Full jet tomography of high-energy nuclear collisions

1.8 MB·English

by  Ben-Wei Zhang

NuclearPhysicsA00(2011)1–8
Full jet tomography of high-energy nuclear collisions
Ben-WeiZhang
InstituteofParticlePhysics,CentralChinaNormalUniversity,Wuhan430079,China
KeyLaboratoryofQuark&LeptonPhysics(CentralChinaNormalUniversity),MinistryofEducation,China
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Abstract
n
a
Parton energy loss in the hot QCD medium will manifest itself not only in leading hadron spectra but also in
J
reconstructedjetproductionsinhigh-energynucleus-nucleuscollisions. Inthispaperwereportonrecenttheoretical
5
effortsinstudyingfulljetobservablesinrelativisticheavy-ioncollisionsbydiscussingthemodificationsofjetshapes,

] inclusive jet cross section and the vector boson accompanied jet production in the presence of the QGP-induced jet
h
quenching.
t
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l Keywords: jetquenching,reconstructedjet,perturbativeQCD
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[ 1. Introduction

1
v Inhigh-energynucleus-nucleuscollisionsadeconfinedmatter,thequark-gluonplasma(QGP)istobeformedand
9 when an energetic parton produced by the initial hard scattering propagates in this hot and dense QCD medium, it
5 will interact with other partons in the hot nuclear medium and be quenched substantially[1, 2, 3, 4, 5]. This parton
8
energy loss mechanism, or jet quenching, has been proposed to be an excellent probe of the QGP and predicted
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thesuppressionofsinglehardonproductionsandthedisappearanceofaway-sidedihadroncorrelationsinheavy-ion
.
1 collisions(HIC),whichlaterhavebeenconfirmedbytheexperimentalmeasurementsatRHICandgivencompelling
0
evidenceoftheexistenceofanewkindofmatterinhigh-energynuclearcollisionsatRHIC[6]. Notsurprisingly,the
1
findingofjetquenchinginheavy-ioncollisionshasbeenregardedasoneofthemostimportantdiscoveriesmadeat
1
: RHICandinitiatedmanytheoreticalexplorationsandverypreciseexperimentalmeasurements[7].
v
Sofarthedominantexperimentalmeasurementsofjetquenchingisabouttheproductionofoneortwohadrons
i
X withalargetransversemomentum,whichareonlytheleadingfragmentsofajet. Thepartonenergylossmechanism
r willnotonlymanifestitselfinleadingparticleproductions,butmoreinterestinglyinfulljetobservables. Recentlyin
a heavy-ioncommunityalargeamountofefforthasbeeninvestedinmeasuringreconstructedjetsinhigh-energynuclear
collisions for the first time[8, 9, 10], and theories to address the novel features of full jet tomography in relativistic
heavy-ioncollisionshaveemerged. Inthisarticlewereviewourtheoreticalstudiesonjetobservablesofhigh-energy
nucleus-nucleus collisions in perturbative Quantum Chromodynamics (pQCD) by focusing on the intra-jet energy
flow,theinclusivejetcrosssectionandZ0/γ∗-taggedjetproduction[11,12,13]aswellaspossiblenon-perturbative
effectsinjetproductions.
B.W.Zhang/NuclearPhysicsA00(2011)1–8 2
√
Figure1: Comparisonofnumericalresultsfromourtheoreticalcalculationtoexperimentaldataondifferentialjetshapesat s=1960GeVby
CDFII[18](leftpanel). Numericalsimulationofjetshapesinvacuum,medium-inducedjetshapes,andtotaljetshapesinmediumforPb+Pb
√
with sNN =5.5TeVatLHC(rightpanel).
2. JetshapesinHIC
Oneofthemostcommonobesevablesofresolvingtheinternaljetstructureisthejetshape,whichdescribesthe
energydistributioninajetas[14]:
(cid:80)(E )Θ(r−R )
Ψint(r;R)= (cid:80)i(ET)iΘ(R−Ri,jet). (1)
i T i i,jet
(cid:113)
Herer,RareLorentz-invariantopeningangles,R = (y −y )2+(φ −φ )2 givesthedistancebetweenaparton
i,jet i jet i jet
iandthejetinthespaceofrapidityyandazimuthalφ.
