1

Vector and Axial Form Factors and Inelastic Structure

FunctionsArie Bodek

University of Rochesterhttp://www.pas.rochester.edu/~bodek/CTEQ04.ppt

Lecture Given in CTEQ04 Summer School, Madison

Wed. June 23,2004 (4pm-5pm)

Plus Three Problems for Students to work out together as a team. Email solution -bodek@pas.rocherster.edu end of week

2

Status of Cross-Sections• Not well-known, especially in region of

NUMI 0.70 off-axis proposal (~2 GeV)

νn→μ –pπ0

νn→μ nπ+

1. Bubble Chamber language. - Exclusive final states

2. Quasi+Resonan - Excitation Form Factors (to nucleons and resonances)

3. Deep Inelastic Scattering -PDFs and fragmentation to excl. final states

Note 2 and 3: Form Factors can be converted to PDFs

/Eν

Eν(GeV)

-------- 1 Pion production ---- Quasielastic W=Mp

1 100.1

------total

--------

DIS W>2GeV

3

MIT SLAC e-p DATA 1970 e.g. E0 = 4.5 and 6.5 GeV

e-P scattering A. Bodek PhD thesis 1972 [ PRD 20, 1471(1979) ] Proton Data

Electron Energy = 4.5, 6.5 GeV Data

‘The Deep Inelastic Region is the “Rutherford Experiment” of the proton. The electron scattering data in the Resonance Region is the “Frank Hertz Experiment” of the Proton. SAID

V. Weisskopf * (former faculty member at Rochester and at MIT when he showed these data at an MIT Colloquium in 1971 (* died April 2002 at age 93)

What doThe Frank Hertz” and “Rutherford Experiment” of the proton’ have in common?

A: Quarks! And QCD

4

Fixed W scattering - form factors(the Frank Hertz Experiment of the Nucleon)

• OLD Picture fixed W: Elastic Scattering, Resonance Production. Electric and Magnetic Form Factors (GE and GM) versus Q2 measure size of object (the electric charge and magnetization distributions).

• Elastic scattering W = Mp = M, single final state nucleon: Form factor measures size of nucleon.Matrix element squared | <p f | V(r) | p i > |2 between initial and final state lepton plane waves. Which becomes:

• | < e -i k2. r | V(r) | e +i k1 . r > | 2

• q = k1 - k2 = momentum transfer • GE (q) = {e i q . r (r) d3r } = Electric form factor is the Fourier

transform of the charge distribution. EXERCISE 1 FOR STUDENTS - SHOW THIS (non-relativsitically) By end of CTEQ4 Week. <<<<<<<<<

• Similarly for the magnetization distribution for GM Form factors are relates to structure function by:

• 2xF1(x ,Q2)elastic = x2 GM2

elastic (Q2) x-1)

• Resonance Production, W=MR, Measure transition form factor between a quark in the ground state and a quark in the first excited state. For the Delta 1.238 GeV first resonance, we have a Breit-Wigner instead of x-1).

• 2xF1(x ,Q2) resonance ~ x2 GM2

Res. transition (Q2) BWW-1.238)

e +i k2 . r

e +i k1.r

rMp Mp

q

Mp

MR

e +i k1 . r

e +i k2 . r

5

A REVIEW OF EXPERIMENTAL DATA ON THE PROTON AND NEUTRON ELASTIC FORM-FACTORS.

Arie Bodek (Rochester U. ),. UR-1376, ER-40685-826, (Jun 1994). 10pp. Presented at 6th Rencontres de Blois: The Heart of the Matter: from

Nuclear Interactions to Quark - Gluon Dynamics, Blois, France, 20-25 Jun 1994. In *Blois 1994, The heart of the matter* 255-264. Scanned Version

(KEK Library) -

Start with Electron Scattering

For elastic scatteringNo structure cross section

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Gep, Gen = electric form factors for proton and neutron

Gmp, Gmn = magnetic form factors for proton and neutron

Normalization at Q2=0: electric charge (Ge)

Q2=0 Anomalous magnetic moment (Gm)

Q2= 0 Axial ga(w) = -1.267 (neutron lifetime)

Q2= axial ga(Z0) hard to measure

Q2 Dependence--> How are Electric, Magnetic and Axial Weak charge as probed by photon, W and Z bosons

distributed? Or how are u, d, s, ubar, dbar, sbar distributed?

