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

2. Outline Physics Motivation Physics Motivation DVCS results (CLAS/Jlab) DVCS results (CLAS/Jlab) - Beam-spin asymmetry - Comparison with theoretical models     electroproduction     electroproduction –Cross section –Beam spin asymmetry –Cross section ratio Conclusion Conclusion

3. Electron Scattering, a clean probe of the Proton Structure Q 2 = -(e-e’) 2 ν = E e – E e’ x B = Q 2 /2M t = (p-p’) 2 1/  Q 2 is the space-time resolution of the virtual  e’e’ p e Q p’ elastic vv e’e’ p e Q X inclusive vv e’e’ p e Q p’  exclusive vv Interaction described by: Reveal different aspects of the proton’s internal structure

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

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

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

7. Universality of GPDs Single Spin Asymmetries Deeply Virtual Meson production Real Compton Scattering Elastic Form Factors Parton Momentum Distributions Deeply Virtual Compton Scattering GPDs ∫H(x,t)dx ∫H(x,ξ,t)dx H(x=ξ,ξ,t) ∫H(x,t)x -1 dx ∫H(x,ξ,t)dx 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. H(x,ξ=0,t=0)=q(x) H(x,ξ=0,t=0)=  q(x) ~

8. Typical GPD integral GPD are real functions due to time reversal invariance, the hard scattering kernel is complex and leads to both a real and an imaginary part of the process amplitude. stands for a generic GPD and principal value integral

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

10. A UL =  sin  +  sin2  Pioneering measurements in 2001 Evidence for twist-2 dominance in asymmetry. DVCS first observed in non-dedicated experiments at HERA and JLab.

11. First DVCS measurement with spin-aligned target Unpolarized beam, longitudinally spin-aligned target:  UL  ~ sin  Im{F 1 H +ξ(F 1 +F 2 ) H +… }d  ~  = 0.252 ± 0.042  = -0.022 ± 0.045 Planned experiment in 2009 will improve accuracy dramatically. CLAS preliminary H=0 ~ ~ A UL sensitive to GPD H ~ fit model model ( H =0) ~ S. Chen, et al., Phys. Rev. Lett 97, 072002 (2006)

12. 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 Q 2 - High -t Region never accessed. Q2Q2 -t      p p’ LL (z)(z) x-   z x+ 

13.      p p’ LL (z)(z) x-   z x+  + t.c. Factorization theorem states that in the limit Q 2  ∞ exclusive electroproduction of mesons is described by hard rescattering amplitude, generalized parton distributions (GPDs), and the distribution amplitude  (z) of the outgoing meson. The prove applies only to the case when the virtual photon has longitudinal polarization Q2  ∞  L ~1/Q 6,  T /  L ~1/Q 2 The full realization of this program is one of the major objectives of the 12 GeV upgrade Collins,Frankfurt,Strikman -1997 High Q 2 Low t Region

14. Factorization in the High t Low Q2 Region It has been argued that exclusive production of photons and mesons at large t, effectively proceeds via a partonic mechanism, and can be again be described in terms the GPD in the nucleon It has been argued that exclusive production of photons and mesons at large t, effectively proceeds via a partonic mechanism, and can be again be described in terms the GPD in the nucleon Theory predicts  L and  T in this kinematics Theory predicts  L and  T in this kinematics Radyushkin 1998 Diehl et al, 1998 Huang, Kroll, 2000

15. High t Low Q 2 Region The expression is written for the pseudoscalar meson production  (z) is the meson distribution amplitude f (z,s,Q2,t) is parton level amplitude R(t) formfactor depends on 1/x moments of GPD  q is polarized parton distribution for quark u,d,s  ~ 1 geV -2

16. Pseudoscalar Mesons In the case of pseudoscalar meson production the amplitude involves the axial vector-type GPDs 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 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 p T, the so- called impact parameter distributions, describes the transverse spatial distribution of quark spin in the proton. The Fourier transform with respect to p T, the so- called impact parameter distributions, describes the transverse spatial distribution of quark spin in the proton.

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

18. Transition from “hadronic” to the partonic degrees of freedom Transition from “hadronic” to the partonic degrees of freedom The extraction of GPD from electroproduction data is a challenging problem. A detailed understanding of the reaction mechanism is essential before one can compare with theoretical calculations The extraction of GPD from electroproduction data is a challenging problem. A detailed understanding of the reaction mechanism is essential before one can compare with theoretical calculations Detailed measurements of observables may test model-independent features of the reaction mechanism, such as t-slopes, flavor ratios, and generally by studying the variation of observables over a wide range of Q 2 and t. Detailed measurements of observables may test model-independent features of the reaction mechanism, such as t-slopes, flavor ratios, and generally by studying the variation of observables over a wide range of Q 2 and t.

