Dilepton production near partonic threshold in transversely polarized p\bar{p} scatterings

• H. Shimizu (Hiroshima U, KEK)

• G. Sterman (SUNY)

• W. Vogelsang (BNL, RBRC)

• H. Yokoya (Niigata U)

RADCOR 2005 @ Shonan Village, JAPAN Oct. 2-7, 2005

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

Title

• Introduction

• Polarized Antiproton experiments @

GSI

• Drell-Yan process and QCD corrections

• Fixed order calculation

• Threshold resummation

• Far IR cut-off

• Numerical results

• NNLL resummation

• Summary

Outline

Polarized Antiproton Beam may be available at the proposed new Proton–Antiproton experiments at GSI.

Motivation : GSI experiment proposal

• PAX experiment proposal LoI, hep-ex/0412064,0505054

a) Asymmetric Collider Experiment :

b) Fixed Target Experiment :

polarized antiproton beam and polarized proton beam

polarized antiproton beam with polarized hydrogen gas target

Drell-Yan dilepton production :

measurement of double transverse spin asymmetry

→ measurement of the transversely polarized PDF :

twist-2 distribution functions, chiral-odd, no gluon function, no measurement so far (first indication by HERMES, first measurement by RHIC?)

advantage for the GSI experiments :

→ both valence quark contribution

→ large asymmetry is expected→ large x ～ 0.5 region will be probed

valence quark structure of trans. pol. nucleon

So far, only the tree level estimations have been done (includes J/ψ production)

Anselmino,Barone,Drago,Nikolaev (’04)Efremov,Goeke,Schweitzer (’04)

We examined the first QCD corrections to the Drell-Yan cross section

for the GSI experiment kinematics.

Drell-Yan dilepton production @ GSI

• Fixed order corrections : LO, NLO, NNLO

• Threshold resummation effects : up to NLL (NNLL)

• Factorization Theorem

Drell-Yan cross section formula

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

Hamberg,van Neerven,Matsuura(’91,’02);van Neerven,Zijlstra(’92,’04)

Partonic cross section (Unpolarized)

LO :

NLO :

NNLO :

Drell,Yan (’70)

NNLOLO NLO

Vogelsang,Weber(’93);Kamal(’96);Contogouris,Kamal,Merebashvili(‘94);Vogelsang(’98)

Partonic cross section (Trans. Polarized)

LO :

NLO :

NNLO :

Ralston,Soper (’79)

not calculated yet

LO NLO NNLO

Threshold resummation Sterman(’87);Catani,Trentadue(’89)

Sudakov Exponent :

Threshold logs become important at large τ

NNLL

Threshold resummation (cont.)

LL NLL

• for NLL accuracy

as well as coefficient function

Kodaira,Trentadue(’82)

Catani,Mangano,Nason,Trentadue(’96)

• no factorial growth

• converge asymptotically

• define the perturbative content from resummation formalism

“Minimal prescription”

“MP” : define the inverse Mellin contour left of the Landau pole

Landau pole singularity at

Numerical results :

with GRV98 (NLO) PDFs

Unpolarized cross section :

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

• convergency seems good, but need rather higher order

terms

Re-expansion of resummed cross section

Far infra-red cut-off

soft-gluon resummation formula includes far infra-red region, where the perturbative treatment of QCD may not be justified.

may be replaced by non-perturbative approach, power suppressed correction, etc

Apply a explicit cut-off to avoid the double counting between pert. and non-pert.

we don’t know the NP pert yet !

but tentatively it tells “how much the far IR region is

involved?”

Far infra-red cut-off (graphs)

no room for pert. QCD?

CERN-WA39 experiment (‘80)

Drell-Yan dimuon production by π-Tungsten scattering

GRV π-PDF, isospin symmetry and no nuclear effects

Resummation(NLL) reproduce experimental data well

A hint of soft-gluon large enhancement

Double spin asymmetry

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

NNLL resummation

NNLL resummation is now available, since the recent calculation

of three-loop splitting functions by Moch,Vermaseren,Vogt (‘04)

Including

gives the resummation at NNLL accuracy

Vogt(‘01); Catani, de Florian, Grazzini,Nason(’03)

by NNLO DY (also C(2))

Good behavior ! : resummation is stable by including NNLL (~10%) even such a low energy cross section.

scale ambiguities are also reduced significantly.

NNLL resummation (graphs)

• Drell-Yan dilepton production measurement :

double spin asymmetry → transversity distributions

fixed target experiment and/or asymmetric collider

valence quark distributions in valence region

• Polarized Antiproton Beam may be available @ GSI

Summary

• We reported on the QCD corrections to the Drell-Yan cross section at GSI Kinematics

K-factor is very large, significant threshold logs enhancement,far IR cut-off dependence is serious for fixed target case

• ATT ~ 30 % is stable under QCD corrections

• NNLL resummation ~10% gives modest corrections

Scale ambiguities

• Truncation of perturbative series at nth order induce the scale dependence (ambiguity) at n+1th order

Scale ambiguities (cont.)

PDF rescaling : effective resummation scheme

Resummed Cross Section with NLO PDFs

→ possible double counting of higher-order enhancement between

partonic CS and PDF

PDF rescaling : effective resummation scheme

Sterman,Vogelsang(’99)

transparency taken from the talk of F.Rathmann in Spin 2004 (Trieste, ITALY)

transparency taken from the talk of F.Rathmann in Spin 2004 (Trieste, ITALY)