Inleadingorderwecanderivethedifferentialjetshapeas[11]
dΨ (r;R) (cid:88) α 2(cid:90) 1−Z
ψ(r;R)= int = s dzzP (z), (2)
dr 2πr a→bc
b zmin
where
(cid:26) r (cid:27)
Z = max z , if r<(R −1)R,
min r+R sep
(cid:40) (cid:41)
r
Z = max z , if r>(R −1)R.
min R R sep
sep
Here1 ≤ R ≤ 2isintroducedtotakeintoaccountfeaturesofexperimentalconealgorithms,employedtoimprove
sep
infraredsafety. InEq.(2)r=(1−z)ρisrelatedtotheopeningangleρbetweenthefinal-statepartons,P (z)isthe
a→bc
splittingkernelinDGLAPevolutionequation,zisthemomentumfractionoftheradiatedpartonrelativetotheparent
parton, z = Emin/E with E representing the transverse momentum of a jet, and Emin the minimum transverse
min T T T T
momentumofapartoninthisjet.
CarryingouttheintegrationofzwegetthejetshapesatLO.Forinstance,thejetshapeforaquarkgives:
(cid:32) (cid:33)
C α 2 1−z 3(cid:104) (cid:105)
ψ (r)= F s 2log min − (1−Z)2−z2 , (3)
q 2π r Z 2 min
B.W.Zhang/NuclearPhysicsA00(2011)1–8 3
√
Figure2: Themeanrelativejetradii(cid:104)r/R(cid:105)inthevacuum,withcompleteenergyloss,andintheQGPmediumfor s=5.5TeVcentralPb+Pb
collisionsattheLHC(leftpanel);Theratiosoftotaljetshapeinheavy-ioncollisionsatLHCtothejetshapeinthevacuum(rightpanel).
Eq.(3)iscollineardivergentwhenr → 0. Togetridofthisdivergence,weneedtomakeSudakovresummation.
Also we could improve the prediction power of our analysis by estimating the non-perturbative effect and include
contributionsoftheinitial-stateradiationandcorrespondingSudakovresummation[14].Takingintoaccountallthese
contributions,wedonumericalsimulationandshowthecomparisonofthetheoreticalresultsforjetshapesin p+ p¯
√
collisionswith s =1960GeVatTevatronwithCDFIIdatainFig.1. Itcouldbeseenthatthetheoreticalmodel
NN
describesCDFIIdataverywell,especiallyjetshapesawayfromr=0[11].
In a hot and dense QCD medium, a propagating fast parton may lose a large amount of energy by medium-
inducedgluonradiation,andsomelostenergycarriedawaybyradiatedgluonmayberecapturedbythejetandthus
gives additional contributions to jet shapes. In our studies, we calculate the radiated gluon angular distribution in
medium within the GLV formalism [4] and compute the medium-induced jet shapes as well as the in-medium jet
crosssections(seeSec.3andSec.4)usingfullnumericalevaluationofthemedium-inducedcontributiontotheparton
showers. In the model energetic inclusive jet production and tagged jet production are rare processes that follow
binarycollisionscaling∼ d2N /d2xwithd2xrepresentingtheareainthetransverseplane;incontrast,themedium
bin
isdistributedaccordingtothenumberofparticipantsdensity∼ d2N /d2xandthelongitudinalBjorkenexpansion
part
oftheQGPincorporated.
ThetotaljetshapesinHICthenisgivenby[11]:
ψtot.(cid:18)Rr(cid:19)∝(cid:90)(cid:15)=10d(cid:15) (cid:88)q,g (1−P(1q,g−((cid:15)f,qE,g))·(cid:15))3 (1−(cid:15))ψqva,gc.(cid:18)Rr;E(cid:48)(cid:19)+ fq,g·(cid:15) ψqm,ged.(cid:18)Rr;E(cid:48)(cid:19), (4)
where(1− f )·(cid:15) givesthefractionoftheenergyoftheparentpartonfallingoutsideofjetareawitharadiusR. In
q,g
therightpanelofFig.1weillustratejetshapesinvacuumψ (r/R),medium-inducedjetshapesψ (r/R),andtotal
√ vac. med.
jet shapes in HIC ψ (r/R) in Pb+Pb collisions with s = 5.5 TeV. It is observed that though medium-induced
tot. NN
jet shapes are quite distinct from jet shapes in vacuum, the difference between jet shapes in p+p collisions and that
inPb+Pbisnotverylarge. Theunderliningreasonforthissurprisingresultisthatalthoughmedium-inducedgluon
radiationproducesabroaderψ (r/R), thiseffectisoffsetbythefactthatjetsloseafiniteamountoftheirenergy,
med.
which will shift jet shapes in vacuum to higher E with steeper profile. The left panel of Fig. 2 shows the mean
T
relative jet radii (cid:104)r/R(cid:105) in the vacuum and in the QGP medium created at the LHC for two different cone selections
R=0.4andR=0.7.Wecanfindthatthebroadeningofradii(cid:104)r/R(cid:105)ofjetshapesinHICismodest,whichimpliesonly
afractionofenergyofjetslostinthehotmediumandtheQGPisrather’gray’insteadof’black’[11]. Thedeviation
of ψ (r/R) from ψ (r/R) is pronounced in the tail of jet shapes for small cone size R = 0.4, as illustrated in the
tot. vac.
rightpanelofFig.2.
B.W.Zhang/NuclearPhysicsA00(2011)1–8 4
Figure3: TransverseenergydependentnuclearmodificationfactorRjet fordifferentconeradiiRatNLOinb = 3fmAu+Aucollisionsat
√ AA
√sNN = 200 GeV (left panel). The ratio of jet yields at R = 0.2 and R = 0.4 in p+p, central Cu+Cu and Central Au+Au collisions with
sNN =200GeVatRHIC(rightpanel).
3. InclusivejetcrosssectionsinHIC
Parton energy loss in the QGP not only changes the energy distribution in a jet, but also alters the inclusive jet
spectruminhigh-energynucleus-nucleusreactions.AfirststudyofinclusivejetproductionsinHICwascarriedoutin
theleadingorder(LO)[11],andrecentlytotakefulladvantageofjetphysicsinreactionswithultra-relativisticnuclei
anext-to-leading(NLO)calculationsatO(α3)havebeenmade[12].
s
Inhadron-hadroncollisionstheinclusivejetcrosssectionatNLOcanbegivenas [15]:
(cid:90) (cid:90)
dσjet 1 dσ[2→2] 1 dσ[2→3]
= d{E ,y,φ} S ({E ,y,φ} )+ d{E ,y,φ} S ({E ,y,φ} ), (5)
dE dy 2! T 2d{E ,y,φ} 2 T 2 3! T 3d{E ,y,φ} 3 T 3
T T 2 T 3
whereE ,y,φ arethetransverseenergy,rapidity,andazimuthalangleofthei-thparticle(i = 1,2,3),respectively,
Ti i i
andσ[2→2],σ[2→3]standforthepartoniccrosssections. InEq.(5)S ,S givethespaceconstraintsandcontain
2 3
the information of the jet-finding algorithm. At leading order, a jet is equivalent to a parton and we always have
S = (cid:80)2 S(i) = (cid:80)2 δ(E −E )δ(y −y). AtNLOduetohigherordercorrectionsS hastwocontributions: one
2 i=1 i=1 Ti T i 3
comingfromthepossibilitythateachjetstillcontainsoneparton;anotherresultingfromthechancethatajetcontains
twopartonsimposedbythejetfindingalgorithm[21]. Numericalsimulationshowsthattheinclusivejetspectrumin
√
p+pcollisionswith s = 200GeVatRHICisdescribedverywellbyaNLOcodeofjetproductioninhadronic
NN
collisions[15],whichwilllaterbeextendedtostudyinclusivejetproductionsatNLOinHIC.
In the same spirit of Eq. (4) for jet shapes in HIC, we derive the related medium-modified jet cross section as
follows[12]:
1 dσAA(R) (cid:90) 1 (cid:88) 1 dσCNM,NLO(R)
= d(cid:15) P ((cid:15),E) q,g . (6)
(cid:104)TAA(cid:105)σgAeAo d2ETdy (cid:15)=0 q,g q,g (1−(1− fq,g)·(cid:15))2 d2ET(cid:48)dy
HereT isthenuclearoverlapfunction,andσgeothegeometricalA+Acrosssection[16].Themeasuredcrosssection
AA AA
isthenaprobabilisticsuperpositionofthecrosssectionsofprotojetsofinitiallylargerenergyE(cid:48) = E /(1−(1−f )·(cid:15)).
T T q,g
Now we are ready to compute the nuclear modification factor of jet cross section Rjet defined as the ratio of jet
AA
crosssectioninHICtothatinp+prescaledbythenumberofbinarycollisions. Thenumericalresultsforthenuclear
√
modificationfactorofinclusivejetsRjet incentralAu+Auwith s = 200GeVatRHICarepresentedintheleft
AA NN
panelofFig.3[12], wherethebandoftheoreticalcalculationsshowsacalculationfora∼ 20%increaseintherate
ofpartonenergylossrelativetoourdefaultsimulation. AcontinuousvariationofRjet withthejetradiusRisfound,
AA
which demonstrates a unique feature of jet production as compared to the single curve of R for pion production
AA
inHIC.Inthecalculationsseveralcoldnuclearmatter(CNM)effectssuchasnuclearshadowing, Cronineffectand
B.W.Zhang/NuclearPhysicsA00(2011)1–8 5
√
Figure4: ExperimentalmeasurementsoffulljetproductioninHICwith sNN =200GeVatRHIC[8,10]:thenuclearmodificationfactorofjet
productioninAu+Aucollisionsatdifferentjetradii(leftpanel);ratiosofjetcrosssectionswithR=0.2tothatwithR=0.4inp+pandAu+Au
collisions(rightpanel).
EMCeffecthavebeentakenintoaccount[19,20]. WeobservethatforR ≤ 0.2thequenchingofjetsapproximates
thealreadyobservedsuppressionintheproductionrateofinclusivehigh-p particles. Inourtheoreticalcalculation
T
CNMeffectscontributesignificantlytotheobservedattenuationatlarge E . WecouldsuppresstheeffectsofCNM
T
by taking the ratios of jet cross sections at different cone radii, which are plotted in the inserts of the left panel of
Fig.3.
Toseethedistinctionofjetproductionsindifferentsystemsmoreclearlyweplottheratio dσAA(R=0.2)/dσAA(R=0.4)
forp+pcollisions, centralCu+CuandcentralAu+Aucollisionswith √s = 200GeVatRHICdEinTdtyherighdtEpTdaynel
NN
ofFig.3. Itshowsthattheratiodecreasesasthesystembecomeslarger,andtheratioinAu+AuatRHICissmaller
thanthoseinp+pandCu+Cucollisionatthesamecollidingenergy,whichimpliesinHICmorecontributionsofjet
yieldscomefromlargeangularradiationascomparedtop+pcollisions.
RecentlyPHENIXandSTARhavemeasuredreconstructedjetsinhigh-energynucleus-nucleuscollisionsatRHIC
andsomepreliminaryresults[8,10]areillustratedinFig.4. FromtheleftpanelofFig.4onecanseethatmeasured
Rjet changeswiththejetradiusandatsmallerradiusthenuclearmodificationfactorofjetsissmaller,whichagrees
AA
withourtheoreticalprediction[11,12]shownintheleftpanelofFig.3. Moreovertheexperimentalmeasurements
alsodemonstratetheratioofjetyieldsatdifferentradiiinAu+Auissmallerthantheoneinp+p(seetherightpanel
ofFig.4)whichconfirmstheinterestingfeatureshowntherightpanelofFig.3withourtheoreticalstudy. Wenotice
thatthoughourtheoreticalpredictionsofinclusivejetsdescribeverywelltheoveralltrendsofthejetmeasurements
atRHIC,somedeviationsexistifwecomparetheresultsinFig.3withthedatainFig.4. Toconfrontthetheoretical
studies with the experimental data on a more solid base, we should include the correction from non-perturbative
effects of jet productions [21, 22, 23] in our theoretical investigation (please see Sec.5 for more discussions), and
preciseexperimentalmeasurementsofjetsinHICwithlargestatisticswillalsobeneeded.
4. TaggedjetproductionsinHIC
A natural way to extend the study of the inclusive jet production in high-energy nucleus-nucleus reactions is to
consider tagged jet productions in HIC, especially the jet production accompanied with a vector boson ( γ or Z0 )
in nuclear collisions. In the leading order, the vector boson and the accompanied jet are produced back-to-back in
thecenter-of-massframeandthetransversemomentumofthevectorbosonEVB isthesameasthatofthetaggedjet
T
Ejet beforetheytravelintheQGP.Becausethevectorbosondoesn’tinteractwiththemediumstronglyitstransverse
T
momentumofthevectorbosonisintact. BymeasuringEVBandEjetinthefinalstageofheavy-ioncollisionswemay
T T
knowexactlytheenergylossofthejetbyassessingEVB−Ejet. Thereforethevectorboson+jetproductionhasbeen
T T
consideredasanoptimalchanneltopinpointthepartonenergylossintheQGPandrevealthedetailedinformationof
B.W.Zhang/NuclearPhysicsA00(2011)1–8 6
Figure5: ComparisonofthetheoreticalcalculationofZ0/γ∗ taggedjetproductioninLOandNLOwithMCFMtoexperimentalresultsfrom
√
theFermiLabTevatronCollider[26]forthecrosssectionofjetsassociatedwithZ0/γ∗ → µ++µ− in p+p¯ collisionsat s = 1.96TeV(left
panel). TheNLO pT-differentialcrosssectionpernucleonpairforjetstaggedwithZ/γ∗ → µ++µ−inp+pandcentralPb+Pbreactionswhen
92.5GeV<pjet<112.5GeV(rightpanel).
T
thehotanddenseQCDmediumformedinrelativisticHIC.However,higherordercorrectionswillbreakthemomenta
balancebetweentaggedjetandthevectorbosonduetoadditionalradiation. Herewewillreviewourrecentstudyof
Z0/γ∗+jetproductioninPb+PbreactionsatNLOandforamoredetaileddiscussionwereferto[13,24].
ForthebaselineevaluationoftaggedjetcrosssectionsatNLOinhadron-hadronreactionsweusetheMonteCarlo
forFeMtobarn(MCFM)numericalcode[25]. TheconfrontationoftheoreticalcomputationoftaggedjetatMCFM
NLO against the experiment measurement for p+ p¯ collisions at Tevatron in the left panel of Fig. 5 attests to the
validityofpQCDcalculations. Inheavy-ioncollisionsthemedium-inducedpartonenergylosswillmodifythetagged
jetspectrumandthequenchedjetcrosssectionisgivenasfollows:
(cid:90) (cid:32) (cid:33)
dσAA (cid:88) 1 dσq,g p
= d(cid:15) P ((cid:15)) Q , (7)
d2p d2p q,g [1−(1− f (ω ,R))(cid:15)]2d2p d2p [1−(1− f )(cid:15))]
(Z) Q q,g q,g min (Z) (jet) q,g
with p = p (1−(1− f )(cid:15)). Eq. (7) implies that the observed tagged jet cross section in A+A reactions is a
Q (jet) q,g
probabilistic superposition of cross sections for jets of higher initial transverse energy. This excess energy is then
redistributedoutsideofthejetduetostrongfinal-stateinteractions. Heredσq,g/d2p d2p arethedifferentialcross
(Z) (jet)
sectionsforaway-sidequarkandgluonjets,respectively.
InsomeexperimentstheZ0/γ∗+jetfinal-statechannelismeasuredwithoutplacingrestrictionsonthemomentum
ofthevectorboson[26]. Inthiscase,wecanintegrateoverp inEq.(7)andderive:
(Z)
(cid:90) (cid:32) (cid:33)
dσAA (cid:88) 1 dσq,g p
= d(cid:15) P ((cid:15)) Q . (8)
d2p q,g [1−(1− f (ω ,R))(cid:15)]2d2p [1−(1− f )(cid:15))]
Q q,g q,g min (jet) q,g
WenoticethattheintegratedtaggedjetcrosssectiondσAA/d2p usuallyunravelsthesamephysicsasthesuppression
Q
ofthecrosssectionininclusivejetproductiondiscussedinSec.3.
TodemonstratenucleareffectsfortaggedjetcrosssectionsinHICwedefineIjet fortaggedjetas:
AA
(cid:44)
1 dσ dσ
Ijet(R,ω )= AA pp . (9)
AA min (cid:104)T (cid:105)σgeodp dp dp dp
AA AA T(Z) T(Q) T(Z) T(jet)
WhileatLOIjet islimitedtotheZ0/γ∗triggermomentumrange,atNLOitwillshowrichfeaturesaswewilldiscuss
AA
below.
√
A numerical simulation of Z0/γ∗ tagged jet productions in p+p and Pb+Pb with s = 4 TeV for a cone size
NN
R = 0.2 is provided in the right panel of Fig. 5 . It is found because part of the jet energy is redistributed outside
B.W.Zhang/NuclearPhysicsA00(2011)1–8 7
Figure6: MagnitudeofthehadronizationandunderlyingeventeffectsusedtocorrecttheinclusivejetcrosssectionmeasuredbyCDFwithjet
radiusR=0.7[21](leftpanel).ModificationofpT ofjetsduetonon-perturbativeeffectsinp+pcollisionsatRHICwithPythia8.142[27](right
panel).Hereforallplotsthecorrectionsaretakenfromhadrontopartonlevel.
ofthejetconethe p spectrumoftaggedjetproductioninHICisdownshiftedtowardsmallertransversemomenta.
T
Moreinterestinglyonecanobserveasharptransitionof Ijet fromtaggedjetenhancementbelow p totaggedjet
AA T(Z)
suppressionabovep .Thisstrikingfeatureprovidesauniquepredictionofjetquenchingfortaggedjetsandwillbe
T(Z)
experimentalevidenceforstrongfinal-stateinteractionsandpartonenergylossintheQGP.Pleasenotethatwhilethe
sameenergyredistributionoccursforinclusivejetproductiondiscussedinSec.3,themonotonicallyfallingspectrum
preventstheobservationofsuchinclusivejetenhancement.
5. Non-perturbativeeffectsinjetproductions
InperturbativeQCDcalculationsofinclusivejetyieldandtaggedjetproduction,ajetisthecombinationofafew
partonsdefinedbyjetalgorithmsandwhatwecalculateistheparton-jet. However,inexperimentswhatwemeasured
isthehadron-jetsincethefinal-stateparticlesarehadrons. Forjetproductionathightransversemomentuminahard
processwithalargemomentumtransfer,thedifferencebetweenparton-jetsandhadron-jetsmaybesmallduetolocal
parton-hadronduality(LPHD)[15,21]. Nevertheless, tomakeamorereliablecomparisonbetweenQCDtheoryof
jetproductionsandthejetmeasurements,thetheoreticalresultofjetcrosssectionswithpQCDshouldbecorrected
tohadronlevel,oronthecontrarytheexperimentaldatashouldbecorrectedtopartonlevel[21,27,28].
Toincludethesecorrectionstwoimportantnon-perturbativeeffectsshouldbetakenintoaccount:thehadronization
effectwhichresultsintheenergylossofajetbecausewhenpartonsinaparton-jethadronize,somehadronsmayfall
outsideofthejet(a”splashing-out”effect);theunderlyingeventeffectswhichgivestheenergygainofajetdueto
interactionofbeam-beamremnantsnotassociatedwiththehardscattering(a”splash-in”effect). Thegoodnewsis
that the hadronization effect and the underlying event effect go in opposite direction and their contributions will be
partiallycancelled.
TheleftpanelofFig.6givesthemagnitudeofnon-perturbativeeffectsusedtocorrectthe p spectrawithacone
√ T
size R = 0.7 for p+ p¯ collisions with s = 1960 GeV by CDF at Tevatron. We find that when p > 200 GeV
NN T
thefractionalcorrectionsduetonon-perturbativeeffectsarewithinfewpercent. However,thisobservationholdstrue
√
onlyforthisspecialcaseandcorrectionsfromthenon-perturbativeeffectsmayvarywiththecollidingenergy s ,
NN
jettransversemomenta p andthe jetradiusR [23,27]. AtRHICwith collidingenergy200GeV themeasuredjet
T
doesnothaveaverylarge p , andwithsmalljetradii(R = 0.2, 0.4formeasurementsinFig.4)thecontributions
T
fromnon-perturbativeeffectsmaybeconsiderable. IntherightpanelofFig.6weshowanumericalsimulationofthe
jet p shifting[27]toinclusivejetproductionduetothehadronizationeffectandtheunderlyingeventeffectsin p+p
T
collisionsatRHICwithPythia8.142[29]. Itcouldbeseenthatwhen p ∼ 12GeVtherelativeshiftingδp/p due
T t T
tohadronizationcouldbeabout8%,anditseffectwillbesignificantlyamplifiedbythesteeplyfalling p spectrumof
T
B.W.Zhang/NuclearPhysicsA00(2011)1–8 8
jetswhenwestudyingthejetcrosssection. Thusitisimportanttotakeintoaccountcorrectionsofnon-perturbative
effectstojetproductionsinHICatRHICandseehowjetspectrawillbemodifiedbythesecorrections[27].
Acknowledgments: The work is finished in collaboration with I. Vitev, S. Wicks and B. Neufeld. I thank
X. N. Wang, J. W. Qiu and G. Soyez for illuminating discussions. This research is supported by the Ministry of
EducationofChinawiththeProgramNCET-09-0411,byNationalNaturalScienceFoundationofChinawithProject
No. 11075062,andCCNUwithProjectNo. CCNU09A02001.
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