1. Hard Exclusive Pseudo-Scalar Meson Production in CLAS Valery Kubarovsky Jefferson Lab Partons in Nucleons and Nuclei Marrakech, Morocco, September 26-30, 2011

2. Outline Physics motivation CLAS data on pseudoscalar meson electroproduction Hard exclusive electroproduction of  0 and  with CLAS12 Conclusion

3. Description of hadron structure in terms of GPDs Nucleon form factors transverse charge & current densities Nobel prize 1961- R. Hofstadter Structure functions quark longitudinal momentum (polarized and unpolarized) distributions Nobel prize 1990 –J.Friedman, H. Kendall, R. Taylor GPDs correlated quark momentum distributions (polarized and unpolarized) in transverse space

4. Generalized Parton Distributions There are 4 chiral even GPDs where partons do not transfer helicity H, H, E, E H and E are “unpolarized” and H and E are “polarized” GPD. This refers to the parton spins. 4 chiral odd GPDs flip the parton helicity H T, H T, E T, E T. H T is connected with transversity ~ ~ ~ ~ ~ ~

5. Basic GPD properties Forward limit Form factors Angular Momentum

6. DVCS and DVMP in leading twist DVCS: the clearest way to access the GPDs Only  T photons participate in DVCS Interference with BH process DVMP: Factorization proven only for  L  L ~1/Q 6,  T /  L ~1/Q 2 Meson distribution amplitude Gluon exchange required Vector and pseudoscalar meson production allows to separate flavor and separate the helicity-dependent and helicity independent GPDs. Factorization theorem Access to fundamental degrees of freedom

7. Transversity in hard exclusive electroproduction of pseudoscalar mesons S. Goloskokov, P. Kroll, 2011, arXiv:1106.4897v1     The data clearly show that a leading-twist calculation of DVMP within the handbag is insufficient. They demand higher-twist and/or power corrections There is a large contribution from the helicity amplitude    Such contribution is generated by the the helicity-flip or transversity GPDs in combination with a twist-3 pion wave function This explanation established an interesting connection to transversity parton distributions. The forward limit of H T is the transversity   (x,0,0)=h 1 (x)

8. Nucleon Tensor Charge from Exclusive  0 Electroproduction Ahmad, Goldstein, Luiti, Phys. Rev. D 79, 054014 (2009), arXiv:1104.5682v1 The quantum numbers and Dirac structure of π 0 electroproduction restrict the possible contributions to the 4 chiral odd GPDs, one of which, H T, is related to the transversity distribution and the tensor charge. This differs from DVCS and both vector and charge    electroproduction, where the axial charge can enter the amplitudes. Contrary the tensor charge enters the  0 process. partonic degrees of freedom interpretation; t-channel exchange diagram

9. 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% Hall-B CLAS Hall-A Hall-C

10. CEBAF Large Acceptance Spectrometer CLAS 424 crystals, 18 RL, Pointing geometry, APD readout CLAS Lead Tungstate Electromagnetic Calorimeter

11. CLAS6: lots of data, cross sections, beam-spin asymmetries CLAS12: Exp. # E12-06-108 CLAS DVMP program

12. 4 Dimensional Grid Rectangular bins are used. Q 2 -7 bins(1.-4.5GeV 2 ) x B -7 bins(0.1-0.58) t- 8 bins(0.09-2.0GeV) φ -20 bins(0-360°)  0 data ~2000 points  data ~1000 points xBxB Q2Q2

13. Monte Carlo Empirical model for the structure cross sections was used for the MC simulation and radiative corrections This model is based on CLAS data MC simulation included the radiative effects and used empirical model for the Born term. 100 M events were simulated with GSIM program.

14. Radiative Corrections Radiative Corrections were calculated using Exclurad package with structure cross sections described by our empirical cross section. Q 2 = 1.15 GeV 2 x B = 0.13 -t = 0.1 GeV 2  00 

15. Structure Functions  U =  T +  L  TT  LT GM Laget Regge model  distribution -t

16.  U =  T +  L W dependence  U ~1/W 1.5-2  U decreases with W at Jlab kinematics This behavior is typical for Regge model Difficult to get such dependence with conventional GPD models

17.  U =  T +  L x B dependence Another way to view the cross section as a function of x B  U increases with x B W=Q 2 (1/x-1)

18. d  U /dt GeV 2 -t

19. t-slope parameter: x B dependence The slope parameter is decreasing with increasing x B. Looking to this picture we can say that the perp width of the partons with x  1 goes to zero.

