1. Single-Spin Asymmetry in pp  X at RHIC Werner Vogelsang BNL Nuclear Theory RSC meeting, RIKEN, 09/29/2006

2. Outline: Phenomenological study of pp  h X Conclusions Some further predictions New theoretical calculation Introduction Work with C. Kouvaris, J.W. Qiu, F. Yuan hep-ph/0609238

3. I. Introduction

4. L R  strikingly large asymmetries at forward angles important: A N in pp  h X is power-suppressed ~1/p  Kane, Pumplin, Repko ‘78 single-inclusive observable, collinear factorization

5. Brahms prel. STAR

6.  Resummation of important higher-order corrections beyond NLO de Florian, WV √s=23.3GeV Bourrely and Soffer Apanasevich et al.

7. II. New theoretical calculation

8. analysis of power-suppressed effects in QCD (Qiu,Sterman; Efremov,Teryaev) x1x1 x2x2 x 2 -x 1 Phase from imaginary part of propagator ~ i  (x 1 -x 2 ) quark-gluon correlation function T F (x 1, x 2 ) provides helicity flip unpol. pdf

10. full structure: Kanazawa,Koike Qiu,Sterman Transversity

12. Position of pole may depend on k  of initial partons

13. “derivative terms” on-shell condition for “unobserved” parton

14. Qiu & Sterman argue: “derivative terms” dominate At forward x F, collisions are asymmetric: large-x parton hits “small-x” parton  T F (x, x) mostly probed at relatively large x

15.  Assumptions in Qiu & Sterman : derivative terms only valence T F only, neglect gluon  pion fragmentation In view of new data, relax these. Kouvaris, Qiu, Yuan, WV

16.  Remarkably simple answer:

17. III. Phenomenological study (…still more illustrative)

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

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

20. solid: Fit I, dashed: Fit II

22. Our T F functions:

23. IV. Some further predictions

24. p T dependence

25. Dependence on pion energy for fixed  :

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

27. A N in jet production:

28. A N in prompt-photon production:

29. V. Conclusions

30. SSA for single-inclusive process: power-suppressed new calculations in Qiu/Sterman formalism: “Non-derivative” terms. Organize in simple form. Moderately important. Data from RHIC are beginning to constrain T F functions. Consistency of theory description of fixed-target and RHIC data is only qualitative Entering era of precision determinations of T F !