Spin and k ┴ dependent parton distributions

1. Spin and k┴ dependent parton distributions - a closer look at the nucleon structure - (with the help of antiprotons) • integrated partonic distributions • the missing piece,transversity • partonic intrinsic motion(TMD) • spinand k┴:transverse Single Spin Asymmetries • SSA in SIDIS and p-p, p-pbar inclusive processes • conclusions Mauro Anselmino, ECT* Trento,04/07/2006

2. (or and are fundamental leading-twist quark distributions depending on longitudinal momentum fraction x K┴ integrated parton distributions quark distribution– well known all equally important quark helicity distribution – known transversity distribution – unknown gluonhelicity distribution – poorly known chiral-even related to chiral-odd related to positivity bound

4. de Florian, Navarro, Sassot

5. Research Plan for Spin Physics at RHIC February 11, 2005 Figure 11: Left: results for Δg(x,Q2 = 5GeV2) 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,Q2)/g(x,Q2) at Q2 = 5 GeV2, using Δg of [2] and its associated band, and the unpolarized gluon distribution of [82].

6. The missing piece, transversity – – + + + = – + + + + + = – in helicity basis – + decouples from DIS (no quark helicity flip) – +

7. h1 must couple to another chiral-odd function. For example – + h1 x h1 – + J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992 – + + – h1 x Collins function – + – + + – J. Collins, 1993

8. No gluon contribution to h1 simple Q2 evolution –1 +1 – + Q2 = 25 GeV2 Q02 = 0.23 GeV2 V. Barone, T. Calarco, A. Drago

9. First ever “transversity”, according to Gary Goldstein, QCD-N06, Villa Mondragone, June 15, 2006

10. h1 in Drell-Yan processes l+ Q2 = M2 l– qT p p qL Elementary LO interaction: 3 planes: plenty of spin effects

11. h1 from at RHIC RHIC energies: small x1 and/or x2 h1q (x, Q2)evolution much slower than Δq(x, Q2)and q(x, Q2)at small x ATTat RHIC is very small smaller swould help Barone, Calarco, Drago Martin, Schäfer, Stratmann, Vogelsang

12. 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

13. 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

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

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

16. data from CERN WA39, π N processes, s = 80 GeV2 H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya

17. uncertainty principle gluon radiation k┴ ±1 ± ± l+ Q2 = M2 l– qT p p qL Partonic intrinsic motion Plenty of theoretical and experimental evidence for transverse motion of partons within nucleons and of hadrons within fragmentation jets qT distribution of lepton pairs in D-Y processes

18. k┴ p xp pT distribution of hadrons in SIDIS Hadron distribution in jets in e+e– processes Large pT particle production in Transverse motion is usually integrated, but there might be important spin-k┴ correlations

19. ? orbiting quarks? spin-k┴ correlations? Transverse Momentum Dependent distribution functions Space dependent distribution functions (GPD)

20. Unpolarized SIDIS, in collinear parton model thus, no dependence on azimuthal angle Фhat zero-th order in pQCD the experimental data reveal that M. Arneodo et al (EMC): Z. Phys. C 34 (1987) 277

21. Cahn: the observed azimuthal dependence is related to the intrinsic k┴of quarks (at least for small PTvalues) assuming collinear fragmentation,φ= Φh These modulations of the cross section with azimuthal angle are denoted as “Cahn effect”.

22. SIDIS with intrinsic k┴ kinematics according toTrento conventions (2004) factorization holds at largeQ2, and Ji, Ma, Yuan

23. one has neglecting terms of order The situation is more complicated as the produced hadron has also intrinsic transverse momentum with respect to the fragmenting parton

24. clear dependence on (assumed to be constant) and assuming: one finds: with Find best values by fitting data onΦhandPTdependences

25. EMC data,µp and µd, E between 100 and 280 GeV M.A., M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin

26. Large PTdata explained by NLO QCD corrections

27. dashed line: parton model with unintegrated distribution and fragmentation functions solid line: pQCD contributions at LO and a K factor (K = 1.5) to account for NLO effects

28. (collinear configurations) factorization theorem X c a b X FF PDF pQCD elementary interactions

29. The cross section elementary Mandelstam variables hadronic Mandelstam variables

30. RHIC data

31. c X F. Murgia, U. D’Alesio a b FNAL data,PLB 73 (1978) X non collinear configurations original idea by Feynman-Field

32. Transverse single spin asymmetries: elastic scattering S y p' x PT θ z p – p – p' Example: 5 independent helicity amplitudes

33. Single spin asymmetries at partonic level. Example: needs helicity flip + relative phase + + – + x + + + + QED and QCD interactions conserve helicity, up to corrections at quark level but large SSA observed at hadron level!

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

35. STAR-RHIC √s = 200 GeV 1.1 < pT < 2.5 AN stays at high energies ….

36. Transverse Λ polarization in unpolarized p-Be scattering at Fermilab

38. “Sivers moment”

39. “Collins moment”

40. φ q Sq φ p┴ S k┴ pq p spin-k┴ correlations Sivers function Collins function Amsterdam group notations

41. spin-k┴ correlations q φ φ Sq SΛ k┴ p┴ p pq Boer-Mulders function polarizing f.f. Amsterdam group notations

42. 8 leading-twistspin-k┴dependent distribution functions

43. from Sivers mechanism M.A., U.D’Alesio, M.Boglione, A.Kotzinian, A Prokudin

44. Deuteron target

45. M. Anselmino, M. Boglione, J.C. Collins, U. D’Alesio, A.V. Efremov, K. Goeke, A. Kotzinian, S. Menze, A. Metz, F. Murgia, A. Prokudin, P. Schweitzer, W. Vogelsang, F. Yuan 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.

46. fit to HERMES data on W. Vogelsang and F. Yuan

47. Hadronic processes: the cross section with intrinsic k┴ intrinsic k┴in distribution and fragmentation functions and in elementary interactions factorizationis assumed, not proven in general; some progress for Drell-Yan processes, two-jet production, Higgs production via gluon fusion (Ji, Ma, Yuan; Collins, Metz; Bacchetta, Bomhof, Mulders, Pijlman)

48. The polarized cross section with intrinsic k┴ helicity density matrix of parton a inside polarized hadron A pQCD helicity amplitudes product of fragmentation amplitudes

49. SSA in p↑p → π X E704 data, E = 200 GeV maximized value of ANwith Collins effects alone fit to ANwith Sivers effects alone M.A, M. Boglione, U. D’Alesio, E. Leader, F. Murgia

50. quark Sivers contribution gluon Sivers contribution Collins contribution Special channels available with antiprotons – Results from U. D’Alesio Maximised(i.e., saturating positivity bounds)contributions toAN