20. Transversity in  0 electroproduction S. Goloskokov, P. Kroll, 2011, arXiv:1106.4897v1 Q 2 =2.71 GeV 2 x B =0.34 Transvers cross section dominates in this model Theory: Goloskokov&Kroll Data: CLAS (preliminary)

21. Transversity in  0 electroproduction S. Goloskokov, P. Kroll, 2011, arXiv:1106.4897v1 Q 2 =1.6 GeV 2 x B =0.19 Q 2 =2.2 GeV 2 x B =0.28 Q 2 =3.2 GeV 2 x B =0.43 Include transversity GPDs H T and. Dominate in CLAS kinematics. The model was optimized for low x B and high Q 2. The corrections t/Q 2 were omitted Nevertheless the model successfully described CLAS data even at low Q 2 Pseudoscalar meson production provides unique possibility to access the transversity GPDs. Q 2 =1.2 GeV 2 x B =0.13 Q 2 =1.8 GeV 2 x B =0.22 Q 2 =2.7 GeV 2 x B =0.34

22. Goldstein and Liuti GPD T model Data – CLAS6 We are looking forward to extend the comparison with GPD-based model in the full kinematic domain of CLAS

23. Beam Spin Asymmetry Ahmad, Goldstein, Luiti, 2009 Data CLAS Blue – Regge model Red – GPD predictions tensor charges δu=0.48, δd =-0.62 transverse anomalous magnetic moments κ u T = 0.6, κ d T = 0.3.

24.    Ratio The dependence on the x B and Q 2 is very week. The ratio in the photoproduction is near 0.2-0.3 (very close to what we have at our smallest Q 2 ). Conventional GPD models predict this ratio to be around 1 (at low –t). KG model predicts this ratio to be ~1/3 at CLAS values of t -t=0.14 GeV 2 -t=0.50 GeV 2 -t=0.30 GeV 2 -t=0.50 GeV 2 _ Indication of large contributions from the GPD E T with the same sign for u and d-quark parts Data: CLAS preliminary

25. CLAS12 Luminosity 10 35 cm 2 s -1 Forward Detector - TORUS magnet - Forward SVT tracker - HT Cherenkov Counter - Drift chamber system - LT Cherenkov Counter - Forward ToF System - Preshower calorimeter - E.M. calorimeter Central Detector - SOLENOID magnet - Barrel Silicon Tracker - Central Time-of-Flight -Polarized target (NSF) Proposed upgrades - Micromegas (CD) - Neutron detector (CD) - RICH detector (FD) - Forward Tagger (FD )

26. E12-06-108 Hard Exclusive Electroproduction of  0 and  with CLAS12 Cross sections of the reactions ep ➝ ep  0, ep ➝ ep  Extract structure functions  T,  L,  TT,  LT  LT’ vs. Q 2, x B, t – Fourier decomposition of the reduced cross section  T +  L,  TT,  LT – Beam-spin asymmetry  LT’ – Rosenbluth separation  T,  L, at energies 11, 8.8 and 6.6 GeV Handbag - 3D nucleon tomography – transversity GPDs H T and data. – Backward pion production (high-t, low-u). Transition distribution amplitudes. CLAS6 data

27. CLAS12 Kinematic Coverage CLAS-6

28. Statistics t-distribution  Q 2 = 2 GeV 2 W=2.75 +/- 0.75 GeV Q 2 -distribution  t= 2 GeV 2

29. Example of the Simulated Cross Section and Asymmetry A=4.5E5+/-6.6E2 B=0.047  0.002 C=0.200+/-0.002 A=0.100+/-0.002 B=0.049+/-0.030 C=0.210+/-0.030 Simulated beam-spin asymmetry Simulated cross section

30. — The discovery of Generalized Parton Distributions has opened up a new and exciting avenue of hadron physics that needs exploration in dedicated experiments. — Moderate to high energy, high luminosity, and large acceptance spectrometers are needed to measure GPDs in deeply virtual exclusive processes. — The JLab 12 GeV Upgrade provides the tools to do this well and explore the nucleon at a much deeper level. Summary

31. The Fin

32. Structure Functions Lines – Regge model Data: CLAS preliminary

33. M. Kaskulov arXiv:1105.1993 and private communication

34. SourceError Acceptance2.5 % Beam Charge0.2 % Particle ID1.0 % Radiative Corrections 1.O %  U =  T +  L 4.0 %  L,   10-30 % Kinematic coverage W=2.75 +/- 0.75 GeV t-distribution Q 2 = 5 GeV 2 Q 2 -distribution t= 1 GeV 2 Examples of the  0 MC simulation Simulated beam-spin asymmetry       Anticipated systematic errors Q 2 =2 GeV 2,t=1 GeV 2 Simulated cross section A=4.5E5+/-6.6E2 B=0.047  0.002 C=0.200+/-0.002 A=0.100+/-0.002 B=0.049+/-0.030 C=0.210+/-0.030 GeV 2 CLAS-6

35. DVCS and DVMP DVCS: the clearest way to access the GPDs Only  T photons participate in DVCS Interference with BH process DVMP: Factorization proven only for  L  L ~1/Q 6,  T /  L ~1/Q 2 Meson distribution amplitude Gluon exchange required Vector and pseudoscalar meson production allows to separate flavor and separate the helicity-dependent and helicity independent GPDs. Factorization theorem Access to fundamental degrees of freedom

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

37. Regge Model (a) Regge poles (vector and axial vector mesons) (b) and (c) pion cuts J.M. Laget 2010 Vector meson cuts

38. d  U /dt GeV 2 -t nb/GeV 2

39. JML Regge model Q 2 = 2.25 GeV 2 x B = 0.34 -t