Real Compton Scattering from the Proton in the Hard Scattering Regime Alan M. Nathan SLAC Experimental Seminar December 2, 2003 I. Compton Scattering from Nucleon at Large p  Reaction Mechanisms Nucleon Structure II. JLab E the experiment preliminary results III. Summary & Outlook Ph.D. Students: A. Danagoulian, D. Hamilton, V. Mamyan, M. Roedelbronn

Hard Scattering Regime (s, -t, -u >> m 2 ) (p  large) Factorization: calculable in pQCD nonperturbative structure process-independent

Real Compton Scattering on the Nucleon in the Hard Scattering Limit Some Possible Factorization Schemes hard gluon exchange: *3 active quarks *2 hard gluons *3-body “form factor” handbag: *1 active quark *0 hard gluons *1-body form factor The physics issues: Which, if either, dominates at few GeV? What does RCS teach us about nucleon structure?

I. Asymptotic (pQCD) Mechanism Brodsky/LePage, Kronfeld, Vanderhaeghen, Dixon... momentum shared by hard gluon exchange 3 active quarks valence configuration dominates soft physics in distribution amplitude  (x 1, x 2, x 3 ) constituent scaling: d  /dt = f(  CM )/s 6 dominates at “sufficiently high energy”

Constituent Scaling s 6 d  /dt Cornell data approximately support scaling but... When is this the dominant mechamism? Asymptotic (symmetric) DA x 1 x 2 x 3 KS COZ Cornell 1977 data

II. “Handbag” Mechanism One active parton—rest are spectators Momentum shared by soft overlap: GPD’s Central assumptions: -- s,-t,-u >> m 2 -- struck quark nearly real and ~co-linear with proton Formally power correction to leading-twist -- asymptotically subdominant but... (Radyushkin; Diehl, Kroll, et al.) pQCD Generalized Parton Distribution

Handbag Description of RCS See Kroll, hep-ph/ Various approximations improve as s,-t,-u  m 2 Factorization is simple product Hard scattering: Klein-Nishina (KN) from nearly on-shell parton Soft physics: form factors R V (t), R A (t) | R V +/- R A | 2 : active quark spin parallel/antiparallel to proton spin Important feature:  /  KN ~ s-independent at fixed t KN R v,R A,R T

RCS and Form Factors: GPD’s Generalized Parton Distributions (GPD’s) links among diverse processes GPDx -1 momentx 0 momentt=0 limit R v (t)F 1 (t)q(x) R A (t)G A (t)  q(x) R T (t)F 2 (t)2J(x)/x - q(x) RCS sensitive to unskewed (  =0) GPD’s at high –t, moderate x

R ~ 1/t 2 for -t = 3-10 GeV 2  n  6 scaling (accidental!) d  /dt ~ s -2 t -4 Asymptotically R ~ 1/t 4  n  10 scaling  ultimately subdominant (when?) Handbag gives right order of magnitude for Cornell data Scaling of Cross Sections at fixed  CM : d  /dt ~ (1/s) 2 R 2 (t)

Polarization of Recoil Proton: Longitudinal     p Robust prediction: depends only on ratio of form factors

R T : hadron helicity flip pQCD: -t F 2 /F 1 ~ constant JLab G Ep expt: -t ½ F 2 /F 1 ~ constant Does R T /R V behave similarly? pQCD -K LT Polarization of Recoil Proton: Transverse

Goals of JLab E Measure cross sections to 5% + 5% over broad kinematic range of s, t --  /  KN vs. fixed t --1/s fixed  cm --detailed comparison with handbag Measure K LL and K LT at s=7, -t=4

Experimental Setup Kinematic Range :  e-e- Experiment ran in Hall A in 2002 mixed e-  beam  e-p/RCS discrimination needed  background & calibrations good angular resolution FPP Polarimeter Proton Spectrometer LH 2 e-e- Radiator Deflection magnet Lead-Glass Calorimeter e-e- γ

Some Experimental Details e - beam: 5-40  A, GeV, 75% polarization radiator: 6% Cu, 10 cm from target target: 15 cm LH 2  beam: sec -1 equivalent photons deflection magnet: 10 cm, 1 T calorimeter: 704 blocks, 4 cm x 4 cm x 40 cm lead glass proton spectrometer: HRS-L,  =6 msr, P p  4.3 GeV/c proton polarimeter: 6 MWDC’s, 60 cm CH 2, 60 cm C

Event Identification RCS deflected ep 00 e or  p  1/2 = m  /E '' e'e' RCS: p( ,  )p ep: p(e,e)p  0 : p( ,  0 )p   

tt yy xx  x vs E RCS Event Identification RCS ep 00 00 RCS+ep

 =270 o  max sensitivity to L,T no sensitivity to N Analyzing the Recoil Proton Polarization: Proton Spin Precession FPP

Analyzing the Recoil Proton Polarization: Focal Plane Polarimeter spin-orbit interaction FPP calibration from ep Transformation from Lab to CM L and T get mixed Dilution due to  0 background easily measured

K LL consistent with single-quark mechanism with active quark carrying proton spin (R A  R v ) Longitudinal Polarization Transfer: Preliminary Result from E …final results by Fall 2003 Kroll K LL Vanderhaeghen Dixon

K  LL  K RCS LL  K KN LL predicted by handbag five more points measured but not yet analyzed (75 o -130 o)

Transverse Polarization Transfer: Preliminary Result from E pQCD Conclusion:  R T /R V  (0.5  0.4) F 2 /F 1 Calculation by Kroll -K LT Hard to draw any conclusions with this precision

this and the next few slides show preliminary cross sections (good to about 20%) s -6 scaling at fixed  CM works only approximately Leading twist still badly underestimates cross section

d  /d  KN Prediction of s-independence at fixed t not well followed But... Preliminary Cross Sections

Prediction of s-independence at fixed t not well followed But...not so bad for data with s,-t,-u > 2.5 GeV 2 Higher energy data would be desirable

For handbag, t 4 d  /d  KN nearly independent of s,t Data for s,-t,-u > 2.5 GeV 2 in rough agreement Preliminary Cross Sections Calculations by Kroll et al.

Measure K LL,K LT,P N : confirm single-quark dominance s = 7.0 ; -t: ; -u: [GeV] 2 Determine form factors: R A /R V : Δu(x)/u(x) R T /R V : F 2 /F 1 Observe NLO effects nonzero P N A New Experiment: JLab E03-003:

Summary of Goals of E s = 7 GeV 2

Summary and Outlook E successfully completed *K LL and K LT at s=7, -t=4 K LL is “large” and positive –Suggestive of single-quark mechanism –Similar result for  0 photoproduction –Consistent with handbag prediction K LT /K LL consistent with F 2 /F 1, with poor statistics *d  /dt over broad kinematic range t 4  /  KN roughly constant for s,-t,-u > 2.5 GeV 2 s -6 scaling at fixed  CM works only approximately *Lots of p( ,  0 ) to be mined Planned extension *JLab E03-003: angular distribution of K LL, K LT, P N at s=7 Higher energy desirable