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New polarization transfer method measure Ge/Gm ratio

Separation of Ge, Gm requires cross section+ Rosenbluth method (rad cor)

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1

9

Neutrino Quasi-Elastic scattering

Note in electron scattering this is called Elastic. The term Quasi for used for scattering from bound nucleons in nuclei

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Electric vector

Pseudo-scalar

~(m-lepton)

Magnetic vector

Axial (W)

Dipole Form

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Most up to date Constants

2003-BBA-Form Factors and constants (Bodek, Budd Arrington)

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Neutron GMN is negative Neutron (GM

N / GM

N dipole )

At low Q2 Our Ratio to Dipole similar to that nucl-ex/0107016 G. Kubon, et alPhys.Lett. B524 (2002) 26-32

Neutron (GMN

/ GMN

dipole )

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Neutron GEN is positive New

Polarization data gives Precise non

zero GEN hep-ph/0202183(2002)

Neutron, GEN

is positive -

Imagine N=P+pion cloud

Neutron (GEN

/ GEP

dipole )

Krutov

(GEN)2

show_gen_new.pict

Galster fit Gen

14

Functional form and Values of BBA Form Factors•GE

P.N (Q2) = {e i q . r (r) d3r } = Electric form factor is the Fourier transform of the charge

distribution for Proton And Neutron (therefore, odd powers of Q should not be there at low Q)

•EXERCISE - 2 FOR STUDENTS - SHOW that Odd powes of Q should not be there near Q2=0.<<<<<<<

15

• The dotted curve shows their calculation using their fit value of 1.07 GeV

• They do unbinned likelyhood to get MA

No shape fit• Their data and their curve is taken from

the paper of Baker et al.• The dashed curve shows our calculation

using MA = 1.07 GeV using their assumptions

• The 2 calculations agree.• If we do shape fit to get MA

• With their assumptions -- MA=1.079 GeV• We agree with their value of MA

• If we fit with BBA Form Factors and our constants - MA=1.055 GeV.

• Therefore, we must shift their value of MA down by -0.024 GeV.

• Baker does not use a pure dipole• The difference between BBA-form factors

and dipole form factors is -0.049 GeV

Determining mA , Baker et al. – BNL deuterium

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Summary of Results

17

Hep-ph/0107088 (2001)

Difference in Ma between Electroproduction And neutrinos is understood

For MA from QE neutrino expt. On free nucleons No theory

corrections needed

1.11=MA

-0.026-0.028

Neutrinos 1.026+-0.021-=MA

average

From

Neutrino

quasielastic

From charged Pion Electroproduction Average value of

1.069->1.014 when corrected

for theory hadronic effects to compare to

neutrino reactions

=1.014 when corrected for hadronic effect to compare to neutrino reactions

Ma=1.06+-0.14 (using dipole FF) from K2K goes down to 1.01 with BBA form factors

For updated MA expt. need to be reanalyzed with new gA, and GEN

More correct to use 1.00+-0.021=MA

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• We solve for FA by writing the cross section as

• a(q2,E) FA(q2)2 + b(q2,E)FA(q2) + c(q2,E)• if (d/dq2)(q2) is the measured cross

section we have: • a(q2,E)FA(q2)2 + b(q2,E)FA(q2) + c(q2,E)

– (d/dq2)(q2) = 0 • For a bin q1

2 to q22 we integrate this

equation over the q2 bin and the flux• We bin center the quadratic term and

linear term separately and we can pull FA(q2)2 and FA(q2) out of the integral. We can then solve for FA(q2)

• Shows calculated value of FA for the previous experiments.

• Show result of 4 year Minerνa run• Efficiencies and Purity of sample is

included.

Measure FA(q2)

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• For Minerνa - show GEP for

polarization/dipole, FA errors , FA data from other experiments.

• For Minerνa – show GEP cross

section/dipole, FA errors.• Including efficiencies and purities.• Showing our extraction of FA

from the deuterium experiments.• Shows that we can determine if

FA deviates from a dipole as much as GE

P deviates from a dipole.• However, our errors, nuclear

corrections, flux etc., will get put into FA.

• Is there a check on this?

FA/dipole - Current versus future data

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• d(d/dq2)/dff is the % change in the cross section vs % change in the form factors

• Shows the form factor contributions by setting ff=0

• At Q2 above 2 GeV2 the cross section become insensitive to FA

• Therefore at high Q2, the cross section is determined by the electron scattering data and nuclear corrections.

• Anti-neutrino data serve as a check on FA.

Do we get new information from anti-neutrinos?

21

The Structure of the Nucleon3 decades of investigation

1973-2004 A personal historical viewArie Bodek, University of Rochester

As the majority of advances in High Energy Physics, progress in this area was accomplished by:

1. Higher Energies (new accelerators and machines)

And more importantly in combination with2. Higher Precision (new experimental

techniques)3. Better understanding (new theoretical tools)4. Higher Luminosities (more statistics)5. Different probes (new beams)

But most important - Mentor new graduate students and postdocs

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The Structure of the Nucleon3 decades of investigation1973-2004Arie Bodek, University of Rochester

In the beginning there was hadron Spectroscopy and quarks were only mathematical objects

and then came the MIT-SLAC

electron scattering

experiments 1967-1973

And Quarks became Real Particles

by 2000: Nucleon Structure is well understood and NNLO QCD works from Q2=1 GeV2 to the highest values currently accessible in hadron colliders. How did we get there?

