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Threshold resummation studies in the Polarized Drell-Yan process at modest collision energies

Threshold resummation studies in the Polarized Drell-Yan process at modest collision energies. Ref. H.Shimizu, G.Sterman, W.Vogelsang, HY, Phys.Rev.D71,114007,2005 (hep-ph/0503270). Drell-Yan Cross section Formula. Factorization. : PDFs. : partonic cross section. parton luminosity.

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Threshold resummation studies in the Polarized Drell-Yan process at modest collision energies

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  1. Threshold resummation studiesin the Polarized Drell-Yan process at modest collision energies Ref.H.Shimizu, G.Sterman, W.Vogelsang, HY, Phys.Rev.D71,114007,2005 (hep-ph/0503270)

  2. Drell-Yan Cross section Formula • Factorization : PDFs : partonic cross section parton luminosity

  3. Higher-order Calculations LO NLO NNLO (unpol.)

  4. threshold log → Threshold logs • large corrections arise from the partonic threshold : due to the energy conservation, only soft-gluon can be emitted. threshold logs need to sum up these logs to all-order of = threshold resummation • going to Mellin-moment space, threshold logs can be summed up to all-order into the Sudakov exponent

  5. LL NLL NNLL … LO 1 NLO NNLO … Threshold resummation Sterman(’87);Catani,Trentadue(’89) • General Formula : Sudakov Exponent • NNLL : 3-loop split. func. gives Moch,Vermaseren,Vogt(’04)

  6. Threshold resummation Kramer,Laenen,Spira(‘98); Catani,de Florian,Grazzini(‘02); Kulesza,Sterman,Vogelsang(’02,’04) • collinear improvement & qg mixing : collinear (non-soft) gluon radiation factor is universal recover full evolution kernel ; reproduce the terms to all orders numerically sizable ( is negative in MS scheme) • employ the “Minimal Prescription” : Catani,Mangano,Nason,Trentadue(’96) define the inverse Mellin contour as the left of the Landau pole

  7. Numerical results resummation up to LL, NLL, NNLL power expansion to • K-factorfor NNLL resummed : 3 ~ 10 • 1st order ⇔ NLO, 2nd order ⇔ NNLO agree very well

  8. Scale ambiguities

  9. PDF uncertainties test PDFs : GRV(NLO), CTEQ(NLO),MRST(NNLO),Alekhin(NNLO) with NNLL+NNLO prediction

  10. FNAL-E772 Experiment D.M. Alde et al., PRL 64, 2479 (‘90) QCD correction : K = 2 ~ 3

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

  12. Talk by M. Stratmann (12/1 2005, KEK)

  13. Talk by M. Stratmann (12/1 2005, KEK)

  14. Summary • At the J-PARC (DY) experiment, • QCD higher-order corrections beyond (NLO,NNLO) • may be required. • qg subprocess contributesto the cross section • and the spin asymmetry. • Contributions from the sea-quark is relatively important. • Unpolarized sea-quark PDF is still uncertain.

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