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Harut Avakian (JLab)

Modification of transverse momentum distributions in nuclei. Harut Avakian (JLab). Workshop on Nuclear Chromo-Dynamic Studies with a Future Electron Ion Collider Argonne National Laboratory, April 7 - 9, 2010. TMDs and spin-orbit correlations k T -distributions Higher twists in SIDIS

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Harut Avakian (JLab)

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  1. Modification of transverse momentum distributions in nuclei Harut Avakian (JLab) Workshop on Nuclear Chromo-Dynamic Studies with a Future Electron Ion Collider Argonne National Laboratory, April 7 - 9, 2010 • TMDs and spin-orbit correlations • kT-distributions • Higher twists in SIDIS • MC-simulations • Projections for observables • Conclusions H. Avakian, Argonne, April 8

  2. 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, Argonne, April 8

  3. l’ l total transverse momentum broadening squared lT x,k’T l’T spectator system nucleus Tang,Wang & Zhou Phys.Rev.D77:125010,2008 kT and FSI l l’ BHS 2002 Collins 2002 Ji,Yuan 2002 x,kT spectator system proton soft gluon exchanges included in the distribution function (gauge link) • The difference is coming from final state interactions (different remnant) H. Avakian, Argonne, April 8

  4. SIDIS: partonic cross sections kT p┴ PT = p┴+zkT Ji,Ma,Yuan Phys.Rev.D71:034005,2005 Is the info on x-kT correlations accessible in kT integrated observables? 4 H. Avakian, Argonne, April 8

  5. Quark distributions at large kT: models q Dq Du/u JMR model MR, R=s,a (dipole formfactor), J.Ellis, D-S.Hwang, A.Kotzinian Effect of the orbital motion on theq- may be most significant (H.A.,S.Brodsky, A.Deur,F.Yuan 2007) Higher probability to find a quark anti-aligned with proton spin at large kT 5 H. Avakian, Argonne, April 8

  6. Quark distributions at large kT: lattice B.Musch arXiv:0907.2381 Higher probability to find a quark anti-aligned with proton spin at large kT Higher probability to find a d-quark at large kT Understanding the transverse structure is crucial! 6 H. Avakian, Argonne, April 8

  7. Lattice Anselmino Collins A1 PT-dependence arXiv:1003.4549 A1 PT PT CLAS data suggests that width of g1 is less than the width of f1 New CLAS data would allow multidimensional binning to study kT-dependence for fixed x H. Avakian, Argonne, April 8

  8. H. Avakian, Argonne, April 8

  9. Quark distributions at large kT bigger effect at large z PT = p┴+zkT Higher probability to find a hadron at large PT in nuclei kT-distributions may be wider in nuclei? 9 H. Avakian, Argonne, April 8

  10. Jet limit: Higher Twist azimuthal asymmetries H.A.,A.Efremov,P.Schweitzer,F.Yuan arXiv:1001.5467 Twist-2 Twist-3 T-odd “interaction dependent” No leading twist, provide access to quark-gluon correlations 10 H. Avakian, Argonne, April 8

  11. Modification of Cahn effect Bag model arXiv:1001.3146 Gao, Liang & Wang • Nuclear modification of Cahn may provide info on kT broadening and proton TMDs • Large cosnf moments observed at COMPASS H. Avakian, Argonne, April 8

  12. fs y PT fS= p/2+fh fS fh x fh y PT fS=p/2 x fh y PT fS=p x Collins mechanism for SSA PT FC fragmentation of transversely polarized quarks into unpolarized hadrons FC fh Fragmenting quark polarization x HT function related to force on the quark. M.Burkardt (2008) 12 H. Avakian, Argonne, April 8

  13. Q2 EIC EIC JLab12 Electroproduction kinematics: JLab12→EIC collider experiments EIC (4x60): H1, ZEUS 10-4<xB<0.02 gluons (and quarks) EIC 10-4<xB<0.3 fixed target experiments COMPASS 0.006<xB<0.3 HERMES 0.02<xB<0.3 gluons/valence and sea quarks JLab  0.1<xB<0.7JLab@12GeV valence quarks Study of high x domain requires high luminosity, low x higher energies H. Avakian, Argonne, April 8

