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.
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