208;576, 18;577, 109Wang, Z.-M.,574, 169Wang, Z.M.,571, 11;572, 133;575, 208;576, 18;577, 109Wanke, R.,576, 43Warchol, J.,574, 169Ward, C.P.,572, 8; 577, 18, 93Ward, D.R.,572, 8; 577, 18, 93Washbrook, A.J.,576, 29Watkins, P.M.,572, 8; 577, 18, 93

Watson, A.T.,572, 8; 577, 18, 93Watson, N.K.,572, 8; 577, 18, 93Watts, G.,574, 169Wayne, M.,574, 169Weber, A.,573, 46Weber, C.,572, 56Weber, M.,571, 11;572, 133;575, 208;576, 18;577, 109Weber, M.M.,575, 290Webster, M.,571, 139;572, 21;575, 190Weerts, H.,574, 169Weigel, H.,572, 196Weisel, G.J.,574, 8Weiser, C.,576, 29Weiskopf, C.,577, 37Weissmann, L.,576, 55Wells, P.S.,572, 8; 577, 18, 93Wendland, J.,577, 37Wengler, T.,572, 8; 577, 18, 93Wermes, N.,572, 8; 577, 18, 93Wessoleck, H.,573, 46West, B.J.,573, 46West, P.,575, 333Wetterich, C.,574, 269Wetterling, D.,572, 8; 577, 18, 93Whisnant, K.,576, 303White, A.,574, 169Whiteson, D.,574, 169Whitmore, J.J.,573, 46Wick, K., 573, 46Wicke, D.,576, 29Wickens, J.,576, 29Widhalm, L.,576, 43Wiedenhöver, I.,571, 155Wiegers, B.,572, 127Wieland, F.W.,572, 127Wienemann, P.,571, 11;572, 133;575, 208;576, 18;577, 109Wiggers, L.,573, 46Wijngaarden, D.A.,574, 169Wilbert, J.,577, 37Wilhelmsen Rolander, K.,576, 55Wilkens, H.,571, 11;572, 133;575, 208;576, 18;577, 109Wilkinson, G.,576, 29Willis, S., 574, 169Wilquet, G.,575, 198Wilson, G.W.,572, 8; 577, 18, 93Wilson, J.A.,572, 8; 577, 18, 93Wilson, J.R.,571, 139;572, 21;575, 190Wimpenny, S.J.,574, 169Wing, M., 573, 46Winhart, A.,576, 43Winston, R.,576, 43Winter, K.,575, 198Winter, M.,576, 29Wislicki, W., 576, 43Wiss, J.,571, 139;572, 21;575, 190


Wißkirchen, J.,572, 127Witała, H.,574, 8Witek, M., 576, 29Wolf, G., 572, 8; 573, 46;577, 18, 93Wollnik, H., 573, 80Womersley, J.,574, 169Wood, D.R.,574, 169Wörtche, H.J.,576, 253Wotton, S.A.,576, 43Wu, C.,571, 21;572, 127Wu, Y.-S.,576, 209Wyatt, T.R.,572, 8; 577, 18, 93Wynhoff, S.,571, 11;572, 133;575, 208;576, 18;577, 109Wyss, R.A.,572, 152

Xia, L., 571, 11;572, 133;575, 208;576, 18;577, 109Xu, Q.,574, 169Xu, Z.Z.,571, 11;572, 133;575, 208;576, 18;577, 109Xue, S.-S.,573, 33

