Deeply Virtual Compton Scattering and Pseudoscalar Meson Electroproduction with CLAS

1. Deeply Virtual Compton Scattering and Pseudoscalar Meson Electroproduction with CLAS Valery KubarovskyJefferson Lab XII Workshop on High Energy Spin Physics September 5, 2007, Dubna

2. Outline • Physics Motivation • DVCS results (CLAS/Jlab) - Beam-spin asymmetry - Comparison with theoretical models • p0/helectroproduction • Cross section • Beam spin asymmetry • Cross section ratio • Conclusion

3. elastic inclusive exclusive gv gv gv p, r, g e’ e’ e’ p’ p’ X e e e Q Q Q Q2 = -(e-e’)2 ν = Ee – Ee’ xB = Q2/2Mn t = (p-p’)2 p p p 1/Q2is the space-time resolution of the virtual g Electron Scattering, a clean probe of the Proton Structure Reveal different aspects of the proton’s internal structure Interaction described by:

4. D. Mueller, X. Ji, A. Radyushkin, …1994 -1997 M. Burkardt, A. Belitsky… Interpretation in impact parameter space ? Structure functions, quark longitudinal momentum & spin distributions Proton form factors, transversecharge & current densities Correlatedquark momentum and helicity distributions in transverse space - GPDs How are the proton’s charge densities related to its quark momentum distribution?

5. –t – Fourier conjugate to transverse impact parameter Basic Process – Handbag Mechanism Deeply Virtual Compton Scattering (DVCS) x – longitudinal quark momentum fraction 2x – longitudinal momentum transfer GPDs depend on 3 variables, e.g. H(x, x, t). They probe the quark structure at the amplitude level. xB x = 2-xB

6. Quark-quark correlations Proton’s gravitational form factors Quark angular momentum Universality of GPDs 3D Imaging of quark distributions GPDs Forces on quarks

7. H(x,ξ=0,t=0)=q(x) H(x,ξ=0,t=0)=Dq(x) ~ Universality of GPDs ∫H(x,t)dx Elastic Form Factors Parton Momentum Distributions Real Compton Scattering GPDs ∫H(x,t)x-1dx Single Spin Asymmetries ∫H(x,ξ,t)dx ∫H(x,ξ,t)dx Deeply Virtual Compton Scattering H(x=ξ,ξ,t) Deeply Virtual Meson production Experimental measurements of the exclusive processes is a challenge, requiring high luminosity to compensate for the small cross section and detectors capable of ensuring the exclusivity of the final state.

8. Ds 2s s+ - s- s+ + s- A = = Unpolarized beam, longitudinal target: ~ ~ H(x,t) DsUL~ sinf{F1H+ξ(F1+F2)(H+ξ/(1+ξ)E) -.. }df Kinematically suppressed Unpolarized beam, transverse target: H(x,t), E(x,t) DsUT~ sinf{k(F2H – F1E) + …..}df Kinematically suppressed MeasuringGPDsthrough polarization ξ~ xB/(2-xB) ~ k = t/4M2 Polarized beam, unpolarized target: ~ H(x,t) DsLU~ sinf{F1H+ ξ(F1+F2)H+kF2E}df Kinematically suppressed

9. AUL=asinf+bsin2f Pioneering measurements in 2001 DVCS first observed in non-dedicated experiments at HERA and JLab. Evidence for twist-2 dominance in asymmetry.

10. ~ H fit model ~ model (H=0) First DVCS measurement with spin-aligned target Unpolarized beam, longitudinally spin-aligned target: ~ DsUL~ sinfIm{F1H+ξ(F1+F2)H+…}df AUL sensitive to GPD S. Chen, et al., Phys. Rev. Lett 97, 072002 (2006) CLAS preliminary ~ H=0 ~ H=0 a = 0.252 ± 0.042 b = -0.022 ± 0.045 Planned experiment in 2009 will improve accuracy dramatically.

11. p0, h, r0, w, f... -2x g*L F(z) x+x x-x p p’ z Deeply Virtual Meson Electroproduction • High Q 2 - Low -t Complement DVCS experiment. Unique access to spin dependent GPDs • Low Q 2 - High -t New form factors related to 1/x moments of GPDs • High Q2 - High -t Region never accessed. Q2 -t

12. p0, h, r0, w, f... -2x g*L F(z) x+x x-x p p’ z High Q2 Low t Region Collins,Frankfurt,Strikman -1997 • Factorization theorem states that in the limit Q2∞ exclusive electroproduction of mesons is described by hard rescattering amplitude, generalized parton distributions (GPDs), and the distribution amplitude F(z) of the outgoing meson. • The prove applies only to the case when the virtual photon has longitudinal polarization • Q2∞ sL~1/Q6 , sT/sL~1/Q2 • The full realization of this program is one of the major objectives of the 12 GeV upgrade + t.c.

13. Pseudoscalar Mesons • In the case of pseudoscalar meson production the amplitude involves the axial vector-type GPDs • These GPDs are closely related to the distributions of quark spin in the proton. The function reduces to the polarized quark/antiquark densities in the limit of zero momentum transfer • The Fourier transform with respect to pT, the so-called impact parameter distributions, describes the transverse spatial distribution of quark spin in the proton.

14. Flavor Separation and Helicity-Dependent GPDs • DVCS is the cleanest way of accessing GPDs. However, it is difficult to perform a flavor separation. • Vector and pseudoscalar meson production allows one to separate flavor and isolate the helicity-dependent GPDs.

