1. Deeply Virtual Meson Production and Transversity GPDs Valery Kubarovsky Jefferson Lab 1 Exclusive Meson Production and Short-Range Hadron Structure January 22-24, 2015, Jlab

2. Outline Physics motivation CLAS data on pseudoscalar meson electroproduction Transversity GPD and structure functions Flavor decomposition of Transversity GPDs Conclusion 2

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 3 D. Mu ̈ller ’94, X. Ji ‘96, A. Radyushkin ‘96 Picture from the review: Belitsky, Radyushkin (2005)

4. Generalized Parton Distributions GPDs are functions of three kinematic variables: x,  and t, x-quark momentum fraction of the nucleon, skewedness  xB/(2-x B ), t=(p-p’) 2. There are 4 chiral even GPDs where partons do not flip 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 ~ ~ ~ ~ 4

5. 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 5

6. Structure functions and GPDs Leading twist  L The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) 6

7. Structure functions and GPDs Leading twist  L The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) 7 S. Goloskokov and P. Kroll S. Liuti and G. Goldstein  L suppressed by a factor coming from:

8. Structure functions and GPDs Leading twist  L The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) 8 S. Goloskokov and P. Kroll S. Liuti and G. Goldstein  L suppressed by a factor coming from:

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

10. 10 A. Kim, to be published

11. Structure functions and GPDs t-dependence at t=t min is determined by the interplay between Direct access to the Transversity GPDs 11 H T and E T =2H T +E T _ ~ Transversity GPD model S. Goloskokov and P. Kroll S. Liuti and G. Goldstein  L <<  T Transversity dominance

12. 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 12

13. e1-dvcs (2005) 424 crystals, 18 RL, Pointing geometry, APD readout CLAS Lead Tungstate Electromagnetic Calorimeter 13

14. 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)  20 bins(0-360°)  0 data ~2000 points  data ~1000 points xBxB Q2Q2 14

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

16. d  U /dt GeV 2 -t 16

17. t-slope parameter: x B dependence The slope parameter is decreasing with increasing x B. The Q 2 dependence is weak. Looking to this picture we can say that proton’s transverse radius shrinks as x  1. 17

18. Structure Functions  T  L )  TT  LT 18 Data: I.Bedlinskiy et al. (CLAS) Phys. Rev. C 90, 039901 (2014) Curves: Goloskokov, Kroll Transversity GPD model

19. CLAS data and GPD theory predictions Solid: S. Goloskokov and P. Kroll Dots: S. Liuti and G. Goldstein 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 describes CLAS data even at low Q 2 Pseudoscalar meson production provides unique possibility to access the transversity GPDs. 19 CLAS collaboration. I Bedlinskiy et al. Phys.Rev.Lett. 109 (2012) 112001

20. W-dependence of the total cross section  tot (Q 2,W)(  *p) 20

21. Spin Asymmetries 21 Kroll, Goloskokov Constant term of the double-spin asymmetries may be estimated from unpolarized data Compare with the asymmetry extracted from polarized data (A.Kim)

22. 22 Asymmetry from the unpolarized data Asymmetry from polarized data Theoretical predictions (GK) Double Spin Asymmetry Double-spin asymmetries from unpolarized and polarized data are consistent Theory does not describe data. The main reason for tjis inconsistency is coming from the theoretical description of the unpolarized structure functions Adjustment of the theory parameters will improve the description of the unpolarized data and at the same time double-spin asymmetry Q2=1.87 GeV2 xB=0.27 Q2=1.87 GeV2 xB=0.27 Q2=1.87 GeV2 xB=0.27 Q2=1.87 GeV2 xB=0.27

23. Comparison  0 /  preliminary  U =  T +  L drops by a factor of 2.5 for   TT drops by a factor of 10 The GK GPD model (curves) follows the experimental data The statement about the transversity GPD dominance in the pseudoscalar electroproduction becomes more solid with the inclusion of  data 00  uu  TT 23 Q 2 =2.2 GeV 2 x B =0.28 Q 2 =2.2 GeV 2 x B =0.28 Q 2 =2.2 GeV 2 x B =0.28 Q 2 =2.2 GeV 2 x B =0.28  LT

