Angular decorrelations in Mueller-Navelet jets and DIS(2)

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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