1. Single Target Spin Asymmetries and GPDs Jian-ping Chen, Jefferson Lab, Virginia, USA SSA Workshop, BNL, June 1-3, 2005 Nucleon structure and GPDs DVCS and Wide Angle Compton Scattering Target SSA with 2  exchange to probe GPDs JLab E05-015: neutron SSA with vertically polarized 3 He Summary

2. Nucleon Structure Elastic scattering  nucleon has finite size Dirac Form Factor, F 1 (Q 2 ) - charge distribution Pauli Form Factor, F 2 (Q 2 ) – current distribution DIS  parton distribution functions (PDFs) q(x) – quark longitudinal momentum distribution  q(x) – quark longitudinal spin distribution quark flavors, g(x), … Connection?

3. Beyond charge and quark distributions – Generalized Parton Distributions (GPDs) Elastic: transverse charge & current densities DIS: quark longitudinal momentum & helicity distributions X. Ji, D. Mueller, A. Radyushkin (1994-1997), … Correlated distributions in transverse space - GPDs M. Burkardt, A. Belitsky (2000) …

4. GPDs and ‘Handbag’ Diagram

5. A Unified Description of Hadron Structure Parton momentum distributions Elastic form factors Real Compton scattering at high t Parton spin distributions Deeply Virtual Compton Scattering GPDs Quark angular Momentum

6. Link to DIS and Elastic Form Factors ),,( ~, ~,,txEHEH      J G =  1 1 )0,, q(q()0,, q(q( 2 1 2 1 xE xHxdxJqJq Quark angular momentum (Ji’s sum rule) X. Ji, Phy.Rev.Lett.78,610(1997) DIS at  =t=0 )(),()0,0,( ~ )( ()0,0,( xqxqx H xq xqxH    Form factors (sum rules)  )(),,( ~, )(),,( ~ ) Dirac f.f.(),,(, 1 1, 1 1 1 tGtxEdxtGtxH tF1F1 txH qPqA         ) Pauli f.f.(),,( 1 tF2F2 txEdx    

7. Access GPDs Accessed by cross sections Accessed by beam/target spin asymmetry t=0 Quark distribution q(x) -q(-x) DIS measures at  =0

8. Program to access/determine GPD’s Direct access: -Deep Inelastic Scattering (DIS) -Deep Virtual Compton Scattering (DVCS) -Deep Virtual Meson Production (DVMP) -Doubly Deep Virtual Compton Scattering (DDVCS) Form Factors: Moments of GPDs: -Elastic Scattering -Wide Angle Compton Scattering -Single Target Spin Asymmetry through 2-  exchange

9. SSA in DVCS to probe GPD

10. Accessing GPDs through DVCS d4d4 dQ 2 dx B dtd  ~ | DVCS + BH | 2 BH : given by elastic form factors DVCS: determined by GPDs  LU ~ BH Im( DVCS ) sin  + higher twist. ~ |DVCS| 2 + |BH| 2 + BH *Im( DVCS ) DVCS BH GPDs FF e -’     p  e-e- ** plane ee’  * plane  *p ep ep 

11. Separating GPDs through polarization  LU  ~ sin  {F 1 H +  (F 1 +F 2 ) H +kF 2 E }d  ~ Polarized beam, unpolarized target: Unpolarized beam, longitudinal target:  UL  ~ sin  {F 1 H +  (F 1 +F 2 )( H + … }d  ~ Unpolarized beam, transverse target:  UT  ~ sin  {k(F 2 H – F 1 E) + ….  }d   = x B /(2-x B ) k = t/4M 2 H, H, E Kinematically suppressed H, H ~ H, E A =           = ~

12. First observation of DVCS/BH beam asymmetry GPD analysis of CLAS/HERMES/HERA data in LO/ NLO shows results consistent with handbag mechanism and lowest order pQCD A. Freund, PRD 68,096006 (2003), A. Belitsky, et al. (2003)  sin  +  sin2   << 1 twist-3 << twist-2 e + p e +  X e - p e - pX CLAS 4.3 GeV 2001 0 HERMES 27 GeV -180180  (deg) Q 2 =2.5 GeV 2 Q 2 =1.5 GeV 2  [ rad ] CLAS preliminary 5.75 GeV = 2.0GeV 2 = 0.3 = 0.3GeV 2

13. e p ep  = 2.0GeV 2 = 0.2 = 0.25GeV 2 CLAS preliminary E=5.75 GeV A UL Longitudinally polarized target A UL ~sin  {F 1 H +  (F 1 +F 2 ) H... }d  ~ DVCS/BH target asymmetry Asymmetry observed at about the expected magnitude. Much higher statistics, and broad kinematical coverage are needed. HERMES data on deuterium target

