Electromagnetic Form Factors

John Arrington

Argonne National Lab

Long Range Plan QCD Town Meeting

Piscataway, NJ, 12 Jan 2007

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Nucleon Form Factors

Fundamental properties of the nucleon

– Connected to charge, magnetization distribution

– Crucial testing ground for models of the nucleon internal structure

– Necessary input for experiments probing nuclear structure, or trying to understand modification of nucleon structure in nuclear medium

Recent revolution in experiments: last 5-10 yrs

– Dramatically improved precision, Q2 coverage

– New program of parity-violating measurements

– Revelation of importance of two-photon exchange

Driving renewed activity on theory side

– Models trying to explain all four electromagnetic form factors

– Trying to explain data at both low and high Q2

– Progress in QCD based calculations

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Status Ten Years Ago (end of 1997)

Range allowed by e-d elastic

Proton Neutron

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Unpolarized Elastic e-N Scattering

Nearly all of these measurements used Rosenbluth separation

R = d/d [(1+)/Mott] = GM2 + GE

2 = Q2/4M2

GM2

GE2

=180o =0o

Reduced sensitivity to…

• GM if Q2 << 1

• GE if Q2 >> 1

• GE if GE2<<GM

2 (e.g. neutron)

Form factor extraction is very sensitive to angle-dependent corrections in these cases

Lack of a free neutron target – correct for nuclear effects (FSI, MEC) and proton contributions

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New techniques: Polarization and A(e,e’N)

Mid ’90s brought measurements using improved techniques

– Polarized beams with polarized target or recoil polarimeter

– Large, efficient neutron detectors for 2H(e,e’n)

– Improved models for nuclear corrections

Polarized 3He targetBLAST at MIT-Bates

Focal plane polarimeter – Jefferson Lab

L/T:GM2 + GE

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Pol:GE/GM

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Example: GE /GM from Recoil Polarization

Similar expressions for cross section asymmetry from polarized target

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Progress in the last decade (since 1997)

Magenta: underway or approved

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PRELIMINARY

GEn

GMn

GEp / GMp1H(e,e’p):

2H(e,e’n):

2H(e,e’):

Results from BLAST (unpublished)

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Insight from New Measurements

New information on proton structure

– GE, GM differ for the proton: different charge, magnetization distributions

– Connection to GPDs: spin-space-momentum correlations

Model-dependent extraction of charge, magnetization distribution of proton:

J. Kelly, Phys. Rev. C 66, 065203 (2002)

A.Belitsky, X.Ji, F.Yuan, PRD69:074014 (2004)

G.Miller, PRC 68:022201 (2003)

x=0.7x=0.4x=0.1

1 fm

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Insight from New Measurements

Can test models with data on both proton and neutron form factors

– Previously, precise data and large Q2 range only for GMp, lower precision and limited Q2 range for GEp, GMn, little data for GEn

Data for all FFs at low Q2

– GEp, GMn, GEn known to greater precision – discrepancies resolved

Soon, FFs known to 4-5 GeV2

– GEp changed dramatically, GMp also modified

– Complete data set in “quark core” and “pion cloud” region

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Small Sample of Recent Calculations

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Pion Form Factor: Fπ

The pion form factor is of fundamental importance to our understanding of hadronic structure

The pion is the lightest QCD system and one of the simplest

– “The positronium atom of QCD”

– Excellent test case for non-perturbative models of hadronic structure Test case for study of transition between non-perturbative and

perturbative regions of QCD

Fπ is experimentally challenging to determine

• Above Q2>0.3 GeV2, one must employ the 1H(e,e’π+)n reaction

• At small –t < 0.2 GeV2, the t-channel diagramdominates σL; In the t-pole approximation

2LdF

dt

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Projected JLab 12 GeV Data

Higher Q2 data will challenge QCD-based models in the most rigorous manner and provide a real advance in our understanding of light quark systems

12 GeV JLab upgrade and proposed forward-angle SHMS spectrometer are essential to the measurement

A program that can only be performed at Jefferson Lab• Experiments performed in 1997 and 2003 established the validity of the experimental technique and extended measurements to Q2=2.45 GeV2

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Parity Violating Elastic e-p Scattering

dMG

dEG

uEGuMG

sEGsMG

nMG

nEG

pMG

p,ZEGp,ZMG

pEG

Experiment Q2 APV [ppm] NotesSAMPLE 0.1* 6ppm 1997

0.1* 7 deuterium0.04* 2 deuterium

HAPPEX 0.5 150.1 20.1 6 4He0.5 -

G0 0.1-1 1-100.4* -0.7* -

PVA4 0.1 10.2 50.2* -

* = backward angle

Magneta for planned or ongoing measurements

Nucleon charge, mag. distributions determined by quark distributions

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Recent and near-future measurements: 1997-2007

– Most of the world’s high-Q2 data, most of the world’s high-precision data

– Demonstrated problems with previous GEp AND GMp data

– New program of parity violating elastic scattering

For isovector (proton–neutron) form factors or flavor decomposition, need precise data covering similar Q2 range, careful understanding of systematics, including correlations between measurements

TPE contributions

– Large effect on GEp (up to 100+%), smaller effect on GMp

– Corrections can propagate from proton to neutron (as extracted from 2H)

– While direct TPE corrections to parity violation are small, the effect of TPE corrections to the EM FFs changes the expected asymmetry

Present Status

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Two-Photon Exchange

Proton form factor measurements

– Comparison of precise Rosenbluth and Polarization measurements of GEp/GMp show clear discrepancy at high Q2

Two-photon exchange corrections believed to explain the discrepancy

Compatible with e+/e- ?

– Yes: previous data limited to low Q2 or small scattering angle

Still lack direct evidence of effect on cross section

– Beam normal spin asymmetry the only observable in elastic e-p where TPE observed

M.K.Jones, et al., PRL 84, 1398 (2000)O.Gayou, et al., PRL 88, 092301 (2003)

I.A.Qattan, et al., PRL 94, 142301 (2005)

P.A.M.Guichon and M.Vanderhaeghen, PRL 91, 142303 (2003)

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Two-Photon Exchange Measurements

Comparisons of e+-p and e--p scattering [VEPP-III, JLab-Hall B]

dependence of polarization transfer and unpolarized e-p [JLab-Hall C]

– More quantitative measure of the discrepancy

– Test against models of TPE at both low and high Q2

TPE effects in Born-forbidden observables [JLab-Hall A, Hall C, Mainz]

– Target single spin asymmetry, Ay in e-n scattering

– Induced polarization, py, in e-p scattering

– Vector analyzing power, AN, in e-p scattering

World’s dataNovosibirskJLab – Hall B

Evidence (3 level) for TPE in existing data

J. Arrington, PRC 69, 032201(R) (2004)

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Two-Photon Exchange Calculations

Significant progress in theoretical understanding

– Hadronic calculations appear sufficient up to 2-3 GeV2

– GPD-based calculations used at higher Q2

Experimental program will quantify TPE for several e-p observables

Before TPE

After TPE (Blunden, et al)

– Precise test of calculations

– Tests against different observables

Want calculations well tested for elastic e-p, reliable enough to be used for other reactions

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TPE Beyond the Elastic Cross Section

Two-photon exchange (TPE) corrections

– Direct impact on extraction of form factors

– Important direct and indirect consequences on other experiments

• Neutron form factor measurements

• Strangeness from parity violation

• High-precision quasi-elastic experiments

• - N scattering measurements

• Proton charge radius, hyperfine splittingP.Blunden, et al, PRC72, 034612 (2005)

A.Afanasev, et al., PRD 72, 013008 (2005)

A.Afanasev and C.Carlson, PRL 94, 212301 (2005)

J.Arrington and I.Sick, nucl-th/0612079

D.Dutta, et al., PRC 68, 064603 (2003)

J.Arrington, PRC 69, 022201(R) (2004)

H.Budd, A.Bodek, and J.Arrington, hep-ex/0308005

P.Blunden and I.Sick, PRC 72, 057601 (2005)

S.Brodsky, et al., PRL 94, 022001 (2005)

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Data being analyzed

– BLAST

– JLab: GEn at high Q2

Upcoming experiments

– GEp/GMp at high Q2 (zero crossing?)

– TPE corrections• Cross section, polarization,

Born-forbidden observables– Parity measurements (HAPPEX,G0,A4)

New experiments being planned

– Extend GMn to higher Q2

– Improve GEp/GMp precision at low Q2

Global analysis of form factor, TPE measurements

– Extract corrected proton, neutron, and strangeness form factors

– Precise, complete data set for nucleon form factors to moderate Q2

– Constraints for GPDs, proton and neutron, extending to high Q2

Summary: Next few years

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Extensions with JLab 12 GeV Upgrade

BLUE = CDR or PAC30 approved, GREEN = new ideas under development

~8 GeV2

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Electromagnetic Form Factors

Part of the mission of Hadronic physics

– 2002 Long Range Plan, Hadronic physics milestone (2010)• Electromagentic form factors up to 3.5 GeV2 • Parity measurements up to 1 GeV2

– These measurements completed or currently in progress

– Driving rapid progress in theory

– Pion form factor measurements to challenge QCD-based calculations

Delivered, and still delivering, new insight and surprises

– Decrease of GE/GM at high Q2

• Reexamination and modification of pQCD predictions• Emphasized effects of relativity, quark angular momentum

– Two-photon exchange• Complicated task of making precise extractions• Will be thoroughly tested in next few years

– High Q2 extensions probe quark structure, provide input to GPDs, sensitive to relativity and quark angular momentum

– High precision data at lower Q2, probing “pion cloud” contributions

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Fin…