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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
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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
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3 Beijing, July 2, 2008 Aram Kotzinian Measured Structure Functions and Asymmetries
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4 Beijing, July 2, 2008 Aram Kotzinian Twist-two TMD quark DFs DFs from Q-DQ model
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5 Beijing, July 2, 2008 Aram Kotzinian Twist-two TMD quark FFs FFs from DSS and Anselmino et al parameterisations
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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
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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
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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
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9 Beijing, July 2, 2008 Aram Kotzinian Sivers asymmetry Further comments later
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10 Beijing, July 2, 2008 Aram Kotzinian Collins asymmetry @ COMPASS from Anselmino et al. global analysis
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11 Beijing, July 2, 2008 Aram Kotzinian Collins asymmetry @ HERMES We expect that Q-DQ model will work in the valence quark region:
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12 Beijing, July 2, 2008 Aram Kotzinian and @ COMPASS
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13 Beijing, July 2, 2008 Aram Kotzinian Cahn kinematical corrections
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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
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15 Beijing, July 2, 2008 Aram Kotzinian and @ COMPASS
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16 Beijing, July 2, 2008 Aram Kotzinian and @ COMPASS
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17 Beijing, July 2, 2008 Aram Kotzinian Sivers effect J.Ellis, D-S.Hwang, A.K. preliminary Sivers function a la BHS from FSI
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18 Beijing, July 2, 2008 Aram Kotzinian Sivers effect 2 HERMES Proton target α s =0.3
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19 Beijing, July 2, 2008 Aram Kotzinian Analyzing power of Sivers functions: Positivity Bound Brodsky, Hwang & Schmidt Consider large k T limit
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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
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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.)
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22 Beijing, July 2, 2008 Aram Kotzinian Quark longitudinal polarization For given x the sign of the polarization is changing at high k T
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23 Beijing, July 2, 2008 Aram Kotzinian Quark longitudinal polarization For given x the sign of the polarization is changing at high k T
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24 Beijing, July 2, 2008 Aram Kotzinian Orbital momentum and g 1L Model by Brodsky, Hwang, Ma & Schmidt, NPB 593 (2001) 311
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25 Beijing, July 2, 2008 Aram Kotzinian Positive and negative helicity DFs in Q-DQ model
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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
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27 Beijing, July 2, 2008 Aram Kotzinian HERMES, Vaness Mexner PhD (2005)
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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
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29 Beijing, July 2, 2008 Aram Kotzinian Additional slides
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30 Beijing, July 2, 2008 Aram Kotzinian cos(φ) asymmetry in Q-DQ model (Cahn effect)
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31 Beijing, July 2, 2008 Aram Kotzinian cos(2φ) asymmetry in Q-DQ model (Cahn effect)
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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:
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33 Beijing, July 2, 2008 Aram Kotzinian Subleading twist
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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
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