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SIDIS asymmetries in Quark-Diquark model for Distribution Functions

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

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SIDIS asymmetries in Quark-Diquark model for Distribution Functions

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  1. SIDISasymmetries 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, Armeniaand 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 AramKotzinian

  2. 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 transversepolarization dependent A.K. NPB 441 (1995) 234: Bacchetta et al, JHEP 0702:093,2007 AramKotzinian

  3. Measured Structure Functions and Asymmetries AramKotzinian

  4. Twist-two TMD quark DFs DFs from Q-DQ model AramKotzinian

  5. Twist-two TMD quark FFs FFs from DSS and Anselmino et al parameterisations AramKotzinian

  6. Quark-Diquark model for DFs q Dq R. Jakob, P. Mulders & Rodrigues NP A626, 937 (1997) Choose exponential form-factor: k, m MR, R=s,a Only few commonparameters, mq=0.36, MA=0.8, MS=0.6, Λ=0.5 (GeV/c), for all DFs No x-kT factorization and width of intrinsic transverse momentum depends on x AramKotzinian

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

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

  9. Sivers asymmetry Further comments later AramKotzinian

  10. Collins asymmetry @ COMPASS from Anselmino et al. global analysis AramKotzinian

  11. Collins asymmetry @ HERMES We expect that Q-DQ model will work in the valence quark region: AramKotzinian

  12. and @ COMPASS AramKotzinian

  13. Cahn kinematical corrections AramKotzinian

  14. Interpretation of target transverse spin asymmetries Twist-2 DFs and FFs + kT/Q kinematical corrections: Works Doesn’t work AramKotzinian

  15. and @ COMPASS AramKotzinian

  16. and @ COMPASS AramKotzinian

  17. Sivers effect J.Ellis, D-S.Hwang, A.K. preliminary Sivers function a la BHS from FSI AramKotzinian

  18. Sivers effect 2 HERMES Proton target αs=0.3 AramKotzinian

  19. Analyzing power of Sivers functions: Positivity Bound Consider large kT limit Brodsky, Hwang & Schmidt AramKotzinian

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

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

  22. Quark longitudinal polarization For given xthesign of the polarization is changing at high kT AramKotzinian

  23. Quark longitudinal polarization For given xthesignof the polarization is changing at high kT AramKotzinian

  24. Orbital momentum and g1L Model by Brodsky, Hwang, Ma & Schmidt, NPB 593 (2001) 311 AramKotzinian

  25. Positive and negative helicity DFs in Q-DQ model AramKotzinian

  26. ALL @ 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 AramKotzinian

  27. HERMES, Vaness Mexner PhD (2005) AramKotzinian

  28. JMR q-dq model is a good tool for guidance The kT and pT dependences of (polarized) DFs and FFs can be nontrivial. No x-kT factorization in DFs, flavor dependence of ‹kT›(x), ‹pT›(z) The kTdependenceof DF g1 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 kT 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(Rh(x,z,pT), ALL(pT)…) as a function of all kinematical variables (x, z, PT, Q2) or (x, PT) , (z, PT), (xF, PT) … Concluding remarks AramKotzinian

  29. Additional slides AramKotzinian

  30. cos(φ) asymmetry in Q-DQ model (Cahn effect) AramKotzinian

  31. cos(2φ) asymmetry in Q-DQ model (Cahn effect) AramKotzinian

  32. cos(2φ) asymmetry in Q-DQ model (Cahn effect) 2 Different kT width for S and A form-factors: AramKotzinian

  33. Subleading twist AramKotzinian

  34. Higher twist example 2: predictions for cos(φs) asymmetry JLab 6 JLab 12 HERMES Spectator model Cahn correction for g1T contribution AramKotzinian

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