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

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) Phys.Rev.D71,114007,2005 (hep-ph/0503270) APS/JPS Joint Meeting @ Kapalua, Hawaii 2005.9.21

2. Introduction • Polarized Antiprotonexperiments @ GSI • QCD correction to the Drell-Yan process • Fixed order calculation • Threshold resummation • Far IR cut-off • Numerical results • Summary

3. Polarized Antiproton Beam @ GSI Polarized Antiproton Beam may be available at the proposed Proton – Anti-Proton 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. We report on studies of pQCD correction to the Drell-Yan cross section for GSI p\bar{p} kinematics • Cross Section Formula

6. Partonic Cross Section (unpolarized) LO NLO NNLO 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)

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

8. Threshold Resummation Sterman(’87);Catani,Trentadue(’89) only soft gluon can be emitted (partonic threshold) logarithmic correction, as remnant of IR singularity, become important kth order sum these terms up to all orders → Threshold Resummation givingSudakov Exponent • Mellin-moments space : threshold logs (N → large) Sudakov Exponent :

9. Integral in the exponent is evaluated as functions of • and re-arranged again as the series of alpha_s and lnN. LL NLL NNLL NLL : LL : • For the numerical evaluation, we employ “Minimal Prescription” Catani,Mangano,Nason,Trentadue(’96) • no factorial growth • converge asymptotically • define the perturbative content • from resummation formalism

10. Unpolarized cross section : with GRV98 (NLO) PDFs K-factor become order 101 (103) at the large M !!

11. Far Infrared cut-off soft-gluon resummation formula includes far-infrared region, where the perturbative treatment of QCD may not be justified. may be replaced by non-perturbative approach, power suppressed correction, etc our study simplycut-off the small kT region

12. Far-infrared cut-off dependence K-factor :

13. Double Spin Asymmetry : Model of Transverse PDFs → upper limit of Soffer’s inequality with GRV&GRSV

14. SUMMARY • Polarized Anti-proton Beam may be available @ GSI PAX experiment proposal : fixed target experiment and/or asymmetric collider • dilepton production process: • double spin asymmetry → transversity distributions valence quark distributions in valence region • QCD corrections to the Drell-Yan process at GSI 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

16. New report on the NNLL resummation NNLL resummation is now available, since the historical calculation of three-loop splitting functionsby Moch,Vermaseren,Vogt (‘04) Including gives the resummation at NNLL accuracy Vogt(‘01); Catani et al.(’03)

17. NNLL resummation : unpolarized cross section : effect is at most 15% Good behavior ! : resummation is stable by including NNLL, even such a low energy collision cross section. scale ambiguity is also reduced significantly.

18. Re-expansion of resummed cross section by order by order of αs • 1st order exp.⇔NLO,2nd order exp.⇔NNLO agree very well • Convergency seems good, but need more higher order term

19. Renormalization/Factorization scale dependence : • truncation of perturbative series at nth order induces • scale dependence (ambiguity) at n+1th order

20. Renormalization/Factorization scale dependence : see also pion production@GSIMukherjee,Stratmann,Vogelsang (’05)

21. CERN-WA39 Experiment (‘80) Drell-Yan dimuonproductionby π-Tungsten scattering GRV π-PDF, Isospin symmetry and no nuclear effects Resummation results reproduce experimental data well A hint of soft-gluon large enhancement

22. PDF rescaling : effective resummation scheme of PDF Sterman,Vogelsang(’99) we calculate ResummedCross Section with“NLO”PDFs → possible double counting of higher-order enhancement between partonicCS and PDF PDF rescaling :

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

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