  14. LEPTO/PEPSI: quark distributions Event Generator with polarized electron and nucleon: PEPSI,…. MC with Cahn Acceptance check Design parameters Smearing/resolution routines Use GEANT as input z>0.1 Physics analysis using the “reconstructed” event sample z>0.3 • Implemented in PEPSI modification to LEPTO done by A. Kotzinian • Add different widths for q+ and q- Need to model TMDs in LUND MC H. Avakian, Argonne, April 8

  15. EIC 4x60 (Lumi 1033,cm-2sec-1 , ~1 hour) <x>=0.1, <Q2>=4 s(p) = 0.05 + 0.06*p [GeV] % K*s can be studied with EIC H. Avakian, Argonne, April 8

  16. PT-dependence of beam SSA ssinfLU~FLU~ 1/Q (Twist-3) In the perturbative limit 1/PT behavior expected 4x60 100 days, L=1033cm-2s-1 Perturbative region Nonperturbative TMD Study for SSA transition from non-perturbative to perturbative regime. EIC will significantly increase the PT range. H. Avakian, Argonne, April 8

  17. e p 5-GeV 50 GeV - Boer-Mulders Asymmetry with CLAS12 & EIC Transversely polarized quarks in the unpolarized nucleon sin(fC) =cos(2fh) CLAS12 EIC Perturbative limit calculations available for : J.Zhou, F.Yuan, Z Liang: arXiv:0909.2238 Nonperturbative TMD Perturbative region CLAS12 and EICstudies 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, Argonne, April 8

  18. Summary • Studies of spin and azimuthal asymmetries in semi-inclusive processes at EIC : • Measure nuclear modification of transverse momentum distributions and spin-orbit correlations of partons at small x, in a wide range of Q • Study quark-gluon correlations (HT) in nucleon and nucleus • Provide information on correlations of longitudinal and transverse degrees of freedom • EIC: Studies of nuclear modifications of spin orbit and quark-gluon correlations combined with JLab12 data will help construct a more complete picture about the structure of the nucleon and nuclei. H. Avakian, Argonne, April 8

  19. Support slides…. H. Avakian, Argonne, April 8

  20. Struck quark kinematics (EIC 4x60) qq High energy quarks at small angles H. Avakian, Argonne, April 8

  21. TMD PDFs SIDIS (g*p->pX) x-section at leading twist • Measure Boer-Mulders distribution functions and probe the polarized fragmentation function • Measurements from different experiments consistent H. Avakian, Argonne, April 8

  22. l’ l total transverse momentum broadening squared lT x,k’T l’T spectator system nucleus Tang,Wang & Zhou Phys.Rev.D77:125010,2008 kT and FSI l l’ BHS 2002 Collins 2002 Ji,Yuan 2002 x,kT spectator system proton • The difference is coming from final state interactions (different remnant) H. Avakian, Argonne, April 8

  23. Transverse force on the polarized quarks Quark polarized in the x-direction with kT in the y-direction Force on the active quark right after scattering (t=0) Interpreting HT (quark-gluon-quark correlations) as force on the quarks (Burkardt hep-ph:0810.3589) 23 H. Avakian, Argonne, April 8

  24. 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 EIC-MC Major part of current particles at large angles in Lab frame (PID at large angles crucial). H. Avakian, Argonne, April 8

  25. Q2-dependence of beam SSA ssinfLU(UL) ~FLU(UL)~ 1/Q (Twist-3) 1/Qbehavior expected (fixed x bin) Study for Q2 dependence of beam SSA allows to check the higher twist nature and access quark-gluon correlations. H. Avakian, Argonne, April 8

  26. EIC medium energy EIC@JLab EIC@RHIC Main Features • Electron energy: 3-11 GeV • Proton energy: 20-60 GeV • More symmetric kinematics provides better resolution and particle id • Luminosity: ~ 1034 cm-2 s-1 • in range around s ~ 1000 GeV2 • Polarized electrons and light ions • longitudinal and transverse • Limited R&D needs • 3 interaction regions (detectors) • Potential upgrade with high-energy ring • Electron energy: 4-20 GeV • Proton energy: 50-250 GeV • More symmetric kinematics provides better resolution and particle id • Luminosity: ~ 1033 cm-2 s-1 • in range around s ~ 1000-10000 GeV2 • Polarized electrons and light ions • longitudinal and transverse • Limited R&D needs • ? interaction regions (detectors) • 90% of hardware can be reused • Slides are for a “generic” US version of an EIC (5x50 or 4x60): • polarized beams (longitudinal and transverse, > 70%) • luminosities of at least 1033 H. Avakian, Argonne, April 8

