threshold resummation effects to the drell-yan process at j-parc & gsi

1

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 　

4

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?)

5

• Factorization Theorem

Drell-Yan cross section formula

6

GRV98(NLO)

Parton intensity :

7Status of DY higher order calculations

LO

LO : Drell,Yan (’70)

8

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)

11

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.

21

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 :

23

• 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)