1. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Transversity (transverse spin and transverse motion) Transversity distributions – (some) theory Transversity distributions - experiments Transverse Single Spin Asymmetries (how to test a Quantum Field Theory) Spin and k ┴ dependent parton distributions (TMD)

2. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy 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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy + – – – +++ + + + = + – = in helicity basis – + + – decouples from DIS

4. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Helicity conservation in pQCD or QED

5. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy 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

6. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy

7. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy D. De Florian, G.A. Navarro and R. Sassot, hep-ph/0506326

8. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy – + +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

9. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Elementary LO interaction: 3 planes: plane ┴ polarization vectors, p-γ* plane, l + l – γ* plane Plenty of single and double spin effects plenty of spin effects h 1 in Drell-Yan processes p p Q 2 = M 2 qTqT qLqL l+l+ l–l– γ*γ*

10. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy 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

11. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy 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

12. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy 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

13. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy s=30 GeV 2 s=45 GeV 2 s=210 GeV 2 s=900 GeV 2

14. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy s=30 GeV 2 s=45 GeV 2 s=210 GeV 2 s=900 GeV 2

15. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy data from CERN WA39, π N processes, s = 80 GeV 2

16. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy h 1 x Collins from SIDIS processes Spin effect comes from fragmentation of a transversely polarized quark pqpq φ SqSq p┴p┴ initial q spin is transfered to final q', which fragments SqSq S q’ p┴p┴ x y ΦSΦS ΦhΦh q q’

17. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy 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

18. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy fit to HERMES data on

19. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Extraction of Collins functions from HERMES + BELLE data P 1 depends on (talk by Matthias) M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation

20. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Fits to HERMES Collins data, preliminary results

21. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Fits to BELLE Collins data, preliminary results

22. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Alternative accesses to transversity Inclusive Λ production and measure of Λ polarization (transverse fragmentation function) Two pion production: l p ↑ → π π X (interference fragmentation function) Vector meson production: l p ↑ → ρ X (generalized fragmentation function) Inclusive hadronic production: p p ↑ → π X Single Spin Asymmetry in D-Y processes (higher-twist transversity distribution)

23. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy 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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy S p p'p' – p PTPT θ – p ' z y x ΦSΦS Φ for a generic configuration :

25. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy needs helicity flip + relative phase – + + + x + + + + at quark level large SSA observed at hadron level

26. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy 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, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Unweighted Collins moment:Unweighted Sivers moment:

28. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy X p S + – Brodsky, Hwang, Schmidt model for Sivers function q q diquark needs k ┴ dependent quark distribution in p ↑ : Sivers function

29. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy p ┴ = P T – z k ┴ + O(k ┴ 2 /Q 2 ) Sivers asymmetry in SIDIS

30. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181

31. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Deuteron target

32. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy First p ┴ moments of extracted Sivers functions, compared with models

33. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Predictions for COMPASS, hydrogen target 0.4 ≤ z h ≤ 1 0.2 ≤ P T ≤ 1 GeV/c 0.02 ≤ x B ≤ 1 Q 2 > 1 (GeV/c) 2 W 2 > 25 GeV 2 P T > 0.1 GeV/c E h > 4 GeV 0.2 < z h < 0.9 0.1 < y < 0.9

34. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy Predictions for K production at HERMES

35. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy 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. D’Alesio, F. Murgia M.A, M. Boglione, U. D’Alesio, E. Leader, F. Murgia

36. Mauro Anselmino, Prague, August 1, 2005 Hadron Structure and Hadron Spectroscopy The spin story goes on....... Polarization data has often been the graveyard of fashionable theories. If theorists had their way, they might just ban such measurements altogether out of self-protection. J.D. Bjorken St. Croix, 1987