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•A: Nobel Prize 1990 - Friedman, Kendall, Taylor for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics.” (1967-73)

Front row: Richard Taylor, Jerome Friedman, Henry Kendall.

Second row: Arie Bodek, David Coward, Michael Riordan, Elliott Bloom, James Bjorken, Roger (Les)

Cottrell, Martin Breidenbach, Gutherie Miller, Jurgen Drees, W.K.H. (Pief) Panofsky, Luke Mo, William

Atwood. Not pictured: Herbert (Hobey) DeStaebler Graduate students in italics

Described in detail in"The Hunting of the Quark," (Simon &

Schuster) Michael Riordan

AIP Science Writing Award 1988 & AIP Andrew Gemant Award 2003

Important to share the excitement of science with the public

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N =d d u + sea 1/3 1/3 2/3P = u u d + sea 2/3 2/3 1/3

Large x N/P -> 0.25 Explained by valence d/u PARTONS ARE QUARKS ! [ (1/3) / (2/3)]2 =1/4 Small x : N/P=1 explained by sea quarks

F2P

F2N

F2P

xx

1/4

2/3

Scaling-> Point like PARTONS

1968 - SLAC e-p scaling ==> Point like Partons in the nucleon 1970-74 - Neutron/Proton ratio - Partons are fractionally charged

(quarks)•COMPARISONS OF DEEP INELASTIC ep AND en CROSS-SECTIONS AB et al Phys. Rev. Lett. 30: 1087,1973. (SLAC Exp. E49 PhD thesis)-First result Next Step higher precision• THE RATIO OF DEEP - INELASTIC en TO ep CROSS-SECTIONSINTHE THRESHOLD REGION AB et al Phys.Lett.B51:417,1974 ( SLAC E87) PRL referees - nothing substantially new over 1973

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RP

R=L/ T (small)

quarks are spin 1/2 !

EXTRACTION OF R = L/T FROM DEEP INELASTIC eP AND eD CROSS-SECTIONS. E. Riordan, AB et

al Phys.Rev.Lett.33:561,1974.

EXPERIMENTAL STUDIES OF THE NEUTRON AND PROTONELECTROMAGNETIC STRUCTURE FUNCTIONS. AB et al Phys.Rev.D20:1471-1552,1979.

BUT what is the x and Q2 Dependence of R?What is x, Q2 dependence of u, d, s, c quarks and antiquarks?

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Integral of F2(x) did not add up to 1.0. Missing momentum attributed to “gluons”. GLUONS “DISCOVERED”BUT what is their x Distributions?

Like Pauli’s missing energy in beta decay attributed to neutrinos*Gluons were “Discovered” in 1970, much before PETRA. Scatter shows F2(x, Q2) as expected from bremstrahlung of gluons by struck quarks in initial of final states. BUT QCD NOT FULLY FORMALIZED YET

F2P

F2N

F2D

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• Next Higher Precision: First observation of Scaling Violations SLAC

• E. M. Riorday, AB et al TESTS OF SCALING OF THE PROTON ELECTROMAGNETIC STRUCTURE FUNCTIONS Phys.Lett.B52:249,1974 (more detail in AB et al Phys.Rev.D20:1471-1552,1979

Note in 2000. We show that Higher Twist come from Target Mass + NNLO QCD STUDIES OF HIGHER TWIST AND HIGHER ORDER EFFECTS IN NLO AND NNLO QCD ANALYSIS AB, UK Yang. Eur. Phys. J. C13 (2000) 241 245.

F2P Extracted

from Rosenbluth

separations

Scaling violations SEEN in 1974, Are they deviations from Parton Model e.g. from “gluon” emission, or are they just at Low Q2

1974: PRL Referees - obviously these are uninteresting low Q2 effects

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How are Parton Distributions (PDFs) Extract from various data at large momentum transfer (e/μ/ν and other expts.)

d/u

PDF(x)=

Valence and sea

Also Drell Yan, jets etc

H and D

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"Physics is generally paced by technology and not by the physical laws. We always seem to ask more questions than we have tools to answer. Wolfgang K. H. Panofsky•Questions in 1972-2000 Anti-quarks, strange , charm quarks in nucleons , individual PDFs (u,d,qbar,gluons Q2,x dependence) R= longitudinal structure function (x,Q2), quarks in nuclei , origin of scaling violations- low Q2 higher twist or QCD?,

•A Detailed understanding of Nucleon Structure Required Initiating Measurements at Different Laboratories, New Detectors, New Analysis Techniques and Theoretical Tools - AND also sorting out which experiments are right and which experiments are wrong - incremental but steady progress.

