Angular decorrelations in Mueller-Navelet jets and DIS

We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbative con

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002 tcO 8 ]hp-eph[ 1v8741.017:0viXraAngulardecorrelationsinMueller-NaveletjetsandDIS

Agust´ nSabioVera1 ,FlorianSchwennsen2

1PhysicsDepartment,TheoryDivision,CERN,CH–1211Geneva23,Switzerland,2II.Institutf¨urTheoretischePhysik,Universit¨atHamburg,LuruperChaussee149D–22761Hamburg,Germany.

Abstract

WediscusstheazimuthalangledecorrelationofMueller–NaveletjetsathadroncollidersandforwardjetsinDeepInelasticScatteringwithintheBFKLframeworkwithaNLOkernel.Westresstheneedofcollinearimprovementstoobtaingoodperturbativeconvergence.WeprovideestimatesofthesedecorrelationsforlargerapiditydifferencesattheTevatron,LHCandHERA.

1BFKLcrosssections

Inthiscontributionwediscusstheresultsrecentlyobtainedin[1]whereazimuthalanglecorre-lationsinMueller–Naveletjets[2]andforwardjetsatHERAusingtheBalitsky–Fadin–Kuraev–Lipatov(BFKL)equationinthenext–to–leading(NLO)approximation[3]wereinvestigated(relatedworkscanbefoundin[4]).InthissectionwefocusonnormalizeddifferentialcrosssectionsforMueller–Naveletjets,whicharequiteinsensitivetopartondistributionfunctions.Thisjusti estheuseofpartoniccrosssectionswhichcanbewrittenas

dσ

1

ωY2

2πi

efω( q1, q2),

(1)

whereα¯s=αsNc/π, q1,2arethetransversemomentaofthetaggedjets,andYtheirrelative

rapidity.TheGreen’sfunctioncarriesthebulkoftheYdependenceandisthesolutiontotheNLOBFKLequation,

basisincluding

ω α¯sK 0 α¯2sK 1f ω= 1,

whichactsonthetheazimuthalangle,

(2)

i.e.,

q|ν,n =

1 22

q iν 1

α¯2s

inφdφ

=

π2p21p22n=

∞e ∞

Cn(Y),

(4)

We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbative con

where

Cn(Y)=

1

1

p22

iν

eχ(|n|,

1

χ0(n,γ)8Nc

2

in[6].Thefullcrosssectiononlydependsonthen=0component,

σ =

π3α¯2s

2p21p2

ψ1 γ+n

MSscheme,canbefound

C0(Y).

(7)

Theaverageofthecosineoftheazimuthalangletimesanintegerprojectsoutthecontributionfromeachoftheseangularcomponents:

cos(mφ)

Thenormalizeddifferentialcrosssectionis

1dφ

=

1

C0(Y)

=

1

Cn(Y)

(8)

2

2+ω

+

ω

χ0(n,γ)8Nc

2

+ψ′1 γ+

|n|

2

+Bn

,(10)

whereAnandBnarecollinearcoef cients[1].Afterthiscollinearresummationourobservableshaveagoodphysicalbehaviorandareindependentoftherenormalizationscheme.ItisveryimportanttoremarkthattheasymptoticbehavioroftheBFKLresummationisconvergentfornonzeroconformalspins.Inthissensetheidealdistributionstoinvestigateexperimentallyarethoseoftheform cos(mφ) / cos(nφ) withm,n=0,wewillseethatinthiscasethedifferencebetweentheLOandhigherordersresultsissmall.

We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbative con

2PhenomenologyforMueller–Naveletjets

TheD [8]collaborationanalyzeddataforMueller–Naveletjetsat

√

<cosφ>

=

C2

s=1.8TeVforBFKLatLO

(solid)andNLO(dashed).Theresultsfromtheresummationpresentedinthetextareshownaswell(dash–dotted).

