W ide A ngle C ompton S cattering

1. Wide Angle Compton Scattering Kees de Jager for the Hall A RCS Collaboration QCD-N’06 Workshop June 13, 2006 • I. Compton Scattering off the Nucleon at Large p • Reaction Mechanisms • Nucleon Structure • II. JLab E99-114 • III. Outlook & Summary

2. Real Compton Scattering • Part of JLab program of Hard Exclusive Reactions • Elastic form factors • Real Compton Scattering • Virtual Compton Scattering • Deep Virtual Compton Scattering • Deep Virtual Meson Production • Common issues: • Interplay between hard and soft processes • Threshold for onset of asymptotic region • RCS: a possible clean way to distinguish between competing reaction mechanisms

3. Asymptotic (pQCD) Mechanism • Brodsky/LePage, Kronfeld, Vanderhaeghen, Dixon, Thomson ... • momentum shared through hard gluon exchange • three active quarks • valence configuration dominates • scaling: d/dt = f(CM)/s6 • soft physics in the distribution amplitude f(x1, x2, x3) • dominates at “sufficiently” high energy

4. Soft Overlap Mechanism (Radyushkin; Diehl, Kroll, et al.) • Handbag diagram dominates • hard scattering from single quark • momentum shared by soft overlap • 1-body form factor • soft gluon exchange neglected • Structure contained in GPDs: • Links between diverse processes: • DIS, (e,e), RCS, (,), DVCS, … • New RCS form factors: • RV F1q(x) • RA  GA q(x) • RT  F2 2J(x)/x - q(x)

5. Goals of E99-114 Hyde-Wright, Nathan, Wojtsekhowski Measure cross section to 5% over wide range of (s, t) in order to • Study reaction mechanism: • t dependence at fixed s • s-independence at fixed t • polarization transfer • scaling power n(cm) • Extract form factors: • RV from unpolarized cross section • RA, RT from polarization transfer • For p(,0) • cross section • polarization

6. 1 0 . 5 A 0 L L - 0 . 5 - 1 0 4 0 8 0 1 2 0 1 6 0 ( d e g ) q C M Longitudinal Polarization of Recoil Proton point handbag pQCD

7. Proton Spectrometer/FPP 6% Cu Radiator 15 cm LH2 e- Beam Deflection Magnet  e- Veto Lead-Glass Calorimeter Experimental Setup Kinematic Range: • mixed e- beam • background & calibrations • good angular resolution • Focal Plane Polarimeter Beam: 5-40 µA, 2.5-5.75 GeV, 75 % polarization Target: LH2 15 cm long, 3 cm diameter Luminosity: 1000 higher than Cornell Experiment ran in Hall A Jan-Feb, 2002

8. Separation of RCS Events Two-body kinematics ep events RCS events “pion” events

9. Experimental results: cross section • Identify elastic photon-proton scattering events p --> pthrough correlation of: • in-plane angles • out-off-plane angles • angle vs. energy

10. Experimental results: cross section s scaling for the cross section for n = 8 pQCD prediction is n =6 use only s = 8.9 and 11 GeV2 t-independence Radyushkin

11. pQCD Calculations • Kronfeld and Nizic, PRD 44, 3445 (1991) • Vanderhaeghen, EPJ A 8, 455 (2000) • Brooks and Dixon, PRD 62, 114021 (2000) • Thomson, Pang and C.R. Ji, PRD 73, 045023 (2006) + 335 other diagrams <q2>gluon ≈ 0.02 s u ≈ 1 GeV2

12. Regge (VM) Calculations by Laget In present kinematical region coherence length of hadronic component of virtual photon is long enough that intermediate vector meson dominates in interaction. Hence, photon production amplitude can be obtained from VM production amplitude, modified by the VM decay constant. Interaction ≈ exchange of VMs (Regge trajectories) and two non-perturbative gluons Cano and Laget, PLB 551, 317 (2003)

13. Form factors of RCS and GPDs

14. Polarization Transfer KLL E = 3.2 GeV, cm = 120o (s = 6.9, t = -4 GeV2) Raw asymmetry for ep and p events ep gp raw asymmetry ≈ 0.05, systematics ≤ 10-4

15. Longitudinal Polarization Transfer u ≈ 1.1 GeV2 KLL is the average value of the longitudinal proton spin in the p CM system for a 100% circularly polarized incident photon Conclusion: active quark polarized in same direction as proton

16. ALL- initial-state polarization correlation parameter Day, Wojtsekhowski ALL=KLL in pQCD (mq=0) New proposed at s = 9 GeV2 ALL- KLL difference is a measure of the quark spin flip ~ mq/Eg

17. Future Extensions on the Neutron Need to know the incident photon energy -> Limited luminosity Post-target tagging! For s ≈ 7, t ≈ -4 GeV2 120 hours per kinematics

18. RCS perspective with 12 GeV Jlab beam

19. Summary • Photon scattering from a single quark, without a hard gluon exchange, appears to be the dominant mechanism in the RCS process on the proton in an energy range of a few GeV. • The agreement between the present experimental results and hand-bag based calculations allows the use of the RCS results to constrain GPD models. Wide-angle CS at s ≈ 10-20 GeV2 provides a powerful tool to study the partonic structure at large -t, complimentary to elastic form factor measurements. • How will these RCS results constrain a global “form factor” fit ? • Planned extensions • angular distribution of KLL and KLT at s = 7 GeV2 • measure ALL at same kinematics as KLL in Hall C • RCS on the neutron • 12 GeV

20. E02-013 results are coming Cates, Liyanage, Wojtsekhowski • Nucleon form-factor data provide a constraint for the GPD integral • Data on both the proton and the neutron form factors are needed to constrain the u and d quark GPDs • Experiment E02-013 in Hall A just completed data taking for the neutron electrical formfactor at momentum transfers of 1.2, 1.8, 2.5 and 3.5 GeV2