Meanwhile: the J/Psi was discovered in 1974 ---> and the age of Spectroscopy returned; and then came the Upsilon and there was more spectroscopy to be done.

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Conclusion

Fermilab

CCFR/NuTeV v-N Expt.

μ-N (data)CDF Collider Expt

MINERvA Expt

J-lab

e-N (Data)

JUPITER Expt.

SLAC ESA SLAC NPAS programs

e-N Data

KEK

AMY @ TRISTAN

JHF

CERN μ-N, v-N (data)

CMS Collider

Rochester

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Also thanks to our Collaborators over the past 3.5 decades +FUTURE ( Blue awarded Panofsky Prize)

The Electron Scattering SLAC-MIT collaboration at SLAC End Station A (E49, E87) with Kendall, Friedman, Taylor, Coward, Breidenbach, Riordan, Elias, Atwood& others (1967-1973)

•The Electron Scattering E139, E140, E140x, NE8 collaboration at SLAC ESA/ NPAS injector at SLAC (with Rock, Arnold, Bosted, Phillipone, Giokaris & others) (1983-1993)

•The E379/E595 Hadronic Charm: with Barish, Wojcicki, Merrit. Fisk, Shaevitz& others) Production collaboration at Fermilab lab E (1974-83)

•The AMY e+e- Collaboration at TRISTAN/KEK (with Steve Olsen& others) (1982-1990)•The CCFR-NuTeV Neutrino Collaboration at Fermilab Lab E (with (1974-2004) Barish, Sciulli, Shaevitz, Fisk, Smith,Merritt, Bernstein, McFarland and others)

•The CDF proton-antiproton Collaboration at Fermilab (1988-•And in particular I thank the graduate students and 2004) postdocs over the years, and Rochester Senior Scientists Budd, deBarbaro Sakumoto.+more progress to be made with collaborators at the CMS-LHC experiment,(1995-->)

The New Electron Scattering JUPITER Collaboration at

Jefferson Lab,& the new MINERvA Neutrino (1993-->

Collaboration at Fermilab (McFarland, Morfin, Keppel, Manly),

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Neutrino Experiments REQUIRE good Hadron Calorimetry and Muon Energy calibration (~0.3%) 10 cm Fe Sampling, NuTeV simultaneous neutrino running and hadron and muon test beamsD.A. Harris (Rochester), J. Yu et alNuTeV PRECISION CALIBRATION OF THE NUTEV CALORIMETER. UR-1561 Nucl. Inst. Meth. A447 (2000)W.K. Sakumoto (Rochester), et al. CCFR CALIBRATION OF THE CCFR TARGET CALORIMETER.Nucl.Instrum.Meth.A294:179-192,1990.CCFR Developed Fe-scintillator compensating calorimeter. 3mx3m large counters with wavelength shifting readout

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B: Hadronic Charm Production -Lab E Fermilab E379/E595 Single muons from charm, dimuons from Drell-Yan, vary target density to determine rate of muons from pion decays (1974-1983

Jack L. Ritchie, HADRONIC CHARM PRODUCTION BY PROTONS AND PIONS ON IRON. UR-861 (1983) Ph.D. Thesis (Rochester). Dexter Prize, U of Rochester - Now Professor at UT Austin

Hadronic Charm Production is about 20 mb. Distribution is peaked at small Feynman x and is dominated by quark-quark and gluon-gluon processes. No Intrinsic Charm quarks in the nucleon - in contradiction with ISR results.

•Intrinsic C(x) = 0

B: Are there charm quarks in nucleon ?

34

C: Strange Quarks in the Nucleon - Caltech-Fermilab --> CCFR (Columbia -Chicago-Fermilab-Rochester) and -Later- NuTeV Neutrino Collaborations at Fermilab LAB E.

Dimuon event

Karol Lang, AN EXPERIMENTAL STUDY OFDIMUONS PRODUCED IN HIGH-ENERGY NEUTRINO INTERACTIONS. UR-908 (1985) Ph.D. Thesis (Rochester) Now Professor at UT AustinMost recently M. Goncharov and D. Mason (NuTeV PhDs)

The Strange Sea Anti-quarks are about 1/2 of the average of u and d sea - i.e Not

SU3 Symmetric.

