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Harut Avakian*

Spin-orbit correlation studies with EIC. Harut Avakian*. The 4th Electron Ion Collider Workshop A New Experimental Quest to Study QCD, Hadron Structure, and Nuclear Matter Dates: May 19-23, 2008 Location: Hampton University. *) In collaboration with A. Bruell. Outline. Physics motivation

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Harut Avakian*

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  1. Spin-orbit correlation studies with EIC Harut Avakian* The 4th Electron Ion Collider Workshop A New Experimental Quest to Study QCD, Hadron Structure, and Nuclear Matter Dates: May 19-23, 2008 Location: Hampton University *) In collaboration with A. Bruell H. Avakian, Hampton, May 21

  2. Outline Physics motivation TMD parton distributions and spin-orbit correlations Accessing TMDs in semi-inclusive DIS Projections for transverse SSAs at EIC and comparison with other experiments Boer-Mulders TMD Sivers TMD Pretzelosity TMD Summary H. Avakian, Hampton, May 21

  3. EMC at CERN (85):~20% from Deep Inelastic Scattering (DIS) ~0.6 from QCD-sum rule “spin crisis” RHIC Spin & SIDIS Proton’s spin J q The Spin Structure of the Nucleon Describe the complex nucleon structure in terms of partonic degrees of freedom of QCD Understanding of the orbital motion of quarks crucial and requires understanding of spin-orbit correlations!!! H. Avakian, Hampton, May 21

  4. Wpu(k,rT) “Mother” Wigner distributions d2kT d2rT GPDs/IPDs TMD PDFs f1u(x,kT), .. h1u(x,kT) d2kT Structure of the Nucleon quark polarization PDFs f1u(x), .. h1u(x) • Gauge invariant definition (Belitsky,Ji,Yuan 2003) • Universality of kT-dependent PDFs (Collins,Metz 2003) • Factorization for small kT. (Ji,Ma,Yuan 2005) H. Avakian, Hampton, May 21

  5. Miller/”pretzelosity” GPD-ET Spin densities from Lattice (QCDSF and UKQCD Collaborations) quark spin Proton spin GPD-E H. Avakian, Hampton, May 21

  6. - - TMDs in SIDIS at leading twist Correlation between the transverse momentum and transverse spin of quarks Correlation between the quark transverse momentum and transverse spin of the proton Collins (2002) Meissner, Metz & Goeke (2007) H. Avakian, Hampton, May 21

  7. Beam polarization Target polarization SIDIS kinematical plane and observables PT U unpolarized L long.polarized T trans.polarized sin(f-fS) moment of the cross section for unpolarized beam and transverse target H. Avakian, Hampton, May 21

  8. QCD large-x limit, Brodsky & Yuan (2006) (perturbative limit) - Pretzelosity Unpolarized quarks TMDs and spin-orbit correlations Transversely polarized quarks H. Avakian, Hampton, May 21

  9. Pretzelosity Transversely polarized quarks in transversely polarized proton positivity conditions Large Nc P. Schweitzer F. Yuan • The difference between transversity and helicity distributions is measure of relativistic effects! H. Avakian, Hampton, May 21

  10. Hard Scattering Processes: Kinematics Coverage HERA collider experiments H1, ZEUS(EIC) 10-4<xB<0.02 (0.3):gluons (and quarks) in the proton fixed target experiments COMPASS, HERMES  0.006/0.02<xB<0.3 : gluons/valence and sea quarks JLab/JLab@12GeV  0.1<xB<0.7: valence quarks 27 GeV Q2 EIC JLab (upgraded) compass hermes JLab@6GeV Study of high x domain requires high luminosity, low x higher energies H. Avakian, Hampton, May 21

  11. EIC: Kinematics Coverage e p xF>0 (CFR) 5 GeV 50 GeV xF<0 ( TFR) e’p+X all xF>0 z>0.3 EIC-MC 100 days,L=1033cm-2s-1 EIC-MC (PYTHIA based) Major part of current particles at large angles in Lab frame (PID at large angles crucial). H. Avakian, Hampton, May 21

  12. e p 5-GeV 50 GeV - Nonperturbative TMD Perturbative region Boer-Mulders Asymmetry with CLAS12 & EIC Transversely polarized quarks in the unpolarized nucleon CLAS12 sin(fC) =cos(2fh) EIC CLAS12 and ELICstudies of transition from non-perturbative to perturbative regime will provide complementary info on spin-orbit correlations and test unified theory (Ji et al) H. Avakian, Hampton, May 21

  13. Sivers SSA proton deuteron • Transverse asymmetries measured at HERMES and COMPASS • Effects are largeat large x H. Avakian, Hampton, May 21

  14. Sivers from HERMES Disagreement in shape and magnitude of PT-dependences Need precision measurements of PT-dependences on proton and deuteron H. Avakian, Hampton, May 21