Yager, P.M.,571, 139;572, 21;575, 190Yahiro, M.,571, 223Yamada, K.,571, 21Yamada, R.,574, 169Yamada, S.,573, 46Yamaguchi, M.,573, 123Yamaguchi, Y.,571, 21Yamamoto, A.,577, 10Yamamoto, J.,571, 11;572, 133;575, 208;576, 18;577, 109Yamamoto, Y.,577, 10Yamashita, S.,572, 8; 577, 18, 93Yamashita, T.,573, 46Yamato, K.,577, 10Yamazaki, Y.,573, 46Yamin, P.,574, 169Yang, B.Z.,571, 11;572, 133;575, 208;576, 18;577, 109Yang, C.G.,571, 11;572, 133;575, 208;576, 18;577, 109Yang, H.J.,571, 11;572, 133;575, 208;576, 18;577, 109Yang, J.-J.,574, 35, 225Yang, M.,571, 11;572, 133;575, 208;576, 18;577, 109Yao, Y.-P.,572, 37Yasuda, T.,574, 169Yasui, Y.,571, 163Yatsunenko, Y.A.,574, 169Ybeles Smit, G.,577, 37Yee, J.H.,574, 111Yeh, S.C.,571, 11;572, 133;575, 208;576, 18;577, 109Yen, S.,577, 37Yip, K., 574, 169Yoon, C.S.,575, 198Yoshida, A.,571, 21Yoshida, R.,573, 46Yoshida, T.,577, 10Yoshimura, K.,577, 10You, Y., 571, 85

Youngman, C.,573, 46Yu, J.,574, 169Yu, J.-Y.,574, 232Yuan, C.Z.,574, 41Yuan, F.,575, 45Yue, C.,575, 25Yushchenko, O.,576, 29Yushchenko, O.P.,574, 14Yushkov, A.N.,573, 63

Zaharijas, G.,575, 358Zakharov, V.I.,574, 136Zalewska, A.,576, 29Zalewski, P.,576, 29Zalite, An.,571, 11;572, 133;575, 208;576, 18;577, 109Zalite, Yu.,571, 11;572, 133;575, 208;576, 18;577, 109Zallo, A., 571, 139;572, 21;575, 190Zamick, L.,571, 29Zanabria, M.,574, 169Zanon, D.,573, 138Zarnecki, A.F.,573, 46Zatsepin, A.V.,573, 63Zavrtanik, D.,576, 29Zawiejski, L.,573, 46Zelevinsky, V.,574, 27Zell, O.,571, 29Zer-Zion, D.,572, 8; 577, 18, 93Zeuner, W.,573, 46ZEUS Collaboration,573, 46Zeyrek, M.T.,575, 198Zhang, R.-Y.,571, 85Zhang, X.,573, 20;574, 169Zhang, Y.,571, 139;572, 21;575, 190Zhang, Y.-Z.,576, 12Zhang, Z.P.,571, 11;572, 133;575, 208;576, 18;577, 109Zhao, E.-G.,576, 289Zhao, J.,571, 11;572, 133;575, 208;576, 18;577, 109Zhautykov, B.O.,573, 46Zheng, H.,574, 169Zheng, T.,571, 21Zhilich, V.N., 573, 63Zhou, B.,574, 169Zhou, Y.,577, 67Zhou, Z.,574, 169Zhu, G.Y.,571, 11;572, 133;575, 208;576, 18;577, 109Zhu, R.Y.,571, 11;572, 133;575, 208;576, 18;577, 109Zhu, S.-L.,575, 55Zhuang, H.L.,571, 11;572, 133;575, 208;576, 18;577, 109Zhuravlov, V.,576, 29Zichichi, A., 571, 11;572, 133;573, 46;575, 208;576, 18;

577, 109Ziegler, A.,573, 46Ziegler, Ar.,573, 46Zielinski, M., 574, 169


Zieminska, D.,574, 169Zieminski, A.,574, 169Zihlmann, B.,577, 37Zilizi, G., 577, 109Zimin, N.I., 576, 29Zimmermann, B.,571, 11;572, 133;575, 208;576, 18;577, 109Zinchenko, A.,576, 43Zintchenko, A.,576, 29Ziolkowski, M., 576, 43Zivkovic, L., 572, 8; 577, 18, 93Zohrabian, H.,577, 37

Zöller, M., 571, 11;572, 133;575, 208;576, 18;577, 109Zong, H.,575, 25Zong, H.-S.,576, 289Zotkin, S.A.,573, 46Zuber, K.,571, 148Zucchelli, P.,575, 198Zupan, M.,576, 29Zupranski, P.,577, 37Zutshi, V.,574, 169Zverev, E.G.,574, 169Zylberstejn, A.,574, 169

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