K

35

H. Kim (CCFR Columbia PhD); D.Harris (Rochester) et. al. MEASUREMENT OF S (Q2) FROM THE GROSS- LLEWELLYN SMITH SUM RULE. Phys. Rev. Lett. 81, 3595 (1998)

W.G. Seligman et al. (CCFR Columbia PhD), IMPROVED DETERMINATION OF S FROM NEUTRINO NUCLEON SCATTERING. Phys. Rev. Lett. 79 1213 (1997)

Precision High Statistics Neutrino Experiments at Fermilab - Valence, Sea, Scaling Violations, gluons F2 xF3 , Precise

s GLS sum rule (Q2 dependence)

GLS( q2) dependence s

36

Precision Neutrino ExperimentsCCFR/NuTeVUn Ki Yang UR-1583,2000 Ph.D. Thesis, (Rochester) Lobkowicz Prize, U of R; URA Best Thesis Award Fermilab 2001 (now at Univ. of Chicago)Un-Ki Yang et al.. MEASUREMENTS

OF F2 AND XF3 FROM CCFR ν-FE DATA IN A PHYSICS MODEL INDEPENDENT WAY. By CCFR/NuTeV Phys.Rev.Lett.86, 2742,2001

Experiment vs Theory: Ratio of

F2 (neutrino)/F2 (muon)

Resolved 10% to 20% difference between ν and μ data

Same PDFs should describe all processes

37

D Quark Distributions in Nuclei - New Parallel Program at SLAC

AB, J Ritchie FERMI MOTION EFFECTS IN DEEP INELASTIC LEPTON SCATTERING FROM NUCLEAR TARGETS, Phys.Rev.D23:1070,1981; Phys.Rev.D24:1400,1981.

1983 (conference proceeding) surprising report of difference between Iron and Deuterium muon scattering data from the European Muon Collaboration (EMC) Disagreement with Fermi Motion Models.

AB, EMPTY TARGET SUBTRACTIONS AND RADIATIVE CORRECTIONS IN ELECTRON SCATTERING EXPERIMENTS, Nucl. Inst. Meth. 109 (1973). - factor of 6 increase in rate of empty target data by making empty target same radiation length as H2 and D2 targets; - used in SLAC E87 - more payoff later

ELECTRON SCATTERING FROM NUCLEAR TARGETS AND QUARK DISTRIBUTIONS IN NUCLEI. AB et al Phys.Rev.Lett.50:1431,1983.. - Use Empty Target Data from SLAC E87 (1972)(initially rejected by Phys. Rev, Letters)A COMPARISON OF THE DEEP INELASTIC STRUCTURE FUNCTIONS OF DEUTERIUM AND ALUMINUM NUCLEI. AB et al Phys.Rev.Lett.51:534,1983. Use empty target data from SLAC E49B (1970)

38

Quark Distributions in Nuclei AB et al Phys. Rev. Lett. 51: 534, 1983 (SLAC Expt. E49, E87 empty tgt data 1970,1972)

EMC

PRL Referees: (1) How can they claim that there are quarks in nuclei + (2) Obviously uninteresting multiple scattering of electrons in a nucleus- --> later accepted by PRL editors.

39

D. Back to SLAC using High Energy Beam and the Nuclear Physics Injector NPAS - SLAC E139, E140, E140x, E141, NE8

R.G. Arnold et al., MEASUREMENTS OF THE A-DEPENDENCE OF DEEP INELASTIC ELECTRON SCATTERING FROM NUCLEI Phys. Rev. Lett.52:727,1984; (initial results incorrect by 1% since two photon external radiative corrections for thick targets not initially accounted for. Found out later in SLAC E140)

J. Gomez et al., MEASUREMENT OF THE A-DEPENDENCE OF DEEP INELASTIC ELECTRON SCATTERING. Phys.Rev.D49:4348-4372,1994.

Back to SLAC End Station A to measure effect on various nuclei

40

SLAC E140, E140x - . New Precision Measurement of R and F2, and Re-Analysis of all SLAC DIS data to obtain 1% precision. The issues:

(1) Precise Values and Kinematic dependence of R needed to extract F2 from all electron muon and neutrino experiments.

(2) Precise normalization of F2 needed to establish normalization of PDFs for all DIS experiments to 1%. Solution-->SLAC E140 - New hardware, new theoretical tools 1 month run worth years of data, IMPACT all DIS Experiments Past and Future.

(1) Upgrade Cerenkov Counter for ESA 8 GeV spectrometer - N2 with wavelength shifter on phototube

(2) Upgrade Shower Counter from lead-acrylic (to segmented lead glass)

(3) Upgraded tracking (wire chambers instead of scintillator-hodoscope)

(4) Upgraded Radiative Corrections - Improved treatment using Bardin, Complete Mo-Tsai, test with different r.l. targets ( to 0.5%)

(5) Cross normalize all previous SLAC experiment to SLAC E140 by taking data in overlap regions.(Re-analysis with upgraded rad corr).

