Joint resummation for heavy quark production

We present the joint threshold and recoil resummed transverse momentum distributions for heavy quark hadroproduction, at next-to-leading logarithmic accuracy. We exhibit their dependence on the production channel and the color configurations, and compare t

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002 tcO 21 1v9410150/hp-pe:hviXraFebruary2,20084:14WSPC/INSTRUCTIONFILEjr

InternationalJournalofModernPhysicsA

cWorldScienti cPublishingCompanyJOINTRESUMMATIONFORHEAVYQUARKPRODUCTION

ANDREABANFI

CavendishLaboratory,UniversityofCambridge

MadingleyRoad,CB30HECambridge,UK

ERICLAENEN

NIKHEFTheoryGroup

Kruislaan409,1098SJAmsterdam,TheNetherlands

Wepresentthejointthresholdandrecoilresummedtransversemomentumdistributionsforheavyquarkhadroproduction,atnext-to-leadinglogarithmicaccuracy.Weexhibittheirdependenceontheproductionchannelandthecolorcon gurations,andcomparethesedistributionstoeachotherandtoNLO.Keywords:Resummation;heavyquarkproduction.

1.Jointthresholdandrecoilresummation

Theformalism1,2,3ofhadroniccrosssectionsforthejointresummationofdistri-butionssingularatpartonicthresholdandatzerorecoilhassofarbeenappliedtoZ/Wproduction4,Higgsproduction5,andpromptphotonhadroproduction6.Forthelatter2→2process,theformalismimplementsthenotionthat,inthepresenceofQCDradiation,theactualtransversemomentumproducedbythehard

collisionisnotp Tbutratherp T T/2,withQ Tthetotaltransversemomentumsoftrecoilingpartons. Q

ofunobservedThejoint-resummedpartonicpTspectrumtheformofahardscatteringcrosssectionasafunctionofp′T has

T/2|,con-volutedwithaperturbative,albeitresummedQ

Tdistribution.≡We| p

Thave Qextended7thejointresummationformalismtothepTdistributionofheavyquarksproducedinhadroniccollisions.Keydi erenceswiththeprompt-photoncaseare, rst,thepresenceoftheheavyquarkmassm,preventingasingularityinthehardscatteringfunctionwhenQT=2pTand,second,thepossibilityofmultiplecoloredstatesfortheproducedheavyquarkpair.

2.Resummedheavyquarktransversemomentumspectra

WeconsidertheinclusivepTdistributionofaheavyquarkproducedvia√thestronginteractioninahadron-hadroncollisionatcenterofmass(cm)energy

We present the joint threshold and recoil resummed transverse momentum distributions for heavy quark hadroproduction, at next-to-leading logarithmic accuracy. We exhibit their dependence on the production channel and the color configurations, and compare t

2Ban ,Laenen

higherordercorrectionstothedi erential9crosssectionsforthesepartonicprocesseshavebeencomputedtoNLO8,,10,11.UptocorrectionsO(1/p2T),mayatanyorder12theobservable

bewritteninthefollowingfactorizedformdσAB→Q+X

dp(ξT

a,ξb,αs(µ),pT),

(1)

withdσ ab→Q+X/dpTthepartonicdi erentialcross-section,φa/Aandφb/Bparton

densities,andµthefactorization/renormalizationscale.

Thresholdenhancementsessentiallyinvolvetheenergyofsoftgluons.Inthecontextofthefactorization(1)wede nehadronicandpartonicthresholdbytheconditions

S=4m2Tand s=4m2T,respectively,withmTthetransversemassm2S

,

x 2T

=4T

2

.(3)

Thekinematicallyallowedrangefortheinvariantmasslimitedfrombelowby2mT=2

Qoftheheavyquarkpairin

thishardscatteringis′

Q2

=1.

(4)

Arefactorizationanalysis2leadstothefollowingexpressionfortheobservableinEq.(1)

dσAB→Q+X

dpTd2Q

,

(5)

T

We present the joint threshold and recoil resummed transverse momentum distributions for heavy quark hadroproduction, at next-to-leading logarithmic accuracy. We exhibit their dependence on the production channel and the color configurations, and compare t

Jointresummationforheavyquarkproduction3

whereµ¯isacut-o anddσAB→Q+X

e

i b·Q

T(2π)2

dN

M

(N)ln

1(N)+M 8(N)eCAt

m2 22T

4πS2

N+1

4(m2+|p .

T Q

T/2|2) (6)

Noticeinparticularthelastfactor,whichprovidesakinematiclinkbetweenre-coilandthresholde ects.TheexponentialfunctionsEab2,6aretonext-to-leading

logarithmic(NLL)accuracy

Eab(N,b)= Q

dµ′

gb2,N

¯=NeγE,χ(N,b)

Q(7)

wherethecoe cientsAaandAbcanbefoundelsewhere2,andthefunctionχ(N,b)

ischosentoreproduce4eitherNLLresummedrecoilorthresholddistributionsintheappropiatelimits.Wealsoaddedtotheperturbativeexponentthenon-perturbative(NP)Gaussiansmearingterm gb2,intermsoftheimpactparameterb.Wehavet(N)=

introducedthevariables

Q/Ndµ

′,ReL1+β2β= ,β=Q

π1+β

We present the joint threshold and recoil resummed transverse momentum distributions for heavy quark hadroproduction, at next-to-leading logarithmic accuracy. We exhibit their dependence on the production channel and the color configurations, and compare t

4Ban ,Laenen

Fig.1.

TopquarkpTspectraandK-factorsfortheqq¯channel.

overNLOatpT=800GeV.Jointresummationalmostdoublesthate ect:the

joint-resummedenhancementatlargepTe ectivelyconstitutesasmearingofthethreshold-resummedpTspectrumbyaresummedrecoilfunction.Acknowledgments

ThisworkwassupportedbytheNetherlandsFoundationforFundamentalResearchofMatter(FOM)andtheNationalOrganizationforScienti cResearch(NWO).References

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