Nuclear suppression in p-A collisions from induced radiation

0.37 MB·

by  François Arleo

EPJWebofConferenceswillbesetbythepublisher
DOI:willbesetbythepublisher
(cid:13)c Ownedbytheauthors,publishedbyEDPSciences,2016
6
1
0
Nuclear suppression in p–A collisions from induced radiation
2

n
a
FrançoisArleo1,RodionKolevatov2,StéphanePeigné3,a,andTaklitSami3
J

5 1LaboratoireLeprince-Ringuet(LLR),Écolepolytechnique,CNRS/IN2P391128Palaiseau,France
2 2DepartmentofPhysics,UniversityofOslo,PB1048Blindern,0316Oslo,Norway
3SUBATECH,UMR6457,UniversitédeNantes,EcoledesMinesdeNantes,CNRS/IN2P3
] 4rueAlfredKastler,44307Nantescedex3,France
h
p
-
p Abstract.Thecurrentstatusofcoherentenergylossisreviewed,bothintheoryandinits
e phenomenologicalapplicationstop–Acollisions.
h
[

1 Introduction
1
v
2 Thenuclearsuppressionofhadronproductioninproton-nucleus(p–A)withrespecttoproton-proton
5 (p–p)collisionshasbeenwidelydiscussed,butisstillanopenquestionduetothepresenceofvarious
5 competing effects, depending on the precise kinematics and collision energy. Until quite recently,
6
most of the phenomenological approaches assumed hadron nuclear suppression to be due either to
0
hadronnuclearabsorptionortotheshadowingofthegluondistributioninthetargetnucleusexpected
.
1 atsmall x (cid:46) 10−2. Howeveranotherfundamentalphenomenon,namelycoherentpartonenergyloss
2
0
incoldnuclearmatter,couldplayadecisiveroleinhadronnuclearsuppression[1].
6
Medium-inducedcoherentgluonradiationisaQCDpredictionwhichhasnowbeenobtainedin
1
: varioustheoreticalsetups[1–7],andwassuccessfullyappliedtothephenomenologyofquarkonium
v
nuclearsuppressioninp–Acollisions[2,8,9]. Herewereviewthecurrentstatusofcoherentenergy
i
X lossintheory(Sect.2)andinitsphenomenologicalapplicationstop–Acollisions(Sect.3).
r
a
2 Theory of induced energy loss: a brief history
It was first noted by Gavin and Milana [10] that the strong increase of J/ψ suppression with x ob-
F
servedinp–Acollisionscouldbeeasilyreproducedbyassuminganinducedpartonenergyloss∆E
scalingastheenergyE oftheenergeticcc¯pair,namely∆E ∝ E. However,theGavin-Milana‘expla-
nation’ was soon put aside, because of a claim that any induced energy loss ∆E should be bounded
in the E → ∞ limit. It is now understood (see for instance Ref. [11]) that the latter claim is in-
correct, more precisely the induced energy loss is not bounded in general, but only in the specific
situation where the energetic parton is suddenly accelerated (as in deep inelastic scattering) in the
nuclear medium. In the situation where the parton is ‘asymptotic’, i.e. ‘prepared’ at t = −∞ and
‘tagged’ at t = +∞ after crossing a nuclear medium of thickness L (a situation relevant to forward
hadronproductioninp–Acollisions), thebehavior ∆E ∝ E iscorrect[1]. Below webrieflyreview
thefeaturesofinducedradiationinthesetwodifferentsituations.
aTalkgivenatthe6thInternationalConferenceonPhysicsOpportunitiesatanElectron-IonCollider(POETIC2015).
EPJWebofConferences
ω ω
E E
q ℓ
L L
(i) (ii)
Figure1. Twoqualitativelydifferentsituationsrelevanttomedium-inducedpartonenergyloss: (i)partonsud-
denlyacceleratedinamediumand(ii)‘asymptoticparton’crossingamedium.
2.1 Partonsuddenlyproducedinamedium
The case (i) of a parton suddenly created in a medium is sketched in Fig. 1 (left). The associated
medium-induced (soft) gluon radiation spectrum ωdI/dω has been calculated before and is repre-
sentedschematicallyinFig.2(left).
