1. 1 Beijing, July 2, 2008 Aram Kotzinian SIDIS asymmetries in Quark-Diquark model for Distribution Functions Aram Kotzinian CEA-Saclay, IRFU/Service de Physique Nucléaire, 91191 Gif-sur-Yvette, France On leave in absence from YerPhI, Armenia and JINR, Russia PKU-RBRC Workshop on Transverse Spin Physics Introduction Quark-Diquark model of DFs Transverse target polarization depending asymmetries Sivers DF Helicity DFs Concluding remarks

2. 2 Beijing, July 2, 2008 Aram Kotzinian General expression for 1h production cross-section This is a general expression which is also valid for exclusive reactions and for entire phase space of SIDIS (TFR, CFR) Azimuthal modulations: 2 polarization independent 1 single beam polarization dependent 2 single target longitudinal polarization dependent 1 double beam + target longitudinal polarization dependent 5 single target transverse polarization dependent 3 double beam + target transverse polarization dependent A.K. NPB 441 (1995) 234: Bacchetta et al, JHEP 0702:093,2007

3. 3 Beijing, July 2, 2008 Aram Kotzinian Measured Structure Functions and Asymmetries

4. 4 Beijing, July 2, 2008 Aram Kotzinian Twist-two TMD quark DFs DFs from Q-DQ model

5. 5 Beijing, July 2, 2008 Aram Kotzinian Twist-two TMD quark FFs FFs from DSS and Anselmino et al parameterisations

6. 6 Beijing, July 2, 2008 Aram Kotzinian Quark-Diquark model for DFs R. Jakob, P. Mulders & Rodrigues NP A626, 937 (1997) q Dq Choose exponential form-factor: k, m M R, R=s,a Only few common parameters, m q =0.36, M A =0.8, M S =0.6, Λ=0.5 (GeV/c), for all DFs No x-k T factorization and width of intrinsic transverse momentum depends on x

7. 7 Beijing, July 2, 2008 Aram Kotzinian Quark-Diquark model, 2 Proton SU(6) wave function: And same for other DFs Sivers and Boer-Mulders DFs are equal to zero

8. 8 Beijing, July 2, 2008 Aram Kotzinian Interpretation of target transverse spin asymmetries Parton model, Twist-2: Sivers Collins 8 Structure Functions for target transverse spin part Comparison with x-dependence of COMPASS Deuteron target data Nucl.Phys.B765:31,2007; arXiv:0705.2402 ; arXiv:0709.3440

9. 9 Beijing, July 2, 2008 Aram Kotzinian Sivers asymmetry Further comments later

10. 10 Beijing, July 2, 2008 Aram Kotzinian Collins asymmetry @ COMPASS from Anselmino et al. global analysis

11. 11 Beijing, July 2, 2008 Aram Kotzinian Collins asymmetry @ HERMES We expect that Q-DQ model will work in the valence quark region:

12. 12 Beijing, July 2, 2008 Aram Kotzinian and @ COMPASS

13. 13 Beijing, July 2, 2008 Aram Kotzinian Cahn kinematical corrections

14. 14 Beijing, July 2, 2008 Aram Kotzinian Interpretation of target transverse spin asymmetries Twist-2 DFs and FFs + k T /Q kinematical corrections: WorksDoesn’t work

15. 15 Beijing, July 2, 2008 Aram Kotzinian and @ COMPASS

16. 16 Beijing, July 2, 2008 Aram Kotzinian and @ COMPASS

17. 17 Beijing, July 2, 2008 Aram Kotzinian Sivers effect J.Ellis, D-S.Hwang, A.K. preliminary Sivers function a la BHS from FSI

18. 18 Beijing, July 2, 2008 Aram Kotzinian Sivers effect 2 HERMES Proton target α s =0.3

19. 19 Beijing, July 2, 2008 Aram Kotzinian Analyzing power of Sivers functions: Positivity Bound Brodsky, Hwang & Schmidt Consider large k T limit

20. 20 Beijing, July 2, 2008 Aram Kotzinian Analyzing power of Sivers functions, 2 JMR model (dipole formfactor), J.Ellis, D-S.Hwang, A.K. Bacchetta, Schaefer, Yang, PLB 578(2004)109

21. 21 Beijing, July 2, 2008 Aram Kotzinian Analyzing power of Sivers functions, 3 Transverse Quark Spin Effects and the Flavor Dependence of the Boer-Mulders Function L.Gamberg, G.Goldstein & M.Schlegel, 0708.0324v2 Gaussian form-factor (J.Ellis, D.Hwang, A.K.)

22. 22 Beijing, July 2, 2008 Aram Kotzinian Quark longitudinal polarization For given x the sign of the polarization is changing at high k T

23. 23 Beijing, July 2, 2008 Aram Kotzinian Quark longitudinal polarization For given x the sign of the polarization is changing at high k T

24. 24 Beijing, July 2, 2008 Aram Kotzinian Orbital momentum and g 1L Model by Brodsky, Hwang, Ma & Schmidt, NPB 593 (2001) 311

25. 25 Beijing, July 2, 2008 Aram Kotzinian Positive and negative helicity DFs in Q-DQ model

26. 26 Beijing, July 2, 2008 Aram Kotzinian A LL @ JLab Duak-Diquak model M.Anselmino, A.Efremov, A.K & B.Parsamyan PRD 74, 074015 (2006) The case is very similar to Quark-Diquark model results

27. 27 Beijing, July 2, 2008 Aram Kotzinian HERMES, Vaness Mexner PhD (2005)

28. 28 Beijing, July 2, 2008 Aram Kotzinian JMR q-dq model is a good tool for guidance The k T and p T dependences of (polarized) DFs and FFs can be nontrivial. No x-k T factorization in DFs, flavor dependence of ‹k T ›(x), ‹p T ›(z) The k T dependence of DF g 1 is tightly related to quark orbital momentum In valence region this model is able to describe the x-dependence of new 6 transverse spin dependent azimuthal asymmetries Do we understand well dynamical origin of Sivers effect? FSI? Why changing form-factor of nucleon-quark-diquark vertex brings to unphysical k T behavior? How one can resolve this problem? Twist-four? More measurements are needed for better understanding TMD DFs HERMES: 6 asymmetries transversely polarized proton target? For better understanding of SIDIS we need the data for unpolarized x-sections and asymmetries (R h (x,z,p T ), A LL (p T )…) as a function of all kinematical variables (x, z, P T, Q 2 ) or (x, P T ), (z, P T ), (x F, P T ) … Concluding remarks

29. 29 Beijing, July 2, 2008 Aram Kotzinian Additional slides

30. 30 Beijing, July 2, 2008 Aram Kotzinian cos(φ) asymmetry in Q-DQ model (Cahn effect)

31. 31 Beijing, July 2, 2008 Aram Kotzinian cos(2φ) asymmetry in Q-DQ model (Cahn effect)

32. 32 Beijing, July 2, 2008 Aram Kotzinian cos(2φ) asymmetry in Q-DQ model (Cahn effect) 2 Different k T width for S and A form-factors:

33. 33 Beijing, July 2, 2008 Aram Kotzinian Subleading twist

34. 34 Beijing, July 2, 2008 Aram Kotzinian Higher twist example 2: predictions for cos(φ s ) asymmetry Spectator model JLab 6 JLab 12 HERMES Cahn correction for g 1T contribution