Dilepton production near partonic threshold in transversely polarized p\bar{p} scatterings

1. Title 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) Phys.Rev.D71,114007,2005 (hep-ph/0503270) RADCOR 2005 @ Shonan Village, JAPAN Oct. 2-7, 2005

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

3. Motivation : GSI experiment proposal Polarized Antiproton Beam may be available at the proposed new Proton–Antiproton experiments at GSI. • PAX experiment proposal LoI, hep-ex/0412064,0505054 a)Asymmetric Collider Experiment: polarized antiproton beam and polarized proton beam b) Fixed Target Experiment : 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. Drell-Yan dilepton production @ GSI 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. • Fixed order corrections : LO, NLO, NNLO • Threshold resummation effects : up to NLL (NNLL)

6. Drell-Yan cross section formula • Factorization Theorem

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

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

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

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

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

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

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

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 dimuonproductionby 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 functionsby Moch,Vermaseren,Vogt (‘04) by NNLO DY (also C(2)) Including gives the resummation at NNLL accuracy Vogt(‘01); Catani, de Florian, Grazzini,Nason(’03)

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

20. Summary • Polarized AntiprotonBeam may be available @ GSI fixed target experiment and/or asymmetric collider • Drell-Yan dilepton production measurement: • double spin asymmetry → transversity distributions valence quark distributions in valence region • 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 • ATT ~ 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 Sterman,Vogelsang(’99) ResummedCross Section withNLOPDFs → possible double counting of higher-order enhancement between partonicCS and PDF PDF rescaling : effective resummation scheme

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

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