It is useful to recall the different regimes identified in [12] depending on the value of the gluon
formation time t = ω/k2 (for a more detailed discussion in QED and in QCD, see [11]). In the
f ⊥
incoherentorBethe–Heitlerregimet < λ (whereλ isthepartonmeanfreepathinthemedium),
f R R
corresponding to very soft gluons ω < qˆ λ2 (where qˆ ≡ µ2/λ with µ the typical transverse mo-
R R R R
mentum exchange in a single scattering), each scattering center acts as an independent source of
radiation. InthisregimetheenergyspectrumωdI/dωisindependentofω(uptologarithms). Inthe
domain λ < t < L, corresponding to intermediate radiated energies qˆ λ2 < ω < qˆ L2, a group
R f R R R √
of ∼ t /λ scattering centers acts as a single radiator, leading to a relative suppression ∝ 1/ ω of
f R
thegluonradiationspectrumwithrespecttotheBethe-Heitlerregime[12,13]. Thisistheso-called
Landau–Pomeranchuk–Migdal(LPM)suppressionregime. Finally,inthedomainoflargeformation
time t > L (or ω > qˆ L2), called the fully coherent domain in the following, all scattering centers
f R
inthemediumactcoherentlyasasourceofradiation,andtheinducedradiationspectrumbehavesas
∼1/ω[14],i.e.ismorestronglysuppressedthanintheLPMregime.
In the situation (i), the suppression of the radiation spectrum in the fully coherent domain can
be simply understood as follows. For formation times t (cid:29) L, the radiation spectrum must arise
f
dominantlyfromtime-ordereddiagramswherethegluonemissionvertexisfarbeyondthemedium.
The associated gluon emission amplitude is then ∝ ((cid:126)θ −(cid:126)θ )/((cid:126)θ −(cid:126)θ )2 [1], where (cid:126)θ ≡ (cid:126)k /ω and
s s ⊥
(cid:126)θ ≡ (cid:126)p /E arethefinal‘angles’oftheradiatedgluonandenergeticparton,respectively. Thedouble
s ⊥
differential spectrum ωdI/dωd2(cid:126)θ ∝ 1/((cid:126)θ −(cid:126)θ )2 depends on the medium only through (cid:126)θ , which is
s s
relatedtothemediumsizebytherandomwalkestimateθ2 (cid:39)(µ2/E2)·(L/λ )resultingfrommultiple
s R
scattering of the energetic parton across the medium. The spectrum integrated over gluon angles,
(cid:82)
ωdI/dω ∼ d2(cid:126)θ/((cid:126)θ −(cid:126)θ )2, is independent of (cid:126)θ (by a trivial change of variable in the (cid:126)θ-integral)
s s
and thus of L, leading to a strong suppression of the induced energy spectrum. The above heuristic
discussionillustrateswhylargeformationtimest (cid:29) Laresuppressedinsituation(i).
f
Duetothissuppression,thespectrumdecreasesas1/ωwhenω>qˆ L2[14],leadingtoanaverage
R
energylossinsituation(i)effectivelydominatedbyω∼qˆ L2andgivenby(uptologarithms)
R
(cid:90)
dI
∆E ≡ dωω ∼α N qˆ L2 =α C qˆL2, (1)
dω s c R s R
whereC istheenergeticpartoncolorcharge,andqˆ ≡qˆ =µ2/λ thegluontransportcoefficient. For
R g g
arigorousderivationoftheinducedradiationspectrumandassociatedaverageenergylossinsituation
(i),seeRefs.[12,13].
PhysicsOpportunitiesatanElectron-IonCollider
Figure2.Log-logschematicplotshowingtheparametricdependenceoftheinducedradiationspectrumωdI/dω
(dividedbyα ), incase(i)ofapartonproducedinamedium(left)andincase(ii)ofan‘asymptoticparton’
s
(right).Seetextfordetails.
2.2 Fullycoherentenergyloss
Wenowturntothecase(ii)ofanasymptoticparton(seeFig.1,right),whichisrelevanttoforward
hadron production in p–A collisions. The fundamental difference with the case (i) reviewed in the
previoussectionisthatlargeformationtimest (cid:29) Larenotsuppressedanylonger,butonthecontrary
f
