1. Deeply Virtual Meson Production with CLAS and CLAS12 Valery Kubarovsky Jefferson Lab

2. Outline Physics motivation CLAS data on pseudoscalar meson electroproduction  electroproduction 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 GPDs are the functions of three kinematic variables: x,  and t There are 4 chiral even GPDs where partons do not transfer helicity H, H, E, E 4 chiral odd GPDs flip the parton helicity H T, H T, E T, E T The chiral-odd GPDs are difficult to access since subprocesses with quark helicity-flip are suppressed ~ ~ ~ ~ ~

5. Basic properties of chiral-even GPDs Forward limit Form factors Angular Momentum

6. Chiral-odd GPDs Very little known about the chiral-odd GPDs Anomalous tensor magnetic moment (Compare with anomalous magnetic moment) Transversity distribution The transversity describes the distribution of transversely polarized quarks in a transversely polarized nucleon

7. Structure functions and GPDs Leading twist  L Kroll & Goloskokov The brackets denote the convolution of the elementary process with the GPD F (generalized formfactors) Suppressed by a factor coming from:

8. Transversity in electroproduction of pseudoscalar mesons Leading twist pion wave function suppressed Twist-3 pion wave function suppressed by, however (enhanced by chiral condensate)

9. Structure functions and GPDs t-dependence at t=t min is determined by the interplay between

10. Transverse Densities for u and d Quarks in the Nucleon Strong distortions for unpolarized quarks in transversely polarized nucleon Strong distortions for transversely polarized quarks in an unpolarized nucleon Described by E Described by E T =2H T +E T _ ~ Gockeler et al, hep/lat/0612032

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

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

13. 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

14. 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.

15. 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 

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

17.  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

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. CLAS data and GPD theory predictions S. Goloskokov and P. Kroll, S. Liuti and G. Goldstein 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 The model successfully described CLAS data even at low Q 2 Pseudoscalar meson production provides unique possibility to access the transversity GPDs.

21.    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

22. 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 )

23. Exclusive  electroproduction Verify the approach to the small-size regime Q 2 and W -dependence of the cross section Q 2 -dependence of the t-slope L/T ratio Gluonic radius of the nucleon in the valence region relative t-dependence as a function of x B GPD model to disentangle the gluon momentum integral Intrinsic strangeness alternative mechanism near the threshold

24. Kinematical Coverage

25.  L /  T separation S-channel helicity conservation (SCHC) Q 2 =2.5 GeV 2 x B =0.15

26. R=  L /  T Measurements of the ratio R=  L /  T over wide range of Q 2 =2-8 GeV 2 at various fixed x B are one of the major goals of the experiment.

27. d  L /dt in bins of Q 2 and x B exponential and dipole shapes Projected results for the differential cross sections assuming two models exponential t-dependence dipole t-dependence Q 2 =2.5, 4.5 and 6.5 GeV 2  Q 2 =1.0 GeV 2 x B =0.35 +/- 0.05  t=0.2 GeV 2 The t-slope measures the transverse area of the interaction region: Effective size of the target + Size of the produced meson Slope at fixed x B should decrease and become Q 2 independent at high Q 2

28. Transverse spatial distribution of gluons Projected data for the differential cross section in x B and Q 2 bins. The example compares a dipole like t-dependence with the exponential shape. Extraction the transverse image corresponding to the average gluon GPD from the t-dependence of d  L /dt. Good statistical accuracy can be achieved

29. Extrapolation to point d  /dt| t=0 The W-dependence of the cross section is sensitive to the exchange Extrapolation to the unphysical point t=0 eliminate the threshold effects (t min )

30. — The discovery of Generalized Parton Distributions has opened up a new and exciting avenue of hadron physics that needs exploration in dedicated experiments. — Clear indication in CLAS data strong contribution from transition — Within handbag approach transitions are related to transversity GPDs and — The JLab 12 GeV Upgrade provides tools the explore the nucleon at a much deeper level — Exclusive  electroproduction is a clean tool for the extraction of the glue average radius in the valence region 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

40. DVCS and DVMP in leading twist DVCS: the clearest way to access 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

42. 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)

43. 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

45. Structure functions and GPDs Leading twist  L suppressed : Kroll & Goloskokov The brackets denote the convolution of the elementary process with the GPD F (generalized formfactors)

48. Transverse Densities for u and d Quarks in the Nucleon Strong distortions for unpolarized quarks in transversely polarized nucleon Strong distortions for transversely polarized quarks in an unpolarized nucleon Controlled by E Controlled by E T =2H T +E T _ ~ Gockeler et al, hep/lat/0612032

49. Structure functions and GPDs Leading twist  L suppressed : Kroll & Goloskokov The brackets denote the convolution of the elementary process with the GPD F (generalized formfactors) The dominant contributions to the cross section are coming from

50. The transversity describes the distribution of transversely polarized quarks in a nucleon transversely polarized with respect to the direction of the hard probe, i.e., the virtual photon γ ∗. It is the most difficult one to measure. The transversity distribution was first mentioned by Ralston and Soper [39], but re- mains unmeasured until the recent HERMES measurement [40]. The reason is that the transversity is a chiral–odd object, which requires the combination with another chiral– odd object in helicity conserving process. Hence, unlike the other two, it is inaccessible in inclusive measurement of DIS

51. 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’ Handbag - 3D nucleon tomography – transversity GPDs H T and data. – Backward pion production (high-t, low-u). Transition distribution amplitudes. CLAS6 data

52. CLAS12 Kinematic Coverage CLAS-6

53. Statistics t-distribution  Q 2 = 2 GeV 2 W=2.75 +/- 0.25 GeV Q 2 -distribution  t= 2 GeV 2

54. 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

55.  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)

56. Transversity in  0 electroproduction S. Goloskokov, P. Kroll, 2011 G. Goldstein, S. Liuti, 2011 Theory: Goloskokov&Kroll Transvers cros section domunates in this model Data CLAS