InFig.1wecomparetheTevatrondatafor cosφ =C1/C0withourLO,NLOandresummedpredictions.ForTevatron’scuts,wherethetransversemomentumforonejetis20GeVandfortheother50GeV,theNLOcalculationisinstableunderrenormalizationschemechanges.Theconvergenceofourobservablesispoorwheneverthecoef cientassociatedtozeroconformalspin,C0,isinvolved.Ifweeliminatethiscoef cientbycalculatingtheratiosde nedinEq.(8)thenthepredictionsareverystable,seeFig.1.

ThefullangulardependencestudiedattheTevatronbytheD collaborationwaspublishedin[8].InFig.2wecomparethismeasurementwiththepredictionsobtainedinourapproach.ForthedifferentialcrosssectionwealsomakepredictionsfortheLHCatlargerYinFig.3.Weestimatedseveraluncertaintiesinourapproachwhicharerepresentedbygraybands.

We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbative con

dNφ

dNφdφ

inapp¯colliderat

√

dσσ

We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbative con

3ForwardjetsatHERA

InthissectionweapplytheBFKLformalismtopredictthedecorrelationinazimuthalanglebetweentheelectronandaforwardjetassociatedtotheprotoninDeepInelasticScattering(DIS).Whentheseparationinrapidityspacebetweenthescatteredelectronandtheforwardjetislargeandthetransversemomentumofthejetissimilartothevirtualityofthephotonresolvingthehadron,thenthedominanttermsareofBFKLtype.ThisprocessissimilartothatofMueller–Naveletjets,theonlydifferencebeingthesubstitutionofonejetvertexbytheelectronvertexdescribingthecouplingoftheelectrontotheBFKLgluonGreen’sfunctionviaaquark–antiquarkpair.AzimuthalanglesinforwardjetswerestudiedatLOin[10].WeimprovedtheircalculationbyconsideringtheNLOBFKLkernel.

IntheproductionofaforwardjetinDISitisnecessarytoextractapartonwithalargelongitudinalmomentumfractionxFJfromtheproton.Whenthejetischaracterizedbyahardscaleitispossibletouseconventionalcollinearfactorizationtodescribetheprocessandthejetproductionratemaybewrittenas

σ(s)=

dxFJfe (xFJ,µ2σ( s),F)

(11)

withσ ( s)denotingthepartoniccrosssection,andtheeffectivepartondensity[11]being

2

fe (x,µ2F)=G(x,µF)+

4

dYdφ

with

Cn(Y)=

π2α¯2s

=C0(Y)+C2(Y)cos2φ,

(13)

ys

,(14)

wheretheindexintheintegralsignreferstothecuts

20GeV2<Q2<100GeV2,0.05<y<0.7,5·10 3>xBj>4·10 4.

(15)

TheintegrationoverthelongitudinalmomentumfractionxFJoftheforwardjetinvolvesadelta

function xingtherapidityY=lnxFJ/xBjandB(n)isacomplicatedfunctionwhichcanbefoundin[1].

Sincethestructureoftheelectronvertexsinglesoutthecomponentswithconformalspin0and2,thenumberofobservablesrelatedtotheazimuthalangledependenceislimitedwhencomparedtotheMueller–Naveletcase.Themostrelevantobservableisthedependenceoftheaverage<cos2φ>=C2/C0withtherapiditydifferencebetweentheforwardjetandoutgoinglepton.Itisnaturaltoexpectthattheforwardjetwillbemoredecorrelatedfromtheleptonicsys-temastherapiditydifferenceislargersincethephasespaceforfurthergluonemissionopensup.

We discuss the azimuthal angle decorrelation of Mueller-Navelet jets at hadron colliders and forward jets in Deep Inelastic Scattering within the BFKL framework with a NLO kernel. We stress the need of collinear improvements to obtain good perturbative con

ThisisindeedwhatweobserveinournumericalresultsshowninFig.4.We nd

similarresults

totheMueller–Naveletjets

casewhere

the

most

reliable

calculation

is

thatwith

a

collinearly–improvedkernel.Themaineffectofthehigherordercorrectionsistoincreasetheazimuthalanglecorrelationforagivenrapiditydifference,whilekeepingthedecreaseofthecorrelationasYgrows.

.08.06.04.02

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