dominant in ωdI/dω. This can be simply understood as follows. Supposing t (cid:29) L, three types of
f
contributions to the radiation spectrum can emerge: purely final state radiation, where the gluon
emissionvertexisassociatedwithalargepositivetimet(cid:29) Linboththeamplitudeanditsconjugate,
purelyinitialstateradiationcorrespondingtolargenegativeemissiontimesintheamplitudeandits
conjugate, and an interference contribution where the gluon is emitted with t (cid:29) L in the amplitude
and−t (cid:29) Lintheconjugateamplitude(orviceversa). Thetwoformercontributionsaresuppressed
in the induced spectrum, for the same reason as in the case (i), see Sect. 2.1. On the contrary, the
(cid:82)
latterinterferencecontributiontoωdI/dωisoftheform∼ d2(cid:126)θ ((cid:126)θ/θ2)·[((cid:126)θ−(cid:126)θ )/((cid:126)θ−(cid:126)θ )2], andits
s s
dependenceon(cid:126)θ (andthusonL)cannotberemovedbyasimpleshiftinthe(cid:126)θ-integral.Itthussurvives
s
intheinducedspectrum,andactuallygivesthedominantcontributionincase(ii)[1]. Moreover,the
dependenceoftheinterferenceonthepartonscattering‘angle’(cid:126)θ leadstoanexplicitdependenceof
s
theinducedspectrumonthehardexchange(cid:126)q = E(cid:126)θ sufferedbytheparton.
⊥ s
AscanbeseeninFig.2(right),theresultinginducedradiationspectrumintheregiont (cid:29) Lis
f
(cid:112)
logarithmic, uptothescaleωˆ ≡ ( qˆL/M )E (where M ≡ (M2 +q2)1/2 with M thepartonmass),
⊥ ⊥ ⊥
abovewhichitissuppressedas1/ω2. Theresultingaverageenergylossisthusdominatedbyω ∼ ωˆ
andreads[1]
(cid:112)
qˆL
∆E ∼α ωˆ =α E. (2)
s s M
⊥
In summary, the interference contribution, which is absent in the situation (i), leads in the situation
(ii)toanaveragepartonenergylossproportionalto E andarisingfromthefullycoherentdomainof
formationtimest (cid:29) L.
f
Let us remark that for the induced radiation associated with t (cid:46) L, the precise way the parton
f
is produced (in the medium or long before) does not matter. Thus, the induced spectra in the cor-
responding ω-domain, ω < qˆ L2, are parametrically the same in both cases (i) and (ii), see Fig. 2.
R
Notethatincase(ii),thisdomaingivesacontributionto∆E oftheLPMtype(1),butatlargeE this
contributionisnegligiblecomparedtothecoherentenergyloss(2).
EPJWebofConferences
The rigorous calculation of medium-induced coherent radiation has been addressed by several
groups, using different formalisms and considering different particular cases. Ref. [1] (see also [2])
studiedtheinducedcoherentradiationassociatedwiththehardforwardg→ QQ¯process(mediatedby
asinglehardgluonexchangeinthet-channel),thefinalQQ¯ pairbeingamassivepointlikecoloroctet,
inaFeynmandiagramcalculationandatfirstorderintheopacityexpansionformalism[15]. Induced
coherentradiationwasalsostudiedusingasemi-classicalmethodinRefs.[3,4],atfirstorder[3]and
allorders[4]inopacity,andinasimilarkinematicalsetupasthatofRef.[1],howeverfortheq → q
caseofamasslessquarkexperiencingahardscatteringmediatedbyacolorsingletexchangeinthe
t-channel. InRef.[5],inducedcoherentradiationwasrevisitedandderivedtoallordersintheopacity
expansion, for any 1 → 1 hard forward process. A general expression encompassing the particular
casesstudiedbeforewasfoundfortheinduced(soft)coherentspectrum[5],
(cid:32) (cid:33) (cid:112)
dI α ωˆ2 qˆL
ω =(C +C −C) s log 1+ ; ωˆ ≡ E, (3)
dω R R(cid:48) t π ω2 M
⊥
withC ,C theincomingandoutgoingcolorcharges,andC thecolorchargeofthehardt-channel
R R(cid:48) t
exchange.1 Notethatthetransportