Single-Transverse Spin Asymmetries in Hadronic Scattering

1. Single-Transverse Spin Asymmetries in Hadronic Scattering Werner Vogelsang (& Feng Yuan) BNL Nuclear Theory ECT, 06/13/2007

2. Mostly based on: X. Ji, J.W. Qiu, WV, F. Yuan, Phys. Rev. Lett. 97, 082002 (2006) Phys. Rev. D73, 094017 (2006) Phys. Lett. B638, 178 (2006) C. Kouvaris, J.W. Qiu, WV, F. Yuan, Phys. Rev. D74, 114013 (2006) ( C. Bomhof, P. Mulders, WV, F. Yuan, Phys. Rev. D75, 074019 (2007) ) J.W. Qiu, WV, F. Yuan, arXiv:0704.1153 [hep-ph] (Phys. Lett. B, to appear) arXiv:0706.1196 [hep-ph]

3. Outline: • Introduction • Single-spin asymmetries in pp  hX • How are mechanisms for Single-spin asymmetries related ? • Conclusions

4. I. Introduction

5.  L R • SSA with small & measured qT , large scale Q  examples: typical AN measured in lepton-scattering, “back-to-back” jets in pp  need not be suppressed with 1/Q  may have TMD factorization (Sivers & other fcts.) • SSA for single-inclusive process  example: pp  X  a single large scale (pT)  power-suppressed  collinear factorization (Efremov,Teryaev / Qiu,Sterman TF)

6. II. Asymmetry in pphX

7.  L R E704 STAR

8. collinear factorization Brahms y=2.95 STAR

9. STAR

10. • typically, hard-scattering calculations based on LO/NLO fail badly in describing the cross section √s=23.3GeV Apanasevich et al. Bourrely and Soffer  Resummation of important higher-order corrections beyond NLO de Florian, WV

11. “threshold” logarithms Real emission inhibited Only soft/collinear gluons allowed de Florian, WV • higher-order corrections beyond NLO ?

12. Mellin moment in Leading logarithms • expect large enhancement ! de Florian, WV

13. de Florian, WV E706

14. WA70 Effects start to become visible at S=62 GeV… Rapidity dependence ? Spin dependence ?

15. ~ Im • Kane, Pumplin, Repko ‘78 In helicity basis: _ + _ + + _ transversity _ • lesson from this: AN in pph X is power-suppressed !

16. x1 x2 x2-x1 _ • power-suppressed effects in QCD much richer than just mass terms (Efremov,Teryaev; Qiu,Sterman; Kanazawa, Koike)

17. quark-gluon correlation function TF(x1, x2) provides helicity flip unpol. pdf Phase from imaginary part of propagator ~ i (x1-x2) (soft-gluon-pole contributions) • ingredients: Collinear factorization. x1 x2 x2-x1

18. • full structure: Qiu,Sterman Transversity Kanazawa,Koike

21. Position of pole may depend on k of initial partons IS FS

22. Qiu & Sterman argue: At forward xF , collisions are asymmetric: large-x parton hits “small-x” parton  TF (x, x) mostly probed at relatively large x “derivative terms” • plus, non-derivative terms !

23. xF=0.4 xF=0.15

24. Assumptions in Qiu & Sterman : • derivative terms only • valence TF only, • neglect gluonpion fragmentation In view of new data, would like to relax some of these. Kouvaris, Qiu, Yuan, WV

25. Remarkably simple answer: Recently: proof by Koike & Tanaka

26.  Ansatz: usual pdf  Fit to E704, STAR, BRAHMS  for RHIC, use data with pT>1 GeV • for E704, choose pT=1.2 GeV allow normalization of theory to float (~0.5)

27. Fit I: “two-flavor / valence” Fit II: allow sea as well

28. solid: Fit I, dashed: Fit II

30. Our TF functions:

31. pT dependence

32. Dependence on RHIC c.m.s. energy:

33. III. How are the mechanisms for single-spin asymmetries related ?

34. • Boer, Mulders, Pijlman • see interplay of mechanisms in a physical process ? • have two “mechanisms” • tied to factorization theorem that applies Q: In what way are mechanisms connected ?

35. d/dqT qT~Q coll. fact. TF Sivers qT<<Q kT fact. “Unification” / Consistency of formalisms qT QCD • verify at 1-loop X. Ji, J.W. Qiu, WV, F. Yuan QCD << qT << Q same physics ? • consider Drell-Yan process at measured qT and Q

36. Step 1: calculate SSA for DY at qT ~ Q use Qiu/Sterman formalism Because of Q2 ≠ 0, there are also “hard poles”: Propagator (H) has pole at xg0 No derivative terms in hard-pole contributions.

37. soft-pole hard-pole

38. _ • result for qq process is (completely general!) soft-pole hard-pole derivative non-deriv. (recently also: Koike, Tanaka)

39. Unpol. Pol. Step 2: expand this for qT << Q

40. Step 3: calculate various factors in TMD factorized formula Collins, Soper, Sterman Ji, Ma, Yuan At QCD << qT can calculate each factor from one-gluon emission

41. Unpolarized pdf:

42. Sivers function: soft-pole hard-pole w/ correct direction of gauge link

43. Step 4: compare both results and find agreement ! hard-pole soft-pole, deriv. hard-pole soft-pole, non-deriv. Precisely what’s needed to make factorization work and match on to the Qiu/Sterman result at small q! So:

44. + + ) (  + +  Here for soft-pole, but happens separately for: derivative / non-derivative / hard-pole Take a closer look: if one works directly in small q limit  

45. The interesting question now: What happens in more general QCD hard-scattering ? Consider ppjet jet X = jet pair transv. mom. Underlying this: all QCD 22 scattering processes

46. Example: qq’  qq’ • for Qiu/Sterman calculation: subset of diagrams IS FS1 FS2 (these are soft-pole)

47. Simplify: • assume q << P from the beginning • more precisely, assume k’ nearly parallel to hadron A or B and pick up leading behavior in q / P • reproduces above Drell-Yan results

48. k’ parallel to pol. hadron: (partly even on individual diagram level, as in Drell-Yan) Likewise for hard-pole contributions

49. What this means: When k’ nearly parallel to pol. hadron, structure at this order can be organized as

50. • happens for all partonic channels: individual diagrams Some remarks: • highly non-trivial. Relies on a number of “miracles”: color structure no derivative terms when k’ parallel to hadron B … Calculation seems to “know” how to organize itself