14. First Dedicated DVCS Experiments at JLab Azimuthal and Q 2 dependence of Im(DVCS) at fixed . Test Bjorken scaling. => Full reconstruction of all final state particles e, p,  => High luminosity 10 37 Data taking completed , t, Q 2 - dependence of Im(DVCS) in wide kinematics. Constrain GPD models. PbWO 4 Electromagnetic calorimeter s.c. solenoid CLAS Currently taking data Hall A (p and n) LD2

15. Deeply Virtual Exclusive Processes - Kinematics Coverage of 12 GeV Upgrade JLab Upgrade unique to JLab High x B only reachable with high luminosity H1, ZEUS

16. L = 2x10 35 T = 1000 hrs  Q 2 = 1GeV 2  x = 0.05 CLAS12 - DVCS/BH Target Asymmetry Selected kinematics e p ep   ~sin  Im{F 1 H +  (F 1 +F 2 ) H... }d  ~

17. Wide Compton Scattering to probe GPD

18. Wide Angle Compton Scattering WACS access GPD moments Compton Form Factors: JLab Hall A E99-114 nucl-ex/0410001 Data: GPD: Recoil polarization components: P. Kroll, hep-ph/0412169

19. Target SSA with 2  exchange to probe GPD JLab E05-015: vertically polarized n ( 3 He)

20. GPD moment with target SSA with 2  effect JLab E05-015: Spokespersons: T. Averett, J.P. Chen, X. Jiang

38. Summary on target SSA with 2  2  -exchange provides a new tool to probe nucleon dynamics Non-zero A y is a clear signature of 2  -exchange E05-015 goals: Unambiguously establish a non-zero A y First experiment to use 2  A y to study GPDs A y n sensitive to one GPD moment, cleaner interpretation Constraints on E GPD Technically straight-forward measurement, no new equipment needed ~ 1 month beam time to test GPD prediction for A y at 15% level.

39. Summary GPD provides a unified framework DVCS SSA direct access GDPs Results from JLab, HERMES and other labs Dedicated experiments and JLab upgrade Wide Angle Compton Scatting access GPD moments Recent results on K LL and K LS. New way to measure GPD moments: STSA with 2  JLab E05-015: neutron  one moment of GPD constraints on E GPD.

40. Precision measurement of g 2 n Higher twist effects: quark-gluon correlations

41. Quark-Gluon Correlations In simple partonic picture g 2 (x)=0 Wandzura and Wilczek have shown that g 2 can be written in two parts: –twist-2 contributions given by g 1 –the other originating from quark-gluon correlations (twist-3)

42. Jefferson Lab Hall A Experiment E97-103 Precision Measurement of the Neutron Spin Structure Function g 2 n (x,Q 2 ): A Search for Higher Twist Effects T. Averett, W. Korsch (spokespersons) K. Kramer (Ph.D. student) Precision g 2 n, 0.57 2 GeV, at x ~ 0.2. Direct comparison to twist-2 g 2 ww prediction using world g 1 n data. Quantitative measurement of higher twist effects provides information on nucleon structure beyond simple parton model (e.g. quark-gluon correlations).

43. E97-103 Results: g 2 n vs. x Improved precision of g 2 n by an order of magnitude

44. E97-103 results: g 2 n vs. Q 2 Measured g 2 n consistently higher than g 2 ww

45. E97-103 results: g 1 n Agree with NLO fit to world data, evolved to our Q 2

46. JLab E99-117 Precision Measurement of A 1 n at Large x Spokespersons: J. P. Chen, Z. -E. Meziani, P. Souder, PhD Student: X. Zheng Precision A 1 n data at high x 2.7GeV 2 2 GeV Extracting valence quark spin distributions Test our fundamental understanding of valence quark picture SU(6) symmetry Valence quark models pQCD (with HHC) predictions Other models: Statistical Model, Chiral Soliton Model, PDF fits, …. Crucial input for pQCD fit to PDF A 2 n at high x, by-product,  d 2 n

47. A 2 n results By-product Precision better than the world best results Also g 1 n and g 2 n results Improved d 2 n precision by a factor of 2: d 2 n =0.0062 ± 0.0028 PRC 70, 065207 (2004)

48. Summary on g 2 n and d 2 n results Precision measurement of g 2 n at low Q 2 An order of magnitude improvement in precision g 2 n consistently higher than g 2 WW Higher twist effects: quark-gluon correlations Precision spin structure data at high x from JLab Valence quark neutron spin structure A 1 n at high x, an order of magnitude improvement: A 2 n at high x, by-product d 2 n : a factor of 2 improvement, can compare with LQCD