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

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

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bulk of dileptons produced at small Q T large perturbative corrections from gluon radiations make Q T the relevant scale NLO double-spin asymmetries Martin, Schafer, Stratmann, Vogelsang(99) sea-quark region is probed at the scale double-spin asymmetries at a measured

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tD Y transversity KLN cancellation

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

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Kawamura,Kodaira,Shimizu,Tanaka, PTP 115 (06) 667

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All-order resummation IR Landau pole Contour deformation Contour deformation Laenen, Sterman, Vogelsang (00) Kulesza, Sterman, Vogelsang (02) Landau pole cut-off at b max Collins,Soper,Sterman (82)

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

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

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

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Dilepton Q T 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

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

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@ RHIC (y=2, φ=0)

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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 casemoderate-x region

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

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

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

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

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

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

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Summary: Transversely Polarized DY at small Q T in QCD

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