  27. JETSET:Single particle production in hard scattering LUND Fragmentation Functions - Before - After Target remnant quark Lund-MC should be modified to allow checks of sensitivity of measurements to different effects related to the transverse structure H. Avakian, Argonne, April 8

  28. SIDIS kinematical plane and observables Target polarization Cross section is a function of scale variables x,y,z U unpolarized L long.polarized T trans.polarized z Beam polarization sin2f moment of the cross section for unpolarized beam and long. polarized target 28 H. Avakian, Argonne, April 8

  29. CLAS12 EIC4x60 Kaon production in SIDIS FAST-MC L S S* detected s(p) = 0.05 + 0.06*p [GeV] % Identification using the missing mass may be possible H. Avakian, Argonne, April 8

  30. Azimuthal moments with unpolarized target quark polarization 30 H. Avakian, Argonne, April 8 JLab, Nov 25

  31. Azimuthal moments with unpolarized target quark polarization 31 H. Avakian, Argonne, April 8 JLab, Nov 25

  32. SSA with unpolarized target quark polarization 32 H. Avakian, Argonne, April 8 JLab, Nov 25

  33. SSA with unpolarized target quark polarization 33 H. Avakian, Argonne, April 8 JLab, Nov 25

  34. SSA with long. polarized target quark polarization H. Avakian, Argonne, April 8

  35. SSA with long. polarized target quark polarization H. Avakian, Argonne, April 8

  36. SSA with unpolarized target quark polarization H. Avakian, Argonne, April 8

  37. SSA with unpolarized target quark polarization H. Avakian, Argonne, April 8

  38. Single hadron production in hard scattering Target fragmentation Current fragmentation semi-inclusive exclusive semi-exclusive h h FF h DA DA h M PDF GPD PDF 1 -1 xF 0 Fracture Functions kT-dependent PDFs Generalized PDFs xF>0 (current fragmentation) h xF<0 (target fragmentation) xF- momentum in the CM frame Measurements in different kinematical regions provide complementary information on the complex nucleon structure. 38 H. Avakian, Argonne, April 8

  39. L production in the target fragmentation L polarization in TFR provides information on contribution of strange sea to proton spin (ud)-diquark is a spin and isospin singlet s-quark carries whole spin of L xF- momentum in the CM frame xF(L) Study polarized diquark fracture functions sensitive to the correlations between struck quark transverse momentum and the diquark spin. EIC CLAS12 Wide kinematical coverage of EIC would allow studies of hadronization in the target fragmentation region (fracture functions) H. Avakian, Argonne, April 8

  40. hep-ph/9606390 Collins effect p+ leading pion out of page Simple string fragmentation for pions (Artru model) z L r production may produce an opposite sign AUT Leading r opposite to leading p(into page) z r L Fraction of direct kaons may be significantly higher than the fraction of direct pions. LUND-MC H. Avakian, Argonne, April 8

  41. K/K* and L/S separations Detection of K+ crucial for separation of different final states (L,S,K*) H. Avakian, Argonne, April 8

  42. Sivers effect in the target fragmentation A.Kotzinian High statistics of CLAS12 will allow studies of kinematic dependences of the Sivers effect in target fragmentation region H. Avakian, Argonne, April 8

  43. HERA 27 GeV Q2 EIC ENC ENC JLab (upgraded) compass hermes JLab@6GeV Hard Scattering Processes: Kinematics Coverage 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 Q2 EIC(4x60) ENC(3x15) JLab12 Study of high x domain requires high luminosity, low x higher energies H. Avakian, Argonne, April 8

  44. HERA 27 GeV Q2 Q2 EIC ENC ENC JLab (upgraded) EIC compass hermes ENC JLab@6GeV JLab12 Hard Scattering Processes: Kinematics Coverage 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 Study of high x domain requires high luminosity, low x higher energies H. Avakian, Argonne, April 8

  45. hep:arXiv-09092238 H. Avakian, Argonne, April 8

  46. 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, Argonne, April 8

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