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

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

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

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 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 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: ; arXiv:

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

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

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

12 Beijing, July 2, 2008 Aram Kotzinian COMPASS

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

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 Beijing, July 2, 2008 Aram Kotzinian COMPASS

16 Beijing, July 2, 2008 Aram Kotzinian COMPASS

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

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

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 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, v2 Gaussian form-factor (J.Ellis, D.Hwang, A.K.)

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

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

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

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

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

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 Beijing, July 2, 2008 Aram Kotzinian Additional slides

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

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

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 Beijing, July 2, 2008 Aram Kotzinian Subleading twist

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