QCD corrections to the dilepton production near partonic threshold in pp and ppbar collisions

1. QCD corrections to the dilepton production near partonic threshold in pp and ppbar collisions • 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) J-PARC Workshop @ KEK, JAPAN Nov.30- Dec.2, 2005

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

3. Observables • Cross section : mass distribution → simplest and basic : rapidity distribution → x1,x2 distributions : qT-distribution → (hard) gluon radiations see next talk by H.Kawamura • Asymmetry (Ratio) Target (beam) polarization : single spin asymmetry → twist-3, intrinsic-kT double spin asymmetry → twist-2 pol. PDFs Nuclear dependence : → nuclear effects

4. Measurements of DY at J-PARC (GSI) gives : • new information of the PDFs : flavor structure, nuclear effects, polarized PDFs,,, • precise confirmation of the pQCD predictions : scaling violation (i.e. evolution), qT-distribution, absolute cross section,,, • indication ofthe NP corrections (power-suppressed, ISI,,) : ambiguity of PT, renormalon,,, OPE cannot be applied to DY process

5. In this talk, I would examine a phenomenology of the pQCD corrections to the DY X-sec. (fixed order calculation, threshold resummation,,) order (how large?), convergency and ambiguity • Keypoints :

6. Drell-Yan cross section formula • Factorization Theorem

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

20. Renormalization scale ambiguity resum. f.o.

21. Factorization scale ambiguity resum. f.o.

22. Summary ① pQCD corrections to DY process are given for the J-PARC energy K= 3~10, good convergency, scale ambiguities are reduced • Resummation is a powerful tool to know the insight of pQCD • corrections at very higher order, and also the structure of • factorizable hadronic interaction • Resummation also as a tool to find the hint of non-pert. effects • (analytically and/or phenomenologically), • and the connection between pert. and non-pert. regime

24. 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

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

26. 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? ”

27. Far infra-red cut-off

28. Far infra-red cut-off

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

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

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

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

33. Spin asymmetry e.g. Model of Transverse PDFs → upper limit of Soffer’s inequality with GRV&GRSV

34. Parton intensity : GRV98(NLO)

35. Matching to fixed order calc. note : differences only come from the parton intensity

36. 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