41

Sridhara Rao Dasu, PRECISION MEASUREMENT OF X, Q2 AND A-DEPENDENCE OF R = L/T AND F2 IN DEEP INELASTIC SCATTERING. UR-1059 (Apr 1988) . Ph.D. Thesis. (Rochester) SLAC E140 - winner of the Dexter Prize U of Rochester 1988(now Professor a U. Wisconsin, Madison)

S. Dasu (Rochester PhD )et al., MEASUREMENT OF THE DIFFERENCE IN R = L/T, and A/D IN DEEP INELASTIC ed, eFE AND eAuSCATTERING. Phys.Rev.Lett.60:2591,1988;

S. Dasu et al., PRECISION MEASUREMENT OF R = L/T AND F2 IN DEEP INELASTIC ELECTRON SCATTERING. Phys.Rev.Lett.61:1061,1988;

S. Dasu et al., MEASUREMENT OF KINEMATIC AND NUCLEAR DEPENDENCE OF R =

L/T IN DEEP INELASTIC ELECTRON SCATTERING. Phys.Rev.D49:5641-5670,1994.

L.H. Tao (American U PhD) et al., PRECISION MEASUREMENT OF R = L/T ON HYDROGEN, DEUTERIUM AND BERYLLIUM TARGETS IN DEEP INELASTIC ELECTRON SCATTERING. Z.Phys.C70:387,1996 L.W. Whitlow (Stanford PhD), et al. , A PRECISE EXTRACTION OF R = L/T FROM A GLOBAL ANALYSIS OF THE SLAC DEEP INELASTIC ep AND ed SCATTERING CROSS-SECTIONS. Phys.Lett.B250:193-198,1990. L.W. Whitlow, et. al., PRECISE MEASUREMENTS OF THE PROTON AND DEUTERON STRUCTURE FUNCTIONS FROM A GLOBAL ANALYSIS OF THE SLAC DEEP INELASTIC ELECTRON SCATTERING CROSS-SECTIONS. Phys.Lett.B282:475-482,1992.

42

Provided normalization and shape at lower Q2 for all DIS experiments- constrain systematic errors on high energy muon experiments - Perturbative QCD with and without target mass (TM) effects

43

SLAC E140 and the combined SLAC re-analysis provided the first precise values and kinematic dependence of R

Related to F2/2xF1

for use by all DIS experiments to extract F2 from differential cross section data

R

44

Proton-Antiproton (CDF/Dzero) collisions are actually parton-parton collisions (free nucleons)

This is why it is important to know the nuclear corrections for PDFs extracted from nucleons bound in Fe (neutrino) or in Deuterium (d versus u), when the PDFs are used to extract information from collider data

In 1994 uncertainties in d/u from deuteron binding effects contributed to an uncertainty in the W mass (extracted from CDF or Dzero Data of order 75 MeV.

By introducing new techniques, CDF data can provide independent constraints on free nucleon PDFs.

CONSTRAINTS ON PDFS FROM W AND Z RAPIDITY DIST. AT CDF. AB, Nucl. Phys. B, Proc. Suppl. 79 (1999) 136-138. In *Zeuthen 1999, Deep inelastic scattering andQCD* 136-138.

45

E: Proton-Antiproton (CDF/Dzero) collisions are actually parton-parton collisions (free nucleons)

46

Mark Dickson, THE CHARGE ASYMMETRY IN W BOSON DECAYS PRODUCED IN P ANTI-P COLLISIONS. (1994) Ph.D.Thesis (Rochester). (now at MIT Lincoln Labs)Qun Fan, A MEASUREMENT OF THE CHARGE ASYMMETRY IN W DECAYS PRODUCED IN P ANTI-P COLLISIONS. Ph.D.Thesis (Rochester) (now at KLA-Tenor

Proton-antiproton collisions (CDF)-

Measurement of d/u in the proton by using the W+- Asymmetry

47

Need to measure the W Decay lepton Asymmetry at high rapidity where there is no central tracking

Unfortunately W’s decay to electrons and neutrinos - Decay lepton asymmetry is a convolution of the W production Asymmetry

48

A NEW TECHNIQUE FOR DETERMINING CHARGE AND MOMENTUM OF ELECTRONS AND POSITRONS USING CALORIMETRY AND SILICON TRACKING. AB and Q. Fan In *Frascati 1996, Calorimetry in HEP*553- 560 (First used in AMY)

Use silicon vertex detector to extrapolate electron track to the forward shower counters. Compare the extrapolated location to the centroid of the EM shower in a segmented shower counter.

