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Threshold Resummation Effects to the Drell-Yan process at J-PARC & GSI

• H. Shimizu (Hiroshima U,

KEK)

• G. Sterman (SUNY)

• W. Vogelsang (BNL, RBRC)

• H. Yokoya (Niigata U)

KEK 研究会「 QCD とハドロン物理の新展開」

KEK 2006 年 2 月 27 日 ~ 3 月 1 日

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

2Introduction

Drell-Yan process :

: parton distribution functions

: partonic cross section ← perturbatively calculable

3J-PARC & GSI-FAIR experiments

New experiments are 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 should be important 　

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Measurements of DY at J-PARC & GSI gives :

• new information of the PDFs :flavor structure, nuclear effects,

polarized PDFs, higher-twist,,,

• precise confirmation of the pQCD predictions :

scaling violation (i.e. evolution),

qT-distribution, absolute cross section,,,

• indication of the N.P. corrections (power-suppressed, I.S.I.,,) :

ambiguity of PT, renormalon,,,

(beyond pQCD? rest of pQCD?)

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• Factorization Theorem

Drell-Yan cross section formula

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GRV98(NLO)

Parton intensity :

7Status of DY higher order calculations

LO

LO : Drell,Yan (’70)

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virtual : real:

LO NLO

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

LO :

NLO :

Drell,Yan (’70)

qg :

Status of DY higher order calculations

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LO NLO

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

LO :

NLO :

Drell,Yan (’70)

Status of DY higher order calculations

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Hamberg,van Neerven,Matsuura(’91,’02);Harlander, Kilgore(’02)Anastasiou,Dixon,Melnikov,Petriello(Rapidity,’04);

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)

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LO :

NLO :

NNLO :

Status of DY higher order calculations

12Status of DY higher order calculations

K-factor

NLO/LO

NNLO/LO

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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

14Threshold resummation

Sterman(’87);Catani,Trentadue(’89)

• General Formula : Sudakov Exponent

• First, goto Mellin-moment space :

threshold log →

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LL : NLL :

NNLL :

• NNLL : Moch,Vermaseren,Vogt(’04)

Threshold resummation

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

may not complete : NNLO PDFs (we use GRV(NLO)),

precise determination of at NNLO

• collinear improvement : Kramer,Laenen,Spira(‘98),,,

universal collinear (non-soft) gluon →

16Threshold resummation

LL : NLL :

NNLL :

17Threshold resummation

LL : NLL :

NNLL :

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

Convergency

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

power corr. should be added later if required phenomenologicaly

19Renormalization scale ambiguity

f.o.

resum.

20Factorization scale ambiguity

f.o.

resum.

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LL :

NLL+NLO :

NNLL+NNLO :

Matching to fixed order calc.

relevant for all phase space regions

qg sub-process contributions

22GSI : Cross section

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 very higher order

terms

GSI : K-factors

24GSI : Spin Asymmetry

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

25Data in the past

McGaughey,Moss,Peng(’99)

consistent with NLO

CERN-NA3,FNAL-E605,E772

26FNAL-E772 (’90)

DATA / NLO ~ 0.641

W.J.Stirling,M.R.Whalley (’93)

27FNAL-E772 (’90)

DATA consistent with LO (!?)

KNLL = 3 ~ 5

28CERN-WA39 experiment (‘80)

Drell-Yan dimuon production by π-Tungsten scattering

GRV π-PDF, isospin symmetry and no nuclear effects

NLL reproduce data best

29Summary

② pQCD corrections to DY process are estimated for J-PARC & GSI. 　

K=3~10, good convergency, scale ambiguities are reduced

③ Resummation is a powerful tool to know the insight of pQCD

corrections at very higher order, and also a tool to find a hint

of non-pert. effects.

① New experiments of (polarized) Drell-Yan process are proposed at J-PARC & GSI-FAIR.

new infroamtion of (polarized) PDFs, novel distributions,,

lower scale collision → QCD corrections is important,

30Collinear improvement

Taking into account the universal collinear (non-soft) gluon radiation

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

• numerically sizable effects

• correctly re-produce the terms to all orders

• re-cover the full evolution kernel by

• re-arrange the exponent

31Collinear improvement

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

1st order expansion ⇔ NLO

2nd order expansion ⇔ NNLO

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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, however, tentatively

it tells “ how much the far-IR region is

involved? ”

Far infra-red cut-off

33Far infra-red cut-off

34Far infra-red cut-off

35PDF 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)