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QCD prediction for the dimuon Q T spectrum in transversely polarized Drell-Yan process

QCD prediction for the dimuon Q T spectrum in transversely polarized Drell-Yan process. Hiroyuki Kawamura (RIKEN). Dec. 1, 2005 Hadron Physics at JPARC KEK. work in common with J. Kodaira (KEK) H. Shimizu (KEK)

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QCD prediction for the dimuon Q T spectrum in transversely polarized Drell-Yan process

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  1. QCD prediction for the dimuon QT spectrumin transversely polarized Drell-Yan process Hiroyuki Kawamura (RIKEN) Dec. 1, 2005 Hadron Physics at JPARC KEK work in common with J. Kodaira (KEK) H. Shimizu (KEK) K. Tanaka (Juntendo U)

  2. Transeversly polarized DY process ΔTdσ= H (hard part) x δq(x1) xδq(x2) • measurement of PDF : — transversity :δq(x) ↔ angular mom. sum rule, Soffer’s inequality • study of perturbative dynamics : — DGLAP evolution :ΔTP(x) — φdependence :asymmetry  cos(2φ)

  3. QT distribution of dimuon • Double spin asymmetry ATT — very small (a few %) at RHIC : PP collider Martin,Shäfer,Stratmann,Vogelsang (’99) — can be very large at GSI : PP-bar fixed target Shimizu,Yokoya,Stratmann,Vogelsang (‘05) • More informtion from QT distribution of dimuon → We calculated spin dep. part of QT distribution at O(α) (calculation in D-dim. : cumbersome due to φ dependence) ♣ fixed order result : singular at QT=0 — need improvement :QT resummation QT

  4. QT resummation • QT distributionsoft gluon effects • QT  Q : Recoil by hard gluon emission • → Perturbation works well • (good convergence) • QT << Q : Soft gluon emission • → recoil logs • → all order resummation needed Leading logs (LL) Next to Leading Logs (NLL)

  5. General formula Collins, Soper ’81 Collins, Soper, Sterman ‘85 • resummed terms  b: impact parameter “Sudakov factor” : 

  6. QT distribution • Final expression of Q_T distribution Q << QT : resummed part is dominant. Q  QT : other terms also contribute. → resummed terms + fixed order results without double counting  “matching” : O(α), O(α2) terms in resummed term

  7. 1-loop results X: singular at qT =0, Y: finite at qT =0

  8. More on resummation 1. Landau pole in inverse Fourier tr. contour deformation prescription —b integration in complex plane suggested by Kulesza, Sterman, Vogelsang ’02 b C1 bmax bL bmax C2 → • no need to introduce bmax • reproduce the fixed order results by expansion

  9. 2. Non-perturbative effects simplest form : intrinsic kT 3.Remove unphysical singularity at b = 0 in S(b,Q) → expS(b,Q) = 1 at b=0 (correct overall normalization) “unitarity condition” Bozzi, Catani, De Florian, Grazzini, ’05

  10. Numerical studies INPUTS : 1. PDF δq(x) unknown − a model saturating Soffer’s inequality at Q0 (Martin, Shäfer, Stratmannn,Vogelsang ‘98) 2. Non-perturbative function free parameter g = 0  0.8 GeV2

  11. RHIC & JPARC g=0.5 GeV s = 200 GeV, Q = 10 GeV, y=0, φ=0 s = 10 GeV, Q= 10 GeV, y*=0, φ=0

  12. RHIC & JPARC FNP(b)=exp(-gb2) : g = 0  0.8GeV2 s = 200 GeV, Q = 10 GeV, y=0, φ=0 s = 10 GeV, Q= 10 GeV, y*=0, φ=0 more sensitive to NP function — information of NP effects

  13. Double Spin Asymmetry : RHIC & JPARC • Small dependence on NP function • Flat in dominant region • → PDF information

  14. Summary • We calculated QT -distribution of DY pair in tDY process at O(α) in MS-bar scheme. • The soft gluon effects are included by all order resummation and the correct expressions of QT –distribution of dimuon are obtained at NLL accuracy. — contour deformation method for b-integral — unitarity condition • Numerical results — QT spectrum of ∆Tσsensitive of to NP effects. — asymmetry not sensitive to FNP→ extraction of δq(x) — larger asymmetry in JPARC region. • Q_T resummation + threshold resummation (joint resummation) & powoer corrections …

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