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Transversity

Transversity. (transverse spin and transverse motion). (unravelling the spin-orbital motion of partons?). Towards transversity distributions: theory and experiments. Collins mechanism. Transverse Single Spin Asymmetries. Sivers mechanism.

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Transversity

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  1. Transversity (transverse spin and transverse motion) (unravelling the spin-orbital motion of partons?) Towards transversity distributions: theory and experiments Collins mechanism Transverse Single Spin Asymmetries Sivers mechanism Spin and k┴dependent parton distributions (TMD) Transversity 2005

  2. Parton distributions (or and are fundamental leading-twist quark distributions quark distribution– well known all equally important quark helicity distribution – known transversity distribution – unknown gluonhelicity distribution – poorly known chiral-even related to chiral-odd related to positivity bound Transversity 2005

  3. – – + + + = – + + + + + = – in helicity basis – + decouples from DIS (no quark helicity flip) – + Transversity 2005

  4. h1 must couple to another chiral-odd function. For example: D-Y, pp → l+l–X, and SIDIS, l p → l π X, processes – + h1 x h1 – + J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992 – + + – h1 x Collins function – + – + + – J. Collins, 1993 Transversity 2005

  5. No gluon contribution to h1 simple Q2 evolution –1 +1 – + Q2 = 25 GeV2 Q02 = 0.23 GeV2 V. Barone, T. Calarco, A. Drago Transversity 2005

  6. h1 in Drell-Yan processes l+ Q2 = M2 l– γ* qT p p qL Elementary LO interaction: 3 planes: plane polarization vectors, ┴ plenty of spin effects p-γ* plane, l+l–γ* plane Transversity 2005

  7. h1 from at RHIC RHIC energies: small x1 and/or x2 h1q (x, Q2)evolution much slower than Δq(x, Q2)and q(x, Q2)at small x Barone, Calarco, Drago ATTat RHIC is very small smaller s would help Martin, Schäfer, Stratmann, Vogelsang talk by A. Mukherjee Transversity 2005

  8. at GSI h1 from large x1,x2 GSI energies: one measures h1 in the quark valence region: ATTis estimated to be large, between 0.2 and 0.4 PAX proposal: hep-ex/0505054 Talks by M. Contalbrigo, N. Nikolaev, M. Maggiora Transversity 2005

  9. Energy for Drell-Yan processes "safe region": QCD corrections might be very large at smaller values of M: yes, for cross-sections, not for ATTK-factor almost spin-independent Fermilab E866 800 GeV/c H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya, hep-ph/0503270 V. Barone et al., in preparation talks by M. Guzzi, A. Bianconi Transversity 2005

  10. s=30 GeV2 s=45 GeV2 s=210 GeV2 s=900 GeV2 Transversity 2005

  11. s=30 GeV2 s=45 GeV2 s=210 GeV2 s=900 GeV2 Transversity 2005

  12. data from CERN WA39, π N processes, s = 80 GeV2 Transversity 2005

  13. h1 x Collins from SIDIS processes Asymmetry in the fragmentation of a transversely polarized quark φ Sq p┴ pq (Fundamental QCD property? D. Sivers) q’ q y initial q spin is transferred to final q', which fragments Sq Sq’ p┴ “Trento conventions” ΦS Φh x Amsterdam notations Transversity 2005

  14. neglecting intrinsic motion in partonic distributions: Collins function transversity some data available from HERMES, first extraction of Collins functions: W. Vogelsang and F. Yuan(assuming Soffer-saturated h1) Transversity 2005

  15. fit to HERMES data on Transversity 2005

  16. Extraction of Collins functions from HERMES + BELLE data P1 depends on (talk by R. Seidl) M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation Transversity 2005

  17. Fits to HERMES Collins data, preliminary results Transversity 2005

  18. Fits to BELLE Collins data, preliminary results Transversity 2005

  19. HERMES + BELLE:Collins function is not zero Theory: probably universal Collins, Metz Amrath, Bacchetta, Metz, Kundu, Mulders, … Models: few, in disagreement pion-quark vertex ? loop? assumes h1 = ∆q disfavoured Collins functions = 0 Talk by. A. Bacchetta Transversity 2005

  20. Alternative accesses to transversity Inclusive Λ production and measure of Λ polarization transverse fragmentation function p X COMPASS analysisin progress Talk by A. Ferrero Transversity 2005

  21. Two pion production: interference fragmentation function Talks by P. van der Nat, M. Radici Transversity 2005

  22. Vector meson production: (generalized fragmentation function) Inclusive hadronic production: Talk by F. Murgia Single Spin Asymmetry in D-Y processes (Boer-Mulders distribution) Talks by D. Boer, G. Goldstein, M. Radici Transversity 2005

  23. Transverse SSA S y p' x PT θ z p – p – p' Single Spin Asymmetry in elastic scattering. Example: 6 independent helicity amplitudes Transversity 2005

  24. y ΦS Φ x S p' PT θ p – p z – p' for a generic configuration: Transversity 2005

  25. needs helicity flip + relative phase + + – + x + + + + at quark level large SSA observed at hadron level Transversity 2005

  26. BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2 E704 √s = 20 GeV 0.7 < pT < 2.0 STAR-RHIC √s = 200 GeV 1.1 < pT < 2.5 E704 √s = 20 GeV 0.7 < pT < 2.0 SSA, pp → πX Transversity 2005

  27. Unweighted Collins moment: Unweighted Sivers moment: Transversity 2005

  28. Transverse Λ polarization in unpolarized p-Be scattering at Fermilab Transversity 2005

  29. Transversity 2005

  30. Brodsky, Hwang, Schmidt model for Sivers function S p X q q – + diquark diquark needs k┴ dependent quark distribution in p↑: Sivers function Transversity 2005

  31. Amsterdam notations Sivers asymmetry in SIDIS talk by A. Prokudin p┴= PT– zk┴+ O(k┴2/Q2) Transversity 2005

  32. M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181 Transversity 2005

  33. Deuteron target Transversity 2005

  34. M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin First p┴ moments of extracted Sivers functions, compared with models data from HERMES and COMPASS Transversity 2005

  35. SSA in p↑p → π X E704 data, E = 200 GeV maximized value of AN with Collins effects alone fit to AN with Sivers effects alone M.A, M. Boglione, U. D’Alesio, E. Leader, F. Murgia U. D’Alesio, F. Murgia Transversity 2005

  36. HERMES + E704:Sivers function is not zero Talks by M. Burkardt D. Sivers, X. Artru Spin-k┴ partonic correlations in nucleons Theory: not quite universal J. Collins, a “QCD theorem” Models: few, in fair agreement Talk by A. Baccheta chiral models, A. Drago, P. Pobilytsa M. Burkardt Sum rules: talk by O. Teryaev Transversity 2005

  37. Looking forward to an interesting workshop, thanks! Transversity 2005

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