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
An extra knob….s and t dependence

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)
RCS particularly good process to measure
NFPD’s since only involves 1 hadron

5. Measure cross section to 5% over wide range of (s, t) in order to
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. Longitudinal Polarization of Recoil Proton- 1 . 5 4 8 2 6 A L q C M ( d e g )
point
handbag
pQCD

7. Experiment ran in Hall A Jan-Feb, 2002
Experimental Setup
Kinematic Range:
6% Cu Radiator
Proton Spectrometer/FPP
15 cm LH2
Deflection Magnet
Veto
Lead-Glass Calorimeter
e- Beam  e-
mixed e- beam
background & calibrations
good angular resolution
Focal Plane Polarimeter
Beam: 5-40 µA, 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
Template for presentation in Two Photon Workshop
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
Template for presentation in Two Photon Workshop

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
Template for presentation in Two Photon Workshop

11. pQCD Calculations Template for presentation in Two Photon Workshop
Kronfeld and Nizic, PRD 44, 3445 (1991)
Vanderhaeghen, EPJ A 8, 455 (2000)
Brooks and Dixon, PRD 62, (2000)
Thomson, Pang and C.R. Ji, PRD 73, (2006)
+ 335 other diagrams
<q2>gluon ≈ 0.02 s
Template for presentation in Two Photon Workshop
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
Template for presentation in Two Photon Workshop

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
Template for presentation in Two Photon Workshop
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
Template for presentation in Two Photon Workshop
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
Template for presentation in Two Photon Workshop

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 ≈ 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. E 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 E in Hall A just completed data taking for the neutron electrical form factor at momentum transfers of 1.2, 1.8, 2.5 and 3.5 GeV2