  15. Sivers effect: pion electroproduction GRV98, Kretzer FF (4par) S. Arnold et al arXiv:0805.2137 M. Anselmino et al arXiv:0805.2677 GRV98, DSS FF (8par) • EIC measurements at small x will pin down sea contributions to Sivers function H. Avakian, Hampton, May 21

  16. Sivers effect: Kaon electroproduction EIC CLAS12 • At small x of EIC Kaon relative rates higher, making it ideal place to study the Sivers asymmetry in Kaon production (in particular K-). • Combination with CLAS12 data will provide almost complete x-range. H. Avakian, Hampton, May 21

  17. Sivers effect: sea contributions GRV98, DSS FF M. Anselmino et al arXiv:0805.2677 GRV98, Kretzer FF S. Arnold et al arXiv:0805.2137 • Negative Kaons most sensitive to sea contributions. • Biggest uncertainty in experimental measurements (K- suppressed at large x). H. Avakian, Hampton, May 21

  18. positivity bound Pretzelosity @ EIC 5x50 epX p- p+ • EIC measurement combined with CLAS12 will provide a complete kinematic range for pretzelosity measurements H. Avakian, Hampton, May 21

  19. Summary • Correlations of spin and transverse momentum of partons are crucial in understanding of the nucleon structure in terms of partonic degrees of freedom of QCD. • EIC: Measurements related to the spin, spin orbit correlations and orbital angular momentum of the quarks combined with JLab12 HERMES,COMPASS, RHIC,BELLE,J-PARC,GSI data will help construct a more complete picture about the spin structure of the nucleon beyond the collinear approximation. Welcome to the exciting world of 3D parton distributions!!! H. Avakian, Hampton, May 21

  20. Support slides…. H. Avakian, Hampton, May 21

  21. e p 5 GeV 50 GeV Hard Scattering Processes: Kinematics Coverage h Study of high x domain requires high luminosity, low x higher energies H. Avakian, Hampton, May 21

  22. Burkardt (2007) TMDs: QCD based predictions Large-x limit Brodsky & Yuan (2006) Large-Nc limit (Pobilitsa) Do not change sign (isoscalar) All others change sign u→d (isovector) H. Avakian, Hampton, May 21

  23. positivity bound Pretzelosity @ EIC 5x50 ep+X • EIC measurement combined with CLAS12 will provide a complete kinematic range for pretzelosity measurements H. Avakian, Hampton, May 21

  24. this experiment Sivers asymmetry measurements on deuteron and proton target allow model independent extraction of Sivers function for u and d quarks at large x p++p-or p0 AUT for proton doesn’t depend on fragmentation functions Sivers effect on p0: extracting the Sivers function ed→e’p0X ep→e’p0X up down H. Avakian, Hampton, May 21

  25. d d Collins SSA at CLAS @5.7GeV d u u L=1 sin(fC)=sin(fh+fS) • L/R SSA generated in fragmentation • Hadrons from struck quark have opposite sign SSA Anselmino et al CLAS with a transversely polarized target will allow simultaneous measurement of SIDIS asymmetries in current and target fragmentation regions and exclusive r,r+,w asymmetries (background) H. Avakian, Hampton, May 21

  26. Sivers effect: PT-dependence Model calculations Yuan & Vogelsang, Schweizer & Efremov PT-dependence at large PT crucial (not accessible at Hall-A/C). H. Avakian, Hampton, May 21

  27. Acceptance corrections for AUT Esimated acceptance corrections for CLAS using HERMES analysis chain (GMCtrans) H. Avakian, Hampton, May 21

  28. - Sivers Effect Unpolarized quarks: Probability to find a quark with longitudinal momentum x and transverse momentum kT Correlation between the quark transverse momentum and transverse spin of the proton + FSI The shift ~ 0.3 fm related to anomalous magnetic moment of proton (Burkardt 2000) Collins (2002) Meissner, Metz & Goeke (2007) Calculation of moments of f1T┴requires knowledge of kT-dependence in a wide range H. Avakian, Hampton, May 21

  29. H. Avakian, Hampton, May 21

  30. First calculations of “pretzelosity” P.Schweitzer, diquark model F.Yuan, Bag model H. Avakian, Hampton, May 21

  31. CLAS12: Kinematical coverage epX SIDIS kinematics Q2>1GeV2 W2>4 GeV2(10) y<0.85 MX>2GeV x=0.3 → Q2=~2 GeV2 (CLAS), ~5 GeV2 (HERMES) ~15 GeV2 (COMPASS) Large Q2 accessible with CLAS12 are important for separation of HT contributions H. Avakian, Hampton, May 21

  32. SIDIS transverse SSA H. Avakian, Hampton, May 21

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