Energy of electron determined by the shower counter, Sign is determined by investigating if the shower centeroid is to the left or right of the extrapolated track,

All hadron collider physics (Tevatron, LHC) with electrons and positrons can be done better without a central tracker . No Track misID Need Just silicon tracking and segmented EM +HAD

calorimetry

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The d/u ratio in standard PDFs found to be incorrect. Now all new PDF fits include CDF W Asymmetry as a constraint. PDF error on W mass reduced to 10 MeV by using current CDF data.

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With this new technique, one can also significantly reduce the QCD background for very forward Z Bosons.Jinbo Liu, Measurement of d /dy for Drell-Yan e+e Pairs in the Z Boson Region Produced in Proton Anti-proton Collisions at 1.8 TeV. UR-1606, 2000 - Ph.D. Thesis (Rochester). (now at Lucent Technologies) T. Affolder et al. (CDF- article on Rochester PhD Thesis), MEASUREMENT OF d / dY FOR HIGH MASS DRELL-YAN E+ E- PAIRS FROM P ANTI-P COLLISIONS AT 1.8-TEV. Phys.Rev.D63:011101,2001.

NLO QCD describes Z -y distributions better than LO QCD

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F: Phenomenology: PUTTING it ALL TOGETHER The Great Triumph of NNLO QCD Origin of Higher Twist Effects, d/u and PDFs at large X –

PARTON DISTRIBUTIONS, D/U, AND HIGHER TWIST EFFECTS AT HIGH X. AB, UK Yang Phys.Rev.Lett.82:2467-2470,1999 .

STUDIES OF HIGHER TWIST AND HIGHER ORDER EFFECTS IN NLO AND NNLO QCD ANALYSIS OF LEPTON NUCLEON SCATTERING DATA ON F(2) AND R = (L) / (T). AB, UK Yang Eur.Phys.J.C13:241-245,2000

NNLO QCD +target mass corrections describes all of DIS data for Q2>1 GeV2 with NO Need for Higher Twists. GREAT TRIUMPH for QCD . Most of what was called low Q2 higher Twist are accounted for by higher order QCD.

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NNLO QCD+TM black Great Triumph of NNLO QCD. AB, UK Yang Eur.Phys.J.C13:241-245,2000

Size of the higher twist effect with NNLO analysis is very small a2= -0.009 (in NNLO) versus –0.1( in NLO) - > factor of 10 smaller, a4 nonzero

NNLO QCD+Tgt Mass works very well for Q2>1 GeV2

F2P

F2D

R

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Great Triumph of NNLO QCD. AB, UK Yang Eur.Phys.J .C13:24,2000 First extraction of (NNLO PDFs)/(NLO PDFs) ratio

For High Statistics Hardon Collider Physics (run II, LHC), the next step is to extract NNLO PDFs. So declare victory and let theorists and PDF Professionals (MRST and CTEQ) make progress towards the next generation NNLO PDF fits for Tevatron and LHC

High x NNLO PDFs 10% lower than NLO PDFs

Low x NNLO PDFs 2% higher than NLO PDFs

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F2, R comparison of NLO QCD+TM+HT black (Q2>1)(use QCD Renormalons for HT vs NLO QCD+TM only green AB, UK Yang Phys.Rev.Lett.82,1999 PDFs and QCD in NLO + TM + QCD Renormalon Model for Dynamic HT describe the F2

and R data very well, with only 2 parameters. Dynamic HT effects are there but small

NLO QCD + Target Mass + Renormalon HT works. A GREAT QCD TRIUMPH

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2000-2004->2010 (The high Energy Frontier): For Tevatron and Run II and LHC , the path to greater precision is using: NNLO QCD fits with both Q2>1 GeV2 DIS data & very high Q2 Collider Data.-Good for theorists•2000-2004->2010 (The Low Energy Frotier)•Applications to Neutrino Oscillations at Low Energy (Nucleon and Nuclear Structure down to Q2=0) •Here the best approach is to use a LO PDF analysis (including a more sophisticated target mass analysis) and include the missing QCD higher order terms in the form of Empirical Higher Twist Corrections. * Vector Part well understood - Phenomenology AB+U K Yang (2002-2004)•- Axial Part needs further investigation -• future Data 2004-2008 (JUPITER, e-N at Jlab)

• MINERvA, v-N at Fermilab)

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Original approach (NNLO QCD+TM) was to explain the non-perturbative QCD effects at low Q2, but now we reverse the approach: Use LO PDFs and “effective target mass and final state masses” to account for initial target mass, final target mass, and missing higher orders

Modified LO = Pseudo NNLO approach for low energies

Applications to Jlab and Neutrino Oscillations

P=M

q

mf=M*(final state interaction)

Resonance, higher twist, and TM

w=Q2+mf

2 +A

Mν (1+(1+Q2/ν2) )1/2 +BXbj= Q2 /2 Mν

K factor to PDF, Q2/[Q2+C]

