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
7
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