1. Electromagnetic Form Factors John Arrington Argonne National Lab Long Range Plan QCD Town Meeting Piscataway, NJ, 12 Jan 2007

2. 2 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, Q 2 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 Q 2 –Progress in QCD based calculations

3. 3 Status Ten Years Ago (end of 1997) Range allowed by e-d elastic Proton Neutron

4. 4 Unpolarized Elastic e-N Scattering Nearly all of these measurements used Rosenbluth separation  R = d  /d  [  (1+  )/  Mott ] =  G M 2 +  G E 2  = Q 2 /4M 2 GM2GM2 GE2GE2  =180 o  =0 o Reduced sensitivity to… G M if Q 2 << 1 G E if Q 2 >> 1 G E if G E 2 <<G M 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

5. 5 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 2 H(e,e’n) –Improved models for nuclear corrections Polarized 3 He target BLAST at MIT-Bates Focal plane polarimeter – Jefferson Lab L/T:  G M 2 +  G E 2 Pol:  G E /G M

6. 6 Example: G E /G M from Recoil Polarization Similar expressions for cross section asymmetry from polarized target

7. 7 Progress in the last decade (since 1997) Magenta: underway or approved

8. 8 PRELIMINARY G En G Mn G Ep / G Mp 1 H(e,e’p): 2 H(e,e’n): 2 H(e,e ’): Results from BLAST (unpublished)

9. 9 Insight from New Measurements New information on proton structure –G E, G M 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=0.7 x=0.4 x=0.1 1 fm

10. 10 Insight from New Measurements Can test models with data on both proton and neutron form factors –Previously, precise data and large Q 2 range only for G Mp, lower precision and limited Q 2 range for G Ep, G Mn, little data for G En Data for all FFs at low Q 2 –G Ep, G Mn, G En known to greater precision – discrepancies resolved Soon, FFs known to 4-5 GeV 2 –G Ep changed dramatically, G Mp also modified –Complete data set in “quark core” and “pion cloud” region

11. 11 Small Sample of Recent Calculations

12. 12 Pion Form Factor: F π 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 F π is experimentally challenging to determine Above Q 2 >0.3 GeV 2, one must employ the 1 H(e,e’ π + )n reaction At small –t < 0.2 GeV 2, the t-channel diagram dominates σ L ; In the t-pole approximation

13. 13 Projected JLab 12 GeV Data Higher Q 2 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 Q 2 =2.45 GeV 2

14. 14 Parity Violating Elastic e-p Scattering ExperimentQ 2 A PV [ppm]Notes SAMPLE0.1*6ppm1997 0.1*7deuterium 0.04*2deuterium HAPPEX0.515 0.12 0.16 4 He 0.5- G00.1-11-10 0.4*- 0.7*- PVA40.11 0.25 0.2*- * = backward angle Magneta for planned or ongoing measurements Nucleon charge, mag. distributions determined by quark distributions

15. 15 Recent and near-future measurements: 1997-2007 –Most of the world’s high-Q 2 data, most of the world’s high-precision data –Demonstrated problems with previous G Ep AND G Mp data –New program of parity violating elastic scattering For isovector (proton–neutron) form factors or flavor decomposition, need precise data covering similar Q 2 range, careful understanding of systematics, including correlations between measurements TPE contributions –Large effect on G Ep (up to 100+%), smaller effect on G Mp –Corrections can propagate from proton to neutron (as extracted from 2 H) –While direct TPE corrections to parity violation are small, the effect of TPE corrections to the EM FFs changes the expected asymmetry Present Status

16. 16 Two-Photon Exchange Proton form factor measurements –Comparison of precise Rosenbluth and Polarization measurements of G Ep /G Mp show clear discrepancy at high Q 2 Two-photon exchange corrections believed to explain the discrepancy Compatible with e+/e- ? –Yes: previous data limited to low Q 2 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)

17. 17 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 Q 2 TPE effects in Born-forbidden observables [JLab-Hall A, Hall C, Mainz] –Target single spin asymmetry, A y in e-n scattering –Induced polarization, p y, in e-p scattering –Vector analyzing power, A N, in e-p scattering World’s data Novosibirsk JLab – Hall B Evidence (3  level) for TPE in existing data J. Arrington, PRC 69, 032201(R) (2004)

18. 18 Two-Photon Exchange Calculations Significant progress in theoretical understanding –Hadronic calculations appear sufficient up to 2-3 GeV 2 –GPD-based calculations used at higher Q 2 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

19. 19 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 splitting P.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)

20. 20 Data being analyzed –BLAST –JLab: G En at high Q 2 Upcoming experiments –G Ep /G Mp at high Q 2 (zero crossing?) –TPE corrections Cross section, polarization, Born-forbidden observables –Parity measurements (HAPPEX,G0,A4) New experiments being planned –Extend G Mn to higher Q 2 –Improve G Ep /G Mp precision at low Q 2 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 Q 2 –Constraints for GPDs, proton and neutron, extending to high Q 2 Summary: Next few years

21. 21 Extensions with JLab 12 GeV Upgrade BLUE = CDR or PAC30 approved, GREEN = new ideas under development ~8 GeV 2

22. 22 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 GeV 2 Parity measurements up to 1 GeV 2 –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 G E /G M at high Q 2 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 Q 2 extensions probe quark structure, provide input to GPDs, sensitive to relativity and quark angular momentum –High precision data at lower Q 2, probing “pion cloud” contributions

23. 23 Fin…