Threshold Resummation Effects to the Drell-Yan process at J-PARC & GSI

1. Threshold Resummation Effects to the Drell-Yan process at J-PARC & GSI • H. Shimizu(Hiroshima U, KEK) • G. Sterman(SUNY) • W. Vogelsang(BNL, RBRC) • H. Yokoya(Niigata U) ref. Phys.Rev.D71,114007,2005 (hep-ph/0503270) KEK研究会「QCDとハドロン物理の新展開」 KEK 2006年2月27日 ~ 3月1日

2. Introduction Drell-Yan process : : parton distribution functions : partonic cross section ← perturbatively calculable

3. J-PARC & GSI-FAIR experiments New experiments are proposed • J-PARC : • GSI-FAIR (PAX,ASSIA) : • polarization may be available • → (transversely) polarized Drell-Yan measurements • → (transversely) polarized parton distributions • rather lower-energy collisions • → QCD corrections should be important

4. Measurements of DY at J-PARC & GSI gives : • new information of the PDFs : flavor structure, nuclear effects, polarized PDFs, higher-twist,,, • precise confirmation of the pQCD predictions : scaling violation (i.e. evolution), qT-distribution, absolute cross section,,, • indication ofthe N.P. corrections (power-suppressed, I.S.I.,,) : ambiguity of PT, renormalon,,, (beyond pQCD? rest of pQCD?)

5. Drell-Yan cross section formula • Factorization Theorem

6. Parton intensity : GRV98(NLO)

7. Status of DY higher order calculations LO LO : Drell,Yan (’70)

8. Status of DY higher order calculations LO NLO LO : Drell,Yan (’70) Altarelli,Ellis,Martinelli(’78,’79); Kubar-Andre’,Paige(’79); Harada,Kaneko,Sakai(’79) NLO : virtual : real: qg :

9. Status of DY higher order calculations LO NLO LO : Drell,Yan (’70) Altarelli,Ellis,Martinelli(’78,’79); Kubar-Andre’,Paige(’79); Harada,Kaneko,Sakai(’79) NLO :

10. Status of DY higher order calculations 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); Harlander, Kilgore(’02) Anastasiou,Dixon,Melnikov,Petriello(Rapidity,’04);

11. Status of DY higher order calculations LO : NLO : NNLO :

12. Status of DY higher order calculations K-factor NLO/LO NNLO/LO

13. Threshold logs Large corrections come from the partonic threshold region (z~1) • real emission suppressed by the phase space restriction • imbalance occurs between real and virtual gluon corrections (after the cancellation of IR pole) → only soft gluon can be emitted → soft gluon (eikonal) approximation to treat these logs up to all orders

14. threshold log → Threshold resummation Sterman(’87);Catani,Trentadue(’89) • First, goto Mellin-moment space : • General Formula : Sudakov Exponent

15. Threshold resummation LL : NLL: NNLL: • NNLL : 3-loop split. func. gives Moch,Vermaseren,Vogt(’04) may not complete : NNLO PDFs (we use GRV(NLO)), precise determination of at NNLO • collinear improvement : Kramer,Laenen,Spira(‘98),,, universal collinear (non-soft) gluon → • employ “Minimal Prescription” : Catani,Mangano,Nason,Trentadue(’96) define the inverse Mellin contour as the left of the Landau pole

16. Threshold resummation LL : NLL: NNLL:

17. Threshold resummation LL : NLL: NNLL:

18. Convergency not only the convergency of resummation accuracy (NnLL), but also the convergency of the power expansion of Sudakov exponent to note : “Minimal Prescription” defined so that PT has no factorial growth power corr. should be added later if required phenomenologicaly

19. Renormalization scale ambiguity resum. f.o.

20. Factorization scale ambiguity resum. f.o.

21. Matching to fixed order calc. • relevant for all phase space regions • qg sub-process contributions LL : NLL+NLO: NNLL+NNLO:

22. GSI : Cross section Unpolarized cross section : with GRV98 (NLO) PDFs

23. GSI : K-factors • 1st order exp. ⇔ NLO,2nd order exp. ⇔ NNLOagree very well • convergency seems good, but need very higher order terms

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

25. Data in the past CERN-NA3,FNAL-E605,E772 McGaughey,Moss,Peng(’99) consistent with NLO

26. FNAL-E772 (’90) DATA / NLO ~ 0.641 W.J.Stirling,M.R.Whalley (’93)

27. FNAL-E772 (’90) DATA consistent with LO (!?) KNLL = 3 ~ 5

28. CERN-WA39 experiment (‘80) Drell-Yan dimuonproductionby π-Tungsten scattering GRV π-PDF, isospin symmetry and no nuclear effects NLL reproduce data best

29. Summary ① New experiments of (polarized) Drell-Yan process are proposed at J-PARC & GSI-FAIR. new infroamtion of (polarized) PDFs, novel distributions,, lower scale collision → QCD corrections is important, ② pQCD corrections to DY process are estimated for J-PARC & GSI. K=3~10, good convergency, scale ambiguities are reduced ③ Resummation is a powerful tool to know the insight of pQCD corrections at very higher order, and also a tool to find a hint of non-pert. effects.

30. Collinear improvement Kramer,Laenen,Spira(‘98);Catani,de Florian,Grazzini(‘02); Kulesza,Sterman,Vogelsang(’02,’04) Taking into account the universal collinear (non-soft) gluon radiation • re-arrangethe exponent • re-cover the full evolution kernel by • correctly re-produce the terms to all orders • numerically sizable effects

31. Collinear improvement Kramer,Laenen,Spira(‘98);Catani,de Florian,Grazzini(‘02); Kulesza,Sterman,Vogelsang(’02,’04) 1st order expansion ⇔ NLO 2nd order expansion ⇔ NNLO

32. 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, however, tentatively it tells “ how much the far-IR region is involved? ”

33. Far infra-red cut-off

34. Far infra-red cut-off

35. 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