Hiroyuki Kawamura (RIKEN) 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) K. Tanaka (Juntendo U)

Hiroyuki Kawamura (RIKEN) Transeversly polarized DY process Δ T dσ= H (hard part) x δq(x 1 ) xδq(x 2 )  measurement of PDF :  study of perturbative dynamics : — DGLAP evolution : Δ T P(x) — φdependence : asymmetry  cos(2φ) — transversity : δq(x) ↔ angular mom. sum rule, Soffer’s inequality

Hiroyuki Kawamura (RIKEN)  Double spin asymmetry A TT Q T distribution of dimuon — 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 Q T distribution of dimuon → We calculated spin dep. part of Q T distribution at O(α) (calculation in D-dim. : cumbersome due to φ dependence) ♣ fixed order result : singular at Q T =0 — need improvement : Q T resummation QTQT

Hiroyuki Kawamura (RIKEN) Q T resummation  Q T distribution  soft gluon effects Q T  Q : Recoil by hard gluon emission → Perturbation works well (good convergence) Q T << Q : Soft gluon emission → recoil logs → all order resummation needed Leading logs (LL) Next to Leading Logs (NLL)

Hiroyuki Kawamura (RIKEN) Collins, Soper ’81 Collins, Soper, Sterman ‘85  resummed terms General formula  “Sudakov factor” : b: impact parameter 

Hiroyuki Kawamura (RIKEN)  Final expression of Q_T distribution → resummed terms + fixed order results without double counting  “matching” Q T distribution Q << Q T : resummed part is dominant. Q  Q T : other terms also contribute. : O(α), O(α 2 ) terms in resummed term

Hiroyuki Kawamura (RIKEN) 1-loop results X: singular at q T =0, Y: finite at q T =0

Hiroyuki Kawamura (RIKEN) More on resummation contour deformation prescription 1. Landau pole in inverse Fourier tr. — b integration in complex plane b max b bLbL C1C1 C2C2 suggested by Kulesza, Sterman, Vogelsang ’02 no need to introduce b max reproduce the fixed order results by expansion b max →

Hiroyuki Kawamura (RIKEN) 3. Remove unphysical singularity at b = 0 in S(b,Q) → expS(b,Q) = 1 at b=0 (correct overall normalization) Bozzi, Catani, De Florian, Grazzini, ’05 “unitarity condition” 2. Non-perturbative effects simplest form :intrinsic k T

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

Hiroyuki Kawamura (RIKEN)  s = 200 GeV, Q = 10 GeV, y=0, φ=0  s = 10 GeV, Q =  10 GeV, y*=0, φ=0 RHIC & JPARC g=0.5 GeV

Hiroyuki Kawamura (RIKEN) F NP (b) =exp(-gb 2 ) : g = 0  0.8GeV 2 RHIC & JPARC  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

Hiroyuki Kawamura (RIKEN) Double Spin Asymmetry : RHIC & JPARC Small dependence on NP function Flat in dominant region → PDF information

Hiroyuki Kawamura (RIKEN) Summary  We calculated Q T -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 Q T –distribution of dimuon are obtained at NLL accuracy. — contour deformation method for b-integral — unitarity condition  Numerical results — Q T spectrum of ∆ T σ sensitive of to NP effects. — asymmetry not sensitive to F NP → extraction of δq(x) — larger asymmetry in JPARC region.  Q_T resummation + threshold resummation (joint resummation) & powoer corrections …