A : initial binding/target mass effect

plus higher order terms

B: final state mass mf2 , mand photo-

production limit (Q2 =0)

MODELING DEEP INELASTIC CROSS-SECTIONS IN THE FEW GEV REGION. AB, UK Yang Nucl.Phys.Proc.Suppl.112:70,2002

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Initial quark mass m I and final mass ,mF=m * bound in a proton of mass M Summary: INCLUDE quark initial Pt) Get scaling (not x=Q2/2Mν )

for a general parton Model Is the correct variable which is

Invariant in any frame : q3 and P in opposite directions P= P0 + P3,M

PF= PI0,PI

3,mI

€

ξ =PI

0 +PI3

PP0 +PP

3

PI ,P0

quark ⏐ → ⏐ ⏐ ⏐ ⏐

q3,q0

photon← ⏐ ⏐ ⏐ ⏐ ⏐

( )

)0,(})]/1(1[{

2

2

22

22

22222

=+++

++=

=+⋅+→=+

PtmBQM

AmQ

mPqPqPPq

IF

W

FIIFI

ννξ

PF= PF0,PF

3,mF=m*

q=q3,q0

Most General Case: EXERCISE - 3 FOR STUDENTS - SHOW )<<<<<< ‘w= [Q’2 +B] / [ Mν (1+(1+Q2/ν2) ) 1/2 +A] (with A=0, B=0)where 2Q’2 = [Q2+ m F 2 - m I

2 ] + { ( Q2+m F 2 - m I 2 ) 2 + 4Q2 (m I

2 +P2t) }1/2

Bodek-Yang: Add B and A to account for effects of additional m2

from NLO and NNLO (up to infinite order) QCD effects. For case w with P2t =0 see R. Barbieri et al Phys. Lett. 64B, 1717 (1976) and Nucl. Phys. B117, 50 (1976)

Special cases:(1) Bjorken x, xBJ=Q2/2Mν, -> x

For m F 2 = m I 2 =0 and High ν2,

(2) Numerator m F 2 : Slow Rescaling as in charm production

(3) Denominator: Target mass term =Nachtman Variable =Light Cone Variable =Georgi Politzer Target

Mass var. (all the same )

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Describes all vector structure functions from Q2=0 to 100,000 GeV2

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MODELING DEEP INELASTIC CROSS-SECTIONS IN THE FEW GEV REGION. A. Bodek , U.K. Yang Presented at 1st Workshop on Neutrino - Nucleus Interactions in the Few GeV Region (NuInt01), Tsukuba, Japan, 13-16 Dec 2001. Nucl.Phys.Proc.Suppl.112:70-76,2002 e: hep-ex/0203009

HIGHER TWIST, XI(OMEGA) SCALING, AND EFFECTIVE LO PDFS FOR LEPTON SCATTERING IN THE FEW GEV REGION. A Bodek, U.K. Yang Proceedings of 4th International NuFact '02 Workshop (Neutrino Factories Workshop on Neutrino Factories, London, England, 1-6 Jul 2002. J.Phys.G29:1899-1906,2003

MODELING NEUTRINO AND ELECTRON SCATTERING INELASTIC CROSS- SECTIONS IN THE FEW GEV REGION WITH EFFECTIVE LO PDFS IN LEADING ORDER. A. Bodek, U.K. Yang . 2nd International Workshop on Neutrino - Nucleus Interactions in the Few GeV Region (NUINT 02), Irvine, California, 12-15 Dec 2002. Nucl.Phys.Proc.Suppl. hep-ex/0308007

Invited Article to be published in Annual Review of Particle and Nuclear Science 2005

Applications to Neutrino Oscillations at Low Energy

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G: Next: JUPITER at Jlab (Bodek,Keppel) will provided electron-Carbon (also e-H and e-D and other nuclei such as e-Fe) data in resonance region, and final states (Manly)-summer 04 +05.

G : Next: MINERvA at FNAL (McFarland, Morfin) will provide Neutrino-Carbon data at low energies.

G: CDF Run II (now) and CMS, high statistics W’s Z’s and Drell Yan

Phenomenology: Low energy Axial structure functions and resonance fits for both electrons/neutrinos

Maintaining the colorful Program

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CONCLUSION: Progress is made in finite incremental steps as new techniques and methods lead to greater precision (making what was impossible -> possible)

A factor of 2 reduction in error each generation (either statistical or systematic) is worth it, and one can always go back and re-analyze old data with better corrections to reduce systematic errors

In 4 generations of experiments (2)4 = 16 fold reduction in errors

2000: Nucleon Structure well understood. NNLO QCD works from Q2=1 to the highest values currently accessible. Hadron colliders are actually quark and gluon colliders with known and well understood PDFs.

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