24.  /  0 ratio The dependence on x B and Q 2 is very weak. Chiral odd GPD models predict this ratio to be ~1/3 at CLAS kinematics Chiral even GPD models predict this ratio to be around 1 (at low –t). 24 t=-0.5 GeV 2

25.  /  0 ratio The dependence on the x B and Q 2 is very week. Chiral even GPD models predict this ratio to be around 1 (at low –t). Chiral odd GPD models predict this ratio to be ~1/3 at CLAS kinematics 25 Theoretical prediction R=1 for the Chiral-even GPD models (  L >>  T ) Eides,Frankfurt,Strikman PRD 59,114025(1998)

26. Structure functions and GFFs The brackets denote the convolution of the elementary process with the GPD F (Generalized form factors GFFs) 26 CLAS did not separate  T and  L However in the approximation of the transversity GPDs dominance, that is supported by CLAS data,  L <<  T we have direct access to the generalized form factors for  and  production. Goloskokov, Kroll Transversity GPD model E T =2H T +E T _ ~

27. E T > H T for   and  t-dependence is steeper for E T than for H T Estimation of the systematic uncertainties connected with the used approximation is in progress Generalized Form Factors 27  Q 2 GeV 2 xBxB 1.20.15 1.80.22 2.20.27 2.70.34 _ _  

28.  0 Generalized Form Factors 28 Q 2 =2.2 GeV 2, x B =0.27 E T > H T t-dependence is steeper for E T than for H T _ _ | |~ e bt b(E T )=1.27 GeV -2 b(H T )=0.98 GeV -2

29. GPD Flavor Decomposition 29 Similar expressions for E T _ GPDs appear in different flavor combinations for  0 and  The combined  0 and  data permit the flavor (u and d) decomposition for GPDs H T and E T The u/d decomposition was done under simple assumption that the relative phase between u and d is 0 or 180 degrees. _

30.  /  GPDs 30 Q 2 =2.2 GeV 2, x B =0.27      

31.  correction factor 31 Octet-singlet mixing angle Chiral condensate Decay constants 1/K  

32. | | d and | | u seem to have the same signs _ _ Flavor Decomposition of the Transversity GPDs 32 u quarks d quarks u quarks d quarks u and d have different signs for u and d- quarks in accordance with the transversity function h 1 (Anselmino et al.) Q 2 =1.8 GeV 2, x B =0.22 Decisions shown with positive values of u- quark’s GPDs only _

33. Flavor Decomposition of the Transversity GPDs u quarks d quarks u quarks d quarks Q 2 =2.2 GeV 2, x B =0.27 _ _ u and d have different signs for u and d- quarks in accordance with the transversity function h 1 (Anselmino et al.) | | d and | | u seem to have the same signs _ _ Decisions shown with positive values of u- quark’s GPDs only

34. Jlab 12 GeV upgrade CLAS12 High luminosity Large acceptance Wide kinematic coverage High precision Improved particle ID CLAS6

35. Kinematics coverage for deeply exclusive experiments no overlap with other existing experiments compete with other experiments Jlab @ 12GeV complementary & unique

36. Kinematic Coverage at 11 GeV

37. Statistics at W=2.75 GeV

38.  vs Q 2 11 GeV 8.8 GeV 6.6 GeV 00 x B =0.35  x B =0.1 Rosenbluth L/T Separation

39. CLAS  0 and  data support the dominance of the transversity GPDs in the processes of the pseudoscalar meson electroproduction The generalized form factors and are directly connected to the structure functions  T and  TT within handbag approach Exclusive electroproduction of  0 and  mesons allows to extract generalized form factors  and  The combined  0 and  data will provide the way for the flavor decomposition of the transversity GPDs CLAS12 will continue the GPD study with broader kinematics and higher statistics. Summary 39 _ _

40. The End p p’  z x+  LL (z)(z) x-   + =

41. Generalized Form factors 41 HTHT ETET _ Generalized Form factors (extracted in the approximation of the transverse dominance) vs theoretical input to the model The comparison shows that the approximation is reasonable