19. Transition from “hadronic” to the partonic degrees of freedom Transition from “hadronic” to the partonic degrees of freedom ? R p p’ **  p *L*L 

20. “Precocious Factorization” Precocious factorization could be valid already at relatively low Q 2 especially for ratios of cross sections as a function of x B Precocious factorization could be valid already at relatively low Q 2 especially for ratios of cross sections as a function of x B For example  0 and  ratio on the proton For example  0 and  ratio on the proton Eides,Frankfurt,Strikman -1997

21. Cross Section Ratios as a function of x B All data are available.  0 ratio from proton data will be released very soon Eides,Frankfurt,Strikman -1997

22. CLAS JLab Site: The 6 GeV Electron Accelerator  3 independent beams with energies up to 6 GeV  Dynamic range in beam current: 10 6  Electron polarization: 85%

23. CEBAF Large Acceptance Spectrometer CLAS TOF counters Drift chambers Beam line and the target Electromagnetic calorimeters 6 Superconducting coils Cherenkov counters

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

25. CLAS Lead Tungstate Electromagnetic Calorimeter     /E~3% 424 crystals, 18 RL, pointing geometry, APD readout

26. Fit: A LU =  sin  cos  Fully integrated asymmetry and one of 65 bins in Q 2, x, t. First results in wide kinematics A =           =

27. t-dependence of leading twist term  (sinΦ). GPD model predictions VGG parameterization reproduces –t > 0.5GeV 2 behavior, and overshoots asymmetry at small t. The latter could indicate that VGG misses some important contributions to the DVCS cross section. VGG Model (Vanderhaeghen, Guichon, Guidal) Fit: A LU =  sin  cos 

28. 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

29. DVMP: Kinematic Coverage 4 dimensional grid in Q 2, x B, t, and  t Q2Q2 xBxB W

30. 00 00 p

31. p  

32. Kinematics 4 dimensional grid BinsFromToUnits 71.04.6 GeV 2 70.10.58 60.092.0 120360degrees

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

34. Distribution Fit of the  -distribution gives us three structure functions

35. d  /d 

36.  T  L  as a function of t

37.  LT  as a function of t

38.  TT as a function t

39.  T  L )  TT  LT as a function of t t GeV 2 Q 2 =2.3 x B =0.4 Non-zero  TT and  LT imply Non-zero  TT and  LT imply that both transverse that both transverse and longitudinal amplitudes and longitudinal amplitudes participate in the process participate in the process

40.  T  L )  TT  LT in Regge Model (J-M Laget) The dashed lines correspond to the  /b1 Regge poles and elastic rescattering The full lines include also charge pion nucleon and Delta intermediate states. Regge model qualitatively describes Regge model qualitatively describes the experimental data  /b1 elastic rescat. charge pion

41. d  /dt

42. t-Slope Parameter as a Function of x B and Q 2 xBxB B(x B,Q 2 ) B(x B, Q 2 ) is almost independent of Q 2 B(x B ) is decreasing with increasing x B

43. t-dependence xBxB B(x B ) This is not fit of data. This is GPD predictions with Regge inspired t-dependence x  t

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

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

46.  0 and  Beam Spin Asymmetry h is the beam helicity Any observation of a non-zero BSA would be indicative of an L’T interference. If  L dominates  LT    and  L’T go to zero

47.  0 Beam Spin Asymmetry A(  ) X B =0.25 Q 2 =1.95 GeV 2 t=-0.29 GeV 2 Balck curve – A=  sin  Red curve – Regge model

48. A=  sin  as a function of t The red curves correspond to the Regge model (JML) 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 x B and Q 2 BSA are systematically of the order of 0.03- 0.09 over wide kinematical range in x B and Q 2

49. JML Regge Model (a) Pole terms (a) Pole terms (b) Box diagram with elastic rescattering (b) Box diagram with elastic rescattering (c) Box diagram with charge exchange (c) Box diagram with charge exchange In the GPD formalism, only the longitudinal amplitude may be calculated. This data shows non-zero transferse terms. In the GPD formalism, only the longitudinal amplitude may be calculated. This data shows non-zero transferse terms.

50.  Beam Spin Asymmetry

51. BSA summary Sizeable beam-spin asymmetries for exclusive  0 and  mesons electroproduction have been measured above the resonance region for the first time Sizeable beam-spin asymmetries for exclusive  0 and  mesons electroproduction have been measured above the resonance region for the first time These non-zero asymmetries imply that both transverse and longitudinal amplitudes participate in the process These non-zero asymmetries imply that both transverse and longitudinal amplitudes participate in the process Regge model qualitatively describe the experimental data Regge model qualitatively describe the experimental data

52. 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  0 and  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.

53. Questions to theory What will our data tell us? What does t-slope B(Q 2,x B ) tell us ? What does t-slope B(Q 2,x B ) tell us ? What can we learn from the Q 2 evolution of cross section? What can we learn from the Q 2 evolution of cross section? Can  LT and  TT help us to constrain R=  L /  T ? Can  LT and  TT help us to constrain R=  L /  T ? 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?

54. Q: What will come out from our marriage? p p’  z x+  LL (z)(z) x-    + = ?

55. THE END