Dilepton production near partonic threshold in transversely polarized p\bar{p} scatterings
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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
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• 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
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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
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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
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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)
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• Factorization Theorem
Drell-Yan cross section formula
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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
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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
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Threshold resummation Sterman(’87);Catani,Trentadue(’89)
Sudakov Exponent :
Threshold logs become important at large τ
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NNLL
Threshold resummation (cont.)
LL NLL
• for NLL accuracy
as well as coefficient function
Kodaira,Trentadue(’82)
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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
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Numerical results :
with GRV98 (NLO) PDFs
Unpolarized cross section :
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• 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
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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?”
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Far infra-red cut-off (graphs)
no room for pert. QCD?
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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
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Double spin asymmetry
Model of Transverse PDFs → upper limit of Soffer’s inequality with GRV&GRSV
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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))
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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)
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• 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
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Scale ambiguities
• Truncation of perturbative series at nth order induce the scale dependence (ambiguity) at n+1th order
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Scale ambiguities (cont.)
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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)
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transparency taken from the talk of F.Rathmann in Spin 2004 (Trieste, ITALY)
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transparency taken from the talk of F.Rathmann in Spin 2004 (Trieste, ITALY)
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