15. “Precocious Factorization” Eides,Frankfurt,Strikman -1997 • Precocious factorization could be valid already at relatively low Q2 especially for ratios of cross sections as a function of xB • For example p0 and h ratio on the proton

16. Cross Section Ratios as a function of xB Eides,Frankfurt,Strikman -1997 All data are available. h/p0 ratio from proton data will be released very soon

17. CLAS JLab Site: The 6 GeV Electron Accelerator • 3 independent beams with energies up to 6 GeV • Dynamic range in beam current: 106 • Electron polarization: 85%

18. Beam line and the target Electromagnetic calorimeters Drift chambers 6 Superconducting coils TOF counters Cherenkov counters CEBAF Large Acceptance SpectrometerCLAS

19. Large angle EC Panel 2 & 3TOF Panel 4 TOF Panel 1 TOF Cerenkov & Forward angle EC CLAS (forward carriage and side clamshells retracted) Region 3 drift chamber

20. CLAS Lead Tungstate Electromagnetic Calorimeter 424 crystals, 18 RL, pointing geometry, APD readout s/E~3% p0 h

21. Ds 2s s+ - s- s+ + s- A = = First results in wide kinematics Fully integrated asymmetry and one of 65 bins in Q2, x, t . Fit: ALU = asinf/(1 + bcosf)

22. VGG Model (Vanderhaeghen, Guichon, Guidal) GPD model predictions Fit: ALU = asinf/(1 + bcosf) t-dependence of leading twist terma (sinΦ). VGG parameterization reproduces –t > 0.5GeV2 behavior, and overshoots asymmetry at small t. The latter could indicate that VGG misses some important contributions to the DVCS cross section.

23. Regge model prediction While there are good indications that Compton scattering does occur at the quark level a description of the process by Regge model (J-M Laget) is in fair agreement in some kinematic bins with our results. The full significance of this dual description remains to be investigated

24. Q2 xB t W DVMP: Kinematic Coverage4 dimensional grid in Q2, xB, t, and f

25. Kinematics4 dimensional grid

26. Remarks on the following slides • CLAS data • All data are preliminary • No radiative correction were applied • Cross sections are in arbitrary units • No sL/sT separation • 12 GeV: Rosenbluth L/T separation

27. f Distribution Fit of the f-distribution gives us three structure functions

28. ds/df

29. sT + esLas a function of t

30. sLTas a function of t

31. sTT as a function t

32. (sT + esL ) sTTsLTas a function of t Q2=2.3 xB=0.4 Non-zero sTTandsLT imply that both transverse and longitudinal amplitudes participate in the process t GeV2

33. (sT + esL ) sTTsLTin Regge Model (J-M Laget) charge pion elastic rescat. w/r/b1 • The dashed lines correspond to the • w/r/b1 Regge poles and elastic rescattering • The full lines include also charge pion nucleon and Delta intermediate states. • Regge model qualitatively describes • the experimental data

34. ds/dt

35. t-Slope Parameter as a Function of xB and Q2 B(xB ,Q2) • B(xB , Q2) is almost • independent of Q2 • B(xB) is decreasing with • increasing xB xB

36. t-dependence B(xB ) This is not fit of data. This is GPD predictions with Regge inspired t-dependence xat xB

37. Impact Parameter Dependent PDFs • Fourier transform of GPD • For impact parameter dependent parton distributions the perp width should go to zero for x1 • In momentum space, this implies that t-slope should decrease with increasing x, what we observe experimentally

38. From data fit Impact Parameter Profileof axial current distribution X The curve is what we obtained from experimental data The size of the proton decreases with increasing x

39. p0 and h Beam Spin Asymmetry h is the beam helicity Any observation of a non-zero BSA would be indicative of an L’T interference. If sL dominates, sLT, sTT, and sL’T go to zero

40. p0 Beam Spin Asymmetry A(f) XB=0.25 Q2=1.95 GeV2 t=-0.29 GeV2 Balck curve – A=asinf Red curve – Regge model

41. A=asinf, a as a function of t • The red curves correspond to the Regge model (JML) • BSA are systematically of the order of 0.03-0.09 over wide kinematical range in xB and Q2

42. h Beam Spin Asymmetry

43. Conclusion • Beam-spin asymmetries were extracted in the valence quark region, as a function of all variables describing the reaction. Present GPD parameterization describe reasonably well the main features of our data. The measured kinematic dependencies will put stringent constraisins on any DVCS model. • Cross sections and beam-spin asymmetries for the p0 and h exclusive electroproduction in a very wide kinematic range will be released soon • These data will help us to understand better the transition from soft to hard mechanisms • New experiments at 6 GeV with polarized and unpolarized target are coming • CLAS12 will continue the GPD study with broader kinematics at 12 GeV machine.

44. Questions to theoryWhat will our data tell us? • What does t-slope B(Q2,xB) tell us ? • What can we learn from the Q2 evolution of cross section? • Can sLT and sTT help us to constrain R=sL/sT ? • Can we constrain the GPDs within some approximations and corrections which have to be made due to non-asymptotic kinematics? • How big are the corrections? How close are we to asymptote?

45. M -2x g*L F(z) x+x x-x p p’ z Q: What will come out from our marriage? ? = +

46. THE END