1. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 1 Spin dependence: theory and phenomenology Electromagnetic Interactions with Nucleons and Nuclei (EINN 2005) 6th European Research Conference September 21-24, 2005 - Milos, Greece Mauro Anselmino Torino University and INFN

2. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 2 Polarized DIS and helicity distributions, spin carried by quarks and gluons? Spin dependent, k ┴ unintegrated parton distributions: fundamental spin-k ┴ correlations? Transversity distributions, unknown Transverse single spin asymmetries “Partonic spin cases” Polarized fragmentation functions

3. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 3 What do we know, and how, about the proton structure? Main source of information is DIS l, s l’ q p,S X θ X l’, E’ l, E,s p, S

4. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 4 parity conserving case (one photon exchange) measuring dσ one extracts information on the structure functions F 1, F 2, g 1 and g 2 F 1,2 related to q(x,Q 2 ), g(x,Q 2 ) quark, gluon distributions g 1 related to ∆q(x,Q 2 ), ∆g(x,Q 2 ) quark, gluon helicity distributions

5. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 5 q l’ l q p,S X QCD parton model

6. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 6 coefficient functions splitting functions QCD evolution

7. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 7

8. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 8 de Florian, Navarro, Sassot

9. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 9 Research Plan for Spin Physics at RHIC February 11, 2005 Figure 11: Left: results for Δg(x,Q 2 = 5GeV 2 ) from recent NLO analyses [1, 2, 36] of polarized DIS. The various bands indicate ranges in Δg that were deemed consistent with the scaling violations in polarized DIS in these analyses. The rather large differences among these bands partly result from differing theoretical assumptions in the extraction, for example, regarding the shape of Δg(x) at the initial scale. Note that we show xΔg as a function of log(x), in order to display the contributions from various x-regions to the integral of Δg. Right: the “net gluon polarization” Δg(x,Q 2 )/g(x,Q 2 ) at Q 2 = 5 GeV 2, using Δg of [2] and its associated band, and the unpolarized gluon distribution of [82].

10. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 10 Direct measure of Δg needed  large p T di-hadron production in SIDIS,  high p T pions and jets at RHIC,  direct photon production at RHIC,  charm production at RHIC, Small and large x behaviours, flavour decompositions, …. longitudinal spin sum rule, not the whole story… F. Tessarotto R. De Vita

11. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 11 large p T di-hadron production in SIDIS

12. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 12 S p p'p' – p PTPT θ – p ' 5 independent helicity amplitudes z y x Example: Transverse single spin asymmetries in elastic scattering

13. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 13 needs helicity flip + relative phase – + + + x + + + + at quark level but large SSA observed at hadron level! QED and QCD interactions conserve helicity, up to corrections

14. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 14 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

15. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 15 “Sivers moment”

16. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 16 “Collins moment”

17. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 17 Transverse Λ polarization in unpolarized p-Be scattering at Fermilab

18. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 18 “The largest spin effect ever seen by any human”, S. Brodsky, Como 2005

19. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 19 need k ┴ dependent quark distribution in p ↑ z y x ΦSΦS ΦπΦπ X p S PTPT Transverse single spin asymmetries in SIDIS Sivers mechanism or p ┴ dependent fragmentation of polarized quark Collins mechanism (talk by G. Schnell)

20. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 20 X p S + – Brodsky, Hwang, Schmidt model for Sivers function q q diquark

21. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 21 p ┴ = P T – z k ┴ + O(k ┴ 2 /Q 2 ) Sivers asymmetry in SIDIS p S k┴k┴ φ q

22. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 22 M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181

23. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 23 Collins mechanism for SSA Asymmetry in the fragmentation of a transversely polarized quark pqpq φ SqSq p┴p┴ initial q spin is transferred to final q', which fragments SqSq S q’ p┴p┴ x y ΦSΦS ΦhΦh q q’ (Fundamental QCD property? D. Sivers)

24. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 24 neglecting intrinsic motion in partonic distributions: Collins function First extraction of Collins functions from HERMES data: W. Vogelsang and F. Yuan (assuming Soffer-saturated h 1 ) transversity

25. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 25 fit to HERMES data on

26. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 26 Extraction of Collins functions from HERMES + BELLE data P 1 depends on

27. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 27 Fits to HERMES Collins data, preliminary results

28. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 28 Fits to BELLE Collins data, preliminary results M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation

29. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 29 p S k┴k┴ φ q pqpq φ SqSq p┴p┴ Amsterdam group notations spin-k ┴ correlations – Trento conventions Sivers functionCollins function

30. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 30 p SqSq k┴k┴ φ q pqpq φ SΛSΛ p┴p┴ Amsterdam group notations spin-k ┴ correlations Boer-Mulders function polarizing f.f.

31. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 31 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

32. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 32 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 gluon distribution ~ known

33. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 33 + – – – +++ + + + = + – = in helicity basis – + + – decouples from DIS (no quark helicity flip)

34. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 34 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

35. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 35 – + +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

36. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 36 Elementary LO interaction: 3 planes: plane ┴ polarization vectors, p-γ* plane, l + l – γ* plane plenty of spin effects h 1 in Drell-Yan processes p p Q 2 = M 2 qTqT qLqL l+l+ l–l– γ*γ*

37. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 37 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 s = 210 GeV 2 is best energy (talk by P. Reimer at workshop)

38. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 38 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

39. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 39 s=30 GeV 2 s=45 GeV 2 s=210 GeV 2 s=900 GeV 2

40. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 40 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 (Boer-Mulders function) (problematic)

41. EINN 2005 Spin dependence-theory September 23rd, Milos, Greece 41 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 Spin is one of the most fundamental concepts in physics, deeply rooted in Poincare invariance and hence in the structure of space-time itself. All elementary particles we know today carry spin, among them the particles that are subject to the strong interactions, the spin-1/2 quarks and the spin-1 gluons. Spin, therefore, plays a central role also in our theory of the strong interactions, Quantum Chromodynamics (QCD), and to understand spin phenomena in QCD will help to understand QCD itself. RHIC proposal 2005