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Results from BLAST (unpublished)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…