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Soft gluon resummation in transversely polarized Drell-Yan process at small transverse momentum

Soft gluon resummation in transversely polarized Drell-Yan process at small transverse momentum. ― double-spin asymmetries and novel asymptotic formula ―. Kazuhiro Tanaka (Juntendo U). H. Kawamura (RIKEN) J. Kodaira (KEK). NPB777 (’07) 203 and more.

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Soft gluon resummation in transversely polarized Drell-Yan process at small transverse momentum

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  1. Soft gluon resummation in transversely polarized Drell-Yan process at small transverse momentum ―double-spin asymmetries and novel asymptotic formula― Kazuhiro Tanaka (Juntendo U) H. Kawamura (RIKEN) J. Kodaira (KEK) NPB777 (’07) 203and more

  2. Transversely Polarized Drell-Yan （ｔDY) process RHIC,J-PARC,GSI — Transversity • Chiral-odd : unmeasurable in inclusive DIS • First global fit (LO): SIDIS at HERMES, COMPASS + Collins function from BELLE • Anselmino’s talk • Lattice study by QCDSF/UKQCD • tDY data can provide an direct access to QCD corrections

  3. NLO double-spin asymmetries Martin, Schafer, Stratmann, Vogelsang(’99) “sea-quark region” is probed at the scale • double-spin asymmetries at a measured • bulk of dileptons produced at small QT • large perturbative corrections from gluon radiations make QTthe relevant scale

  4. tDY KLN cancellation transversity

  5. Next-to-leading logarithmic (NLL) resummation formula Process-indep.: Kodaira, Trentadue (’82) Davies, Stirling,Webber (’85) Collins, Soper, Sterman ( ‘85)

  6. Kawamura,Kodaira,Shimizu,Tanaka, PTP 115 (’06) 667

  7. IR Landau pole All-order resummation Landau pole Contour deformation Laenen, Sterman, Vogelsang (’00) Kulesza, Sterman, Vogelsang (’02) cut-off at bmax： Collins,Soper,Sterman (’82)

  8. Elaboration of resummation formalism Bozzi, Catani, de Florian, Glazzini (’06) NLL NNLL LL systematic reorganization of the resummed series in the b-space ●all-order resummation is accomplished at the ``partonic level’’ ● NNLL corrections are down by αs uniform accuracy classified by αs ! ●

  9. NLL resummation formula for spin-independent cross section is universal ! Gluon distribution participates ! from Altarelli, Ellis, Greco, Martinelli (’84); Collins, Soper, Sterman (’85) same contour deformation for the b-integration same elaborations in terms of

  10. Nonperturbative inputs x-dep.: Vogelsang et al (’98) Soffer (’95) Transversity distribution μ-dep.: NLO DGLAP evolution Hayashigaki, Kanazawa, Koike (’97) Kumano, Miyama (’97)Vogelsang(’98) Gaussian smearing factor:

  11. Dilepton QT spectrum in tDY Kawamura, Kodaira, Shimizu, Tanaka (’06) pp collision @ RHIC s = 200 GeV, Q = 5GeV, y=2, φ=0 NLL+LO: total (“NLL+Y’’) prediction

  12. 〔Kawamura, Kodaira, Tanaka (’07)〕 flat behavior: universality of soft gluon effects nonuniversal contribution at NLL enhances

  13. @ RHIC (y=2, φ=0)

  14. pp collision@ J-PARC s = 10 GeV, y=0, φ=0 flat behavir due to universal soft gluon effects enhancement mechanism from nonuniversal NLL effects larger asymmetries than the RHIC case moderate-x region

  15. Novel asymptotoic formula Saddle-point formula at the NLL level “degree 0 approximation’’ suggested by CSS (’85)

  16. “very large prefactor” is universal ! gluon distribution decouples ! extension of LL-level saddle point formula by Parisi, Petronzio (’79) to NLL level

  17. Most of soft gluon resummation effets cancel out a part of NLL-level contribution survives unconventional scale associated with saddle point, instead of Clearly demonstrates the enhancement mechanism observed in numerical study NNLL corrections would grow at small-x region probed by RHIC. Useful for direct comparison with experiment

  18. directly probe the valence-quark transversity at GSI For QT unobserved: Barone, Cafarella, Coriano, Guzzi, Ratcliffe (‘05) “threshold resummation’’ at the NNL level Shimizu, Sterman, Yokoya, Vogelsang (’05) Large asymmetries ～ 20-40% QCD corrections are rather small We consider the QCD corrections for QT observed case

  19. @ GSI s = 14.5 GeV, y=0, φ=0 flat behavir due to universal soft gluon effects “valence region” larger asymmetries than RHIC and J-PARC case enhancement mechanism is not significant

  20. unconventional scale does not cause siginificant modification in the valence region probed by GSI NNLL corrections are small Useful for direct comparison with experiment

  21. Transversely Polarized DY at small QT in QCD Summary:

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