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

2. xP P The longitudinal structure of nucleons is simple It has been studied for almost 40 years Q2Q2

3. essentially x and Q 2 degrees of freedom ….

4. Very good or good knowledge of q(x,Q 2 ), g(x,Q 2 ) and Δq(x,Q 2 ) Poor knowledge of Δg(x,Q2) (Research Plan for Spin Physics at RHIC) Talk by L. De Nardo

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

6. The mother of all functions M. Diehl, Trento workshop, June 07 TMDs GPDs Wigner function (Belitsky, Ji, Yuan)

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

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., JHEP 0702 (2007) 093 SIDISLAND

10. SIDIS in parton model with intrinsic k factorization holds at large Q 2, and Ji, Ma, Yuan

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

12. Sivers function Boer-Mulders function

13. 8 leading-twist spin-k dependent distribution functions Courtesy of Aram Kotzinian

14. Collins function Polarizing fragmentation function

16. Large K + asymmetry!

18. Talk by G. Schnell

19. 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

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

21. DSS = de Florian, Sassot, Stratmann KRE = Kretzer HKNS = Hirai, Kumano, Nagai, Sudoh Fragmentation functions

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

25. Predictions for JLab

26. 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. M. Anselmino, M. Boglione, J.C. Collins, U. DAlesio, A.V. Efremov, K. Goeke, A. Kotzinian, S. Menze, A. Metz, F. Murgia, A. Prokudin, P. Schweitzer, W. Vogelsang, F. Yuan Present knowledge of Sivers function (u,d)

27. S number density of partons with longitudinal momentum fraction x and transverse momentum k, inside a proton with spin S M. Burkardt, PR D69, 091501 (2004) What do we learn from the Sivers distribution?

28. Total amount of intrinsic momentum carried by partons of flavour a for a proton moving along the +z-axis and polarization vector S

29. Sivers functions extracted from A N data in give also opposite results, with Numerical estimates from SIDIS data U. DAlesio

30. Sivers function and orbital angular momentum Sivers mechanism originates from then it is related to the quark orbital angular momentum D. Sivers For a proton moving along z and polarized along y

31. 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)

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

34. Fit of BELLE data

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

36. What do we learn (if anything yet) from the transversity distributions and the Collins functions ? h 1u and h 1d have 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 …

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

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

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

40. and A N stays at high energies …. STAR-RHIC s = 200 GeV 1.2 < p T < 2.8 talk by L. Bland

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

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

43. E704 dataSTAR data U. DAlesio, F. Murgia fit prediction

44. Higher-twist partonic correlations (Efremov, Teryaev ; Qiu, Sterman; Kouvaris, Vogelsang, Yuan) twist-3 functions hard interactions contribution to SSA collinear expansion at order k i

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

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

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

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

49. TMDs and SSAs in Drell-Yan processes (returning to safer grounds and looking at future ….) p p Q 2 = M 2 qTqT qLqL l+l+ l–l– γ*γ* factorization holds, two scales, M 2, and

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

51. (Polarized) Drell-Yan cross sections allow to access many TMDs (Boer-Mulders, …) D-YLAND verify whether and offer the golden channel to measure the transversity distribution ! ! ! Talks by R. Kaiser, M. Contalbrigo

52. Conclusions Increasing knowledge about quark transverse motion, and spin-k correlations (Sivers function) First experimental information on h 1 Work in progress on GPDs and quark space distribution (L q ) Towards resolving the orbital motion of quarks in a proton … More data from HERMES, COMPASS, JLab and RHIC Thanks