1. Dilepton production near partonic threshold in transversely polarized p\bar{p} scatterings H. Shimizu (Hiroshima U, KEK) G. Sterman (SUNY) W. Vogelsang (BNL, RBRC) H. Yokoya (Niigata U) RADCOR 2005 @ Shonan Village, JAPAN Oct. 2-7, 2005 Phys.Rev.D71,114007,2005 (hep-ph/0503270) Title

2. Introduction Polarized Antiproton experiments @ GSI Drell-Yan process and QCD corrections Fixed order calculation Threshold resummation Far IR cut-off Numerical results NNLL resummation Summary Outline

3. Polarized Antiproton Beam may be available at the proposed new Proton–Antiproton experiments at GSI. Motivation : GSI experiment proposal PAX experiment proposal LoI, hep-ex/0412064,0505054 a) Asymmetric Collider Experiment : b) Fixed Target Experiment : polarized antiproton beam and polarized proton beam polarized antiproton beam with polarized hydrogen gas target

4. Drell-Yan dilepton production : measurement of double transverse spin asymmetry → measurement of the transversely polarized PDF : twist-2 distribution functions, chiral-odd, no gluon function, no measurement so far (first indication by HERMES, first measurement by RHIC?) advantage for the GSI experiments : → both valence quark contribution → large asymmetry is expected → large x ～ 0.5 region will be probed valence quark structure of trans. pol. nucleon

5. So far, only the tree level estimations have been done (includes J/ψ production) Anselmino,Barone,Drago,Nikolaev ( ’ 04) Efremov,Goeke,Schweitzer ( ’ 04) We examined the first QCD corrections to the Drell-Yan cross section for the GSI experiment kinematics. Drell-Yan dilepton production @ GSI Fixed order corrections : LO, NLO, NNLO Threshold resummation effects : up to NLL (NNLL)

6. Factorization Theorem Drell-Yan cross section formula

7. Altarelli,Ellis,Martinelli(’78,’79); Kubar-Andre’,Paige(’79); Harada,Kaneko,Sakai(’79) Hamberg,van Neerven,Matsuura(’91,’02); van Neerven,Zijlstra(’92,’04) Partonic cross section (Unpolarized) LO : NLO : NNLO : Drell,Yan (’70) NNLO LONLO

8. Vogelsang,Weber(’93);Kamal(’96); Contogouris,Kamal,Merebashvili(‘94); Vogelsang(’98) Partonic cross section (Trans. Polarized) LO : NLO : NNLO : Ralston,Soper (’79) not calculated yet LONLONNLO

9. Threshold resummation Sterman(’87);Catani,Trentadue(’89) Sudakov Exponent : Threshold logs become important at large τ

10. NNLL Threshold resummation (cont.) LLNLL for NLL accuracy as well as coefficient function Kodaira,Trentadue( ’ 82)

11. Catani,Mangano,Nason,Trentadue(’96) no factorial growth converge asymptotically define the perturbative content from resummation formalism “Minimal prescription” “ MP ” : define the inverse Mellin contour left of the Landau pole Landau pole singularity at

12. Numerical results : with GRV98 (NLO) PDFs Unpolarized cross section :

13. 1st order exp. ⇔ NLO, 2nd order exp. ⇔ NNLO agree very well convergency seems good, but need rather higher order terms Re-expansion of resummed cross section

14. Far infra-red cut-off soft-gluon resummation formula includes far infra-red region, where the perturbative treatment of QCD may not be justified. may be replaced by non-perturbative approach, power suppressed correction, etc  Apply a explicit cut-off to avoid the double counting between pert. and non-pert. we don ’ t know the NP pert yet ! but tentatively it tells “ how much the far IR region is involved? ”

15. Far infra-red cut-off (graphs) no room for pert. QCD?

16. CERN-WA39 experiment (‘80) Drell-Yan dimuon production by π-Tungsten scattering GRV π-PDF, isospin symmetry and no nuclear effects Resummation(NLL) reproduce experimental data well A hint of soft-gluon large enhancement

17. Double spin asymmetry Model of Transverse PDFs → upper limit of Soffer’s inequality with GRV&GRSV

18. NNLL resummation NNLL resummation is now available, since the recent calculation of three-loop splitting functions by Moch,Vermaseren,Vogt (‘04) Including gives the resummation at NNLL accuracy Vogt(‘01); Catani, de Florian, Grazzini,Nason(’03) by NNLO DY (also C (2) )

19. Good behavior ! : resummation is stable by including NNLL (~10%) even such a low energy cross section. scale ambiguities are also reduced significantly. NNLL resummation (graphs)

20. Drell-Yan dilepton production measurement : double spin asymmetry → transversity distributions fixed target experiment and/or asymmetric collider valence quark distributions in valence region Polarized Antiproton Beam may be available @ GSI Summary We reported on the QCD corrections to the Drell-Yan cross section at GSI Kinematics K-factor is very large, significant threshold logs enhancement, far IR cut-off dependence is serious for fixed target case A TT ~ 30 % is stable under QCD corrections NNLL resummation ~10% gives modest corrections

22. Scale ambiguities Truncation of perturbative series at nth order induce the scale dependence (ambiguity) at n+1th order

23. Scale ambiguities (cont.)

24. PDF rescaling : effective resummation scheme Resummed Cross Section with NLO PDFs → possible double counting of higher-order enhancement between partonic CS and PDF PDF rescaling : effective resummation scheme Sterman,Vogelsang(’99)

25. transparency taken from the talk of F.Rathmann in Spin 2004 (Trieste, ITALY)