1

Threshold resummation studies in the

Polarized Drell-Yan process at modest

collision energies

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

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

2

• Factorization

Drell-Yan Cross section Formula

parton luminosity

: PDFs

: partonic cross section

3

LO NNLO (unpol.)NLO

Higher-order Calculations

4Threshold logs

• large corrections arise from the partonic threshold :

due to the energy conservation, only soft-gluon can be emitted.

threshold logs

• going to Mellin-moment space,

threshold log →

threshold logs can be summed up to all-order into the Sudakov exponent

need to sum up these logs to all-order of

= threshold resummation

5

• General Formula : Sudakov ExponentSterman(’87);Catani,Trentadue(’89)

Threshold resummation

• NNLL :

Moch,Vermaseren,Vogt(’04)

3-loop split. func. gives

…NNLLNLLLL

…

NNLO

NLO

1LO

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( is negative in MS scheme)

Catani,Mangano,Nason,Trentadue(’96)• employ the “Minimal Prescription” :

define the inverse Mellin contour as the left of the Landau pole

Threshold resummation

• collinear improvement & qg mixing :

Kramer,Laenen,Spira(‘98);Catani,de Florian,Grazzini(‘02);Kulesza,Sterman,Vogelsang(’02,’04)

collinear (non-soft) gluon radiation factor is universal

numerically sizable

reproduce the terms to all orders

recover full evolution kernel ;

7Numerical results

resummation up to LL, NLL, NNLL power expansion to

• K-factor for NNLL resummed : 3 ~ 10

• 1st order ⇔ NLO, 2nd order ⇔ NNLO agree very well

8Scale ambiguities

9PDF uncertainties

test PDFs : GRV(NLO), CTEQ(NLO), MRST(NNLO), Alekhin(NNLO)

with NNLL+NNLO prediction

10FNAL-E772 Experiment

QCD correction :

D.M. Alde et al., PRL 64, 2479 (‘90)

K = 2 ~ 3

11Double Transverse Spin Asymmetry

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

12Talk by M. Stratmann (12/1 2005, KEK)

13Talk by M. Stratmann (12/1 2005, KEK)

14Summary

At the J-PARC (DY) experiment,

• QCD higher-order corrections beyond (NLO,NNLO) may be required.

• qg subprocess contributes to the cross section and the spin asymmetry.

• Contributions from the sea-quark is relatively important. • Unpolarized sea-quark PDF is still uncertain.