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Hiroyuki Kawamura (RIKEN) QCD prediction for the dimuon Q T spectrum in transversely polarized Drell-Yan process Hiroyuki Kawamura (RIKEN) Dec. 1, 2005.

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Presentation on theme: "Hiroyuki Kawamura (RIKEN) QCD prediction for the dimuon Q T spectrum in transversely polarized Drell-Yan process Hiroyuki Kawamura (RIKEN) Dec. 1, 2005."— Presentation transcript:

1 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)

2 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

3 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

4 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)

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

6 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

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

8 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 →

9 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

10 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

11 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

12 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

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

14 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 …


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