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Mauro Anselmino, Torino University and INFN, Vancouver, July 31, 2007

The transverse spin structure of the nucleon. Mauro Anselmino, Torino University and INFN, Vancouver, July 31, 2007. xP. P. The longitudinal structure of nucleons is “simple” It has been studied for almost 40 years. Q 2. essentially x and Q 2 degrees of freedom ….

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Mauro Anselmino, Torino University and INFN, Vancouver, July 31, 2007

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  1. The transverse spin structure of the nucleon Mauro Anselmino,Torino University and INFN,Vancouver, July 31, 2007

  2. xP P The longitudinal structure of nucleons is “simple” It has been studied for almost 40 years Q2

  3. essentiallyxandQ2degrees of freedom ….

  4. Very good or good knowledge ofq(x,Q2),g(x,Q2)andΔq(x,Q2)Poorknowledge ofΔg(x,Q2) (Research Plan for Spin Physics at RHIC) Talk by L. De Nardo

  5. ? The transverse structure is much more interesting and less studied orbiting quarks? spin-k┴ correlations? Space dependent distribution functions Transverse Momentum Dependent distribution functions

  6. The mother of all functionsM. Diehl, Trento workshop, June 07 Wigner function (Belitsky, Ji, Yuan) GPD’s TMD’s

  7. TMDs in SIDIS SSA in SIDIS: Sivers functions Collins function from e+e- unpolarized processes(Belle)and first extraction of transversity SSA in hadronic processes Future measurements and transversity (Trento workshop on “Transverse momentum,spin, and position distributions of partons in hadrons”, June 07)

  8. Main source of information on transverse nucleon structure SIDIS kinematics according toTrento conventions (2004)

  9. Polarized SIDIS cross section, up to subleading order in 1/Q Kotzinian, NP B441 (1995) 234 Mulders and Tangermann, NP B461 (1996) 197 Boer and Mulders, PR D57 (1998) 5780 Bacchetta et al., PL B595 (2004) 309 Bacchetta et al., JHEP0702 (2007) 093 SIDISLAND

  10. factorization holds at largeQ2, and Ji, Ma, Yuan SIDIS in parton model with intrinsick┴

  11. Azimuthal dependence induced by quark intrinsic motion EMC data,µp and µd, E between 100 and 280 GeV M.A., M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin

  12. Sivers function Boer-Mulders function

  13. 8 leading-twistspin-k┴dependent distribution functions Courtesy of Aram Kotzinian

  14. Collins function Polarizing fragmentation function

  15. Large K+ asymmetry!

  16. Talk by G. Schnell

  17. COMPASS measured Collins and Sivers asymmetries for positive (●) and negative (○) hadrons small values due to deuteron target: cancellation between u and d contributions talk by T. Iwata

  18. M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin A fit of HERMES + COMPASS pion data, information on u and d Sivers funtions sea contribution? no sea contribution (Kretzer fragmentation functions)

  19. Fragmentation functions DSS = de Florian, Sassot, StratmannKRE = Kretzer HKNS = Hirai, Kumano, Nagai, Sudoh

  20. M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin fit of HERMES + COMPASS pion and kaon data, with new set of fragmentation functions (de Florian, Sassot, Stratmann)

  21. Predictions for JLab

  22. Present knowledge of Sivers function (u,d) M. Anselmino, M. Boglione, J.C. Collins, U. D’Alesio, A.V. Efremov, K. Goeke, A. Kotzinian, S. Menze, A. Metz, F. Murgia, A. Prokudin, P. Schweitzer, W. Vogelsang, F. Yuan The first and 1/2-transverse moments of the Sivers quark distribution functions. The fits were constrained mainly (or solely) by the preliminary HERMES data in the indicated x-range. The curves indicate the 1-σ regions of the various parameterizations.

  23. S What do we learn from the Sivers distribution? number density of partons with longitudinal momentum fractionxand transverse momentumk┴,inside a proton with spinS M. Burkardt, PR D69, 091501 (2004)

  24. Total amount of intrinsic momentum carried by partons of flavoura for a proton moving along the+z-axisand polarization vector S

  25. Sivers functions extracted fromANdata in give also opposite results, with Numerical estimates from SIDIS data U. D’Alesio

  26. Sivers mechanism originates from then it is related to the quark orbital angular momentum Sivers function and orbital angular momentum D. Sivers For a proton moving alongz and polarized alongy

  27. Sivers function and proton anomalous magnetic moment M. Burkardt, S. Brodsky, Z. Lu, I. Schmidt Both the Sivers function and the proton anomalous magnetic moment are related to correlations of proton wave functions with opposite helicities in qualitative agreement with large z data: related result (M. Burkardt)

  28. j2-p thrust-axis e- j1 e+ e+ Collins function from e+e–processes(spin effects without polarization, D. Boer) BELLE @ KEK e+e- CMS frame:

  29. Fit of BELLE data

  30. Extraction of Collins functions and transversity distributions from fitting HERMES + COMPASS + BELLE data M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin C. Türk

  31. What do we learn (if anything yet) from the transversity distributions and the Collins functions ? h1uandh1dhave opposite signs They are both smaller than Soffer bound Still large uncertainties Tensor charges appear to be smaller than results from lattice QCD calculations M. Wakamatsu, hep-ph/0705.2917 Collins functions well below the positivity bound. Favoured and unfavoured ones have opposite signs, comparable magnitudes Only the very beginning …

  32. X c a b X PDF FF pQCD elementary interactions TMDs and SSAs in hadronic collisions (abandoning safe grounds ….) (collinear configurations) factorization theorem (?)

  33. RHIC data excellent agreement with data for unpolarized cross section, but no SSA

  34. BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2 E704 √s = 20 GeV 0.7 < pT < 2.0 observed transverse Single Spin Asymmetries E704 √s = 20 GeV 0.7 < pT < 2.0 experimental data on SSA

  35. STAR-RHIC √s = 200 GeV 1.2 < pT < 2.8 andAN stays at high energies …. talk by L. Bland

  36. X c a b X SSA in hadronic processes: intrinsic k┴, factorization? Two main different (?) approaches Generalization of collinear scheme (M. A., M. Boglione, U. D’Alesio, E. Leader, F. Murgia, S. Melis)

  37. It generalizes to polarized case plenty of phases main remaining contribution to SSA from Sivers effect

  38. U. D’Alesio, F. Murgia E704 data STAR data prediction fit

  39. contribution to SSA Higher-twist partonic correlations (Efremov, Teryaev; Qiu, Sterman; Kouvaris, Vogelsang, Yuan) hard interactions twist-3 functions “collinear expansion” at order ki┴

  40. fits of E704 and STAR data Kouvaris, Qiu, Vogelsang, Yuan

  41. Gluonic pole cross sections and SSA in Bacchetta, Bomhof, Mulders, Pijlman; Vogelsang, Yuan factorization ? (Collins) Sivers contribution to SSA gluonic pole cross sections take into account gauge links Diagram dependentGauge link Colour factors (breaking of factorization?)

  42. Gluonic pole cross sections and SSA in to be compared with the usual cross section

  43. Non-universality of Sivers Asymmetries: Unique Prediction of Gauge Theory ! Simple QED example: Drell-Yan: repulsive DIS: attractive Same inQCD: As a result:

  44. l+ Q2 = M2 l– γ* qT p p qL TMDs and SSAs in Drell-Yan processes (returning to safer grounds and looking at future ….) factorization holds, two scales, M2, and

  45. Unpolarized cross section already very interesting Collins-Soper frame

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