1

Threshold Resummation Effects

in polarized DY at GSI and J-

PARC

DIS2006 @ EPOCHAL Tsukuba, Tsukuba, JAPAN, 4/20-24(2006)

Ref. H.Shimizu, G.Sterman, W.Vogelsang, HY,

Phys.Rev.D71,114007,2005 (hep-ph/0503270)

Hiroshi Yokoya (Niigata U)

2Introduction

Drell-Yan process :

: parton distribution functions

: partonic cross section ← perturbatively calculable

3J-PARC & GSI-FAIR experiments

New experiments have been proposed

• J-PARC :

• GSI-FAIR (PAX,ASSIA) :

1. polarization may be available → (transversely) polarized Drell-Yan measurements

→ (transversely) polarized parton distributions

2. rather lower-energy collisions → QCD corrections must be important 　

4

Mass Distribution

5

• Factorization Theorem

Drell-Yan cross section formula

6

Hamberg,van Neerven,Matsuura(’91,’02);Harlander,Kilgore(’02)

LO :

NLO :

NNLO :

LO NNLONLO

Status of DY higher order calculations

Altarelli,Ellis,Martinelli(’78,’79);Kubar-Andre’,Paige(’79);Harada,Kaneko,Sakai(’79)

Drell,Yan (’70)

7

LO :

NLO :

NNLO :

Status of DY higher order calculations

8Status of DY higher order calculations

K-factor

NLO/LO

NNLO/LO

9

Large corrections come from the partonic threshold region (z~1)

real emission suppressed by the phase space restriction

imbalance occurs between real and virtual gluon corrections

→ only soft gluon can be emitted

→ soft gluon (eikonal) approximation

to treat these logs up to all orders

(after the cancellation of IR pole)

Threshold logs

10Threshold resummation

Sterman(’87);Catani,Trentadue(’89)

• General Formula : Sudakov Exponent

• First, goto Mellin-moment space :

threshold log →

11

• NNLL : Moch,Vermaseren,Vogt(’04)3-loop split. func. gives

Catani,Mangano,Nason,Trentadue(’96)• employ “Minimal Prescription” :define the inverse Mellin contour as the left of the Landau pole

LL : NLL :

NNLL :

Threshold resummation

• collinear improvement & qg mixing:Kramer,Laenen,Spira(‘98);Catani,de Florian,Grazzini(‘02);Kulesza,Sterman,Vogelsang(’02,’04)

collinear (non-soft) gluon, off-diagonal AD →

12Threshold resummation

LL : NLL :

NNLL :

13

not only the convergence of resummation accuracy (NnLL), but also the convergence of the power expansion of Sudakov exponent to

Convergence

note : “Minimal Prescription” defined so that PT has no factorial growth

power corr. should be added later if required phenomenologicaly

14Double Transverse Spin Asymmetry

Model of Transverse PDFs → upper limit of Soffer’s inequality with GRV&GRSV

Martin,Schafer,Stratmann,Vogelsang

15

Rapidity Distribution

16Rapidity Distribution

Altarelli,Ellis,Martinelli(’79);Kubar,Le Bellac,Meunier,Plaut(’80)

Anastasiou,Dixon,Melnikov,Petriello(’04)

LO :

NLO :

NNLO :

17

• Fourier & Mellin transform

Then,

where

Resummation Formula

Laenen,Sterman(’92);Sterman,Vogelsng(’01);

Mukherjee,Vogelsang(’06)

18

LO :

NLO : in threshold limit (z→1)

In general : ( in threshold limit)

Threshold Limit

mass dist. func.

19

• M dependence in the hard part;

• finally inverse Fourier & Mellin transform : (+ matching with fixed order)

Now resummation !

20Numerical Graphs

rapidity dependent resummed K-factors

(preliminary)

21

become very large at large y

(preliminary)

Numerical Graphs

22Numerical Graphs (Spin asymmetry)

(preliminary)

(to be reported soon)

23Summary

Threshold resummation up to NNLL-NNLO : K=3~10.

really large, but seem to be

controllable!

• QCD corrections to the DY mass distribution 　　 and the rapidity distribution at J-PARC and GSI

• spin asymmetries are rather stable under QCD corrections

• qg subprocess is important for pp collision (J-PARC)