Mauro Anselmino: The transverse spin structure of the nucleon - III

1. Mauro Anselmino:The transverse spin structure of the nucleon - III About SSA in hadronic interactions TMDs and SSA in inclusive hadronic interactions TMDs and SSA in Drell-Yan processes Drell-Yan processes, the transversity golden channel Alternative ways to transversity A fundamental QCD test

2. X c a b X PDF FF pQCD elementary interactions TMDs and SSAs in hadronic collisions (collinear configurations) factorization theorem

3. RHIC, Latest PHENIX data on unpolarized cross section

4. STAR-RHIC √s = 200 GeV 1.2 < pT < 2.8 andAN stays at high energies ….

5. X c a b X SSA in hadronic processes: intrinsic k┴, factorization? Two main different (?) approaches (W. Vogelsang) Generalization of collinear scheme (assuming factorization) first proposed by Field-Feynman

6. (1) (2) (3) (1) (2) (3) Possible sources of SSA, simple approach(one k┴ at a time) suppressed by phases

7. General formalism with helicity amplitudes non planar process, plenty of phases main remaining contribution to SSA from Sivers effect M.A., M. Boglione, U. D’Alesio, E. Leader, S. Melis, F. Murgia, PR D71, 014002 (2005), PR D73, 014020 (2006)

8. Computation of helicity amplitudes Dirac-Pauli helicity spinors if scattering is not planar all Φiare different and many phases remain in the amplitudes; they strongly suppress the results of integrations over k┴

11. 8 leading-twistspin-k┴dependent distribution functions Courtesy of Aram Kotzinian

12. U. D’Alesio, F. Murgia E704 data STAR data prediction fit For a somewhat different approach see lectures by W. Vogelsang, great progresses in the last months

13. l+ Q2 = M2 l– qT 3 planes: p p qL TMDs and SSAs in Drell-Yan processes factorization holds, two scales, M2, and

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

15. For example, the cos 2φ term can be originated by the Boer-Mulders effect Polarized D-Y processes with intrinsic k┴ have a rich structure, similar to SIDIS SSA in D-Y has a contribution from the coupling of the transversity distribution to B-M function B-M

16. Sivers effect in D-Y processes By looking at the cross section one can single out the Sivers effect in D-Y processes

17. Predictions for AN at RHIC, M. A., M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin See later for crucial issue concerning Sivers function in D-Y

18. range of x1, x2 explored depends on l+ Q2 = M2 l– qT p p qL Simple partonic cross section at collinear level

19. Direct access to transversity from double transverse spin asymmetry

20. Possible access transversity: Drell-Yan processes

21. RHIC energies: small x1and/orx2 h1q (x, Q2)evolution much slower than Δq(x, Q2)andq(x, Q2)at smallx Barone, Calarco, Drago ATTat RHIC is very small smaller s would help Martin, Schäfer, Stratmann, Vogelsang ATT for Drell-Yan processes at RHIC upgrades in luminosity expected

22. at GSI h1 from large x1,x2 GSI energies: one measures h1 in the quark valence region: ATTis estimated to be large, between 0.2 and 0.4 PAX proposal: hep-ex/0505054

23. Energy for Drell-Yan processes "safe region": QCD corrections might be very large at smaller values of M: yes, for cross-sections, not for ATTK-factor almost spin-independent Fermilab E866 800 GeV/c H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya M. Guzzi,V. Barone, A. Cafarella,C. Corianò and P.G. Ratcliffe

24. s=30 GeV2 s=45 GeV2 s=210 GeV2 s=900 GeV2

25. s=30 GeV2 s=45 GeV2 s=210 GeV2 s=900 GeV2

26. data from CERN WA39, πN processes, s = 80 GeV2 H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya

27. need to know transverse fragmentation function l p X Some alternative accesses to transversity Inclusive Λ production and measure of Λ polarization COMPASS analysis in progress the Λpolarization vector can be measured by looking at the proton angular distribution as resulting from Λ → πp decay in the Λhelicity rest frame

28. similar result in collinear configuration, no need for intrinsic k┴

29. Two hadron production in SIDISDi-hadron Fragmentation Function (DiFF) Chiral odd fragmentation function of a transversely polarized quark into two hadrons (interference between s and p wave) Bacchetta, Boer, Jaffe, Jakob, Radici …

31. j2-p thrust-axis e- j1 e+ e+ andpolarization are strongly correlated; spin effect in quark fragmentation visible event by event TMDs measurements at BELLE (spin physics without polarization)

32. access to and obtain information on Collins function first ever results on transversity via in SIDIS A similar procedure could be followed with DiFF (accessible also in SSA in ) It requires detection of many particles (low statistics) (M. Boglione seminar)

33. q q – + diquark diquark A fundamental QCD test The Sivers function, being related to gauge links, is not universal, but it changes from process to process or, rather, it enters different processes with different numerical factors … J. Collins Following example taken from a talk prepared by M. Grosse-Perdekamp and delivered by L. Bland, Trento 2007

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

35. Not all spin problems have been solved, but enormous progresses have been made The spin-orbiting structure of quarks in nucleons begins to emerge Theory. Unintegrated PDF and FF play a crucial role; their Q2 evolution is needed. Factorization and universality issues must be clarified, … Experiment. New data from COMPASS (proton target), JLab, RHIC, and GSI. D-Y processes very promising … Thanks and see you again!