1. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 1 Transversity (transverse spin and transverse motion) Towards transversity distributions: theory and experiments Transverse Single Spin Asymmetries Spin and k dependent parton distributions (TMD) (unravelling the spin-orbital motion of partons?) Collins mechanism Sivers mechanism

2. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 2 Parton distributions are fundamental leading-twist quark distributions quark distribution – well known quark helicity distribution – known transversity distribution – unknown all equally important related to positivity bound and (or chiral-even related to chiral-odd gluon helicity distribution – poorly known

3. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 3 + – – – +++ + + + = + – = in helicity basis – + + – decouples from DIS (no quark helicity flip)

4. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 4 h 1 must couple to another chiral-odd function. For example: D-Y, pp l + l – X, and SIDIS, l p l π X, processes + + – + + – + – – – + – + – h 1 x h 1 h 1 x Collins function J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992 J. Collins, 1993

5. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 5 – + +1 –1 No gluon contribution to h 1 simple Q 2 evolution Q 2 = 25 GeV 2 Q 0 2 = 0.23 GeV 2 V. Barone, T. Calarco, A. Drago

6. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 6 Elementary LO interaction: 3 planes: plane polarization vectors, p-γ* plane, l + l – γ* plane plenty of spin effects p p Q 2 = M 2 qTqT qLqL l+l+ l–l– γ*γ* h 1 in Drell-Yan processes

7. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 7 h 1 from RHIC energies: small x 1 and/or x 2 h 1q (x, Q 2 ) evolution much slower than Δq(x, Q 2 ) and q(x, Q 2 ) at small x A TT at RHIC is very small smaller s would help Martin, Schäfer, Stratmann, Vogelsang Barone, Calarco, Drago at RHIC talk by A. Mukherjee

8. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 8 h 1 from GSI energies: large x 1,x 2 one measures h 1 in the quark valence region: A TT is estimated to be large, between 0.2 and 0.4 at GSI PAX proposal: hep-ex/0505054 Talks by M. Contalbrigo, N. Nikolaev, M. Maggiora

9. Mauro Anselmino, Como, September 7, 2005 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 A TT K-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

10. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 10 s=30 GeV 2 s=45 GeV 2 s=210 GeV 2 s=900 GeV 2

11. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 11 s=30 GeV 2 s=45 GeV 2 s=210 GeV 2 s=900 GeV 2

12. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 12 data from CERN WA39, π N processes, s = 80 GeV 2

13. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 13 h 1 x Collins from SIDIS processes Asymmetry in the fragmentation of a transversely polarized quark pqpq φ SqSq p initial q spin is transferred to final q', which fragments SqSq SqSq p x y ΦSΦS ΦhΦh q q Trento conventions (Fundamental QCD property? D. Sivers) Amsterdam notations

14. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 14 neglecting intrinsic motion in partonic distributions: Collins function some data available from HERMES, first extraction of Collins functions: W. Vogelsang and F. Yuan (assuming Soffer-saturated h 1 ) transversity

15. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 15 fit to HERMES data on

16. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 16 Extraction of Collins functions from HERMES + BELLE data P 1 depends on (talk by R. Seidl) M.A, M. Boglione, U. DAlesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation

17. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 17 Fits to HERMES Collins data, preliminary results

18. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 18 Fits to BELLE Collins data, preliminary results

19. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 19 HERMES + BELLE: Collins function is not zero Theory: probably universal Collins, Metz Models: few, in disagreement Amrath, Bacchetta, Metz, Kundu, Mulders, … assumes h 1 = q disfavoured Collins functions = 0 pion-quark vertex ? loop? Talk by. A. Bacchetta

20. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 20 X p Alternative accesses to transversity Inclusive Λ production and measure of Λ polarization transverse fragmentation function COMPASS analysis in progress Talk by A. Ferrero

21. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 21 Two pion production: interference fragmentation function Talks by P. van der Nat, M. Radici

22. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 22 Vector meson production: (generalized fragmentation function) Inclusive hadronic production: Single Spin Asymmetry in D-Y processes (Boer-Mulders distribution) Talk by F. Murgia Talks by D. Boer, G. Goldstein, M. Radici

23. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 23 S p p'p' – p PTPT θ – p ' Single Spin Asymmetry in elastic scattering. Example: 6 independent helicity amplitudes z y x Transverse SSA

24. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 24 S p p'p' – p PTPT θ – p ' z y x ΦSΦS Φ for a generic configuration :

25. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 25 needs helicity flip + relative phase – + + + x + + + + at quark level large SSA observed at hadron level

26. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 26 BNL-AGS s = 6.6 GeV 0.6 < p T < 1.2 E704 s = 20 GeV 0.7 < p T < 2.0 STAR-RHIC s = 200 GeV 1.1 < p T < 2.5 E704 s = 20 GeV 0.7 < p T < 2.0 SSA, pp πX

27. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 27 Unweighted Collins moment:Unweighted Sivers moment:

28. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 28 Transverse Λ polarization in unpolarized p-Be scattering at Fermilab

29. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 29

30. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 30 X p S + – Brodsky, Hwang, Schmidt model for Sivers function q q diquark needs k dependent quark distribution in p : Sivers function

31. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 31 p = P T – z k + O(k 2 /Q 2 ) Sivers asymmetry in SIDIS Amsterdam notations talk by A. Prokudin

32. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 32 M.A, M. Boglione, U. DAlesio, A. Kotzinian, F. Murgia, A. Prokudin hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181

33. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 33 Deuteron target

34. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 34 First p moments of extracted Sivers functions, compared with models M.A, M. Boglione, U. DAlesio, A. Kotzinian, F. Murgia, A. Prokudin data from HERMES and COMPASS

35. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 35 SSA in p p π X fit to A N with Sivers effects alone maximized value of A N with Collins effects alone E704 data, E = 200 GeV U. DAlesio, F. Murgia M.A, M. Boglione, U. DAlesio, E. Leader, F. Murgia

36. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 36 HERMES + E704: Sivers function is not zero Theory: not quite universal J. Collins, a QCD theorem Models: few, in fair agreement Spin-k partonic correlations in nucleons Talks by M. Burkardt D. Sivers, X. Artru chiral models, A. Drago, P. Pobilytsa M. Burkardt Sum rules: talk by O. Teryaev Talk by A. Baccheta

37. Mauro Anselmino, Como, September 7, 2005 Transversity 2005 37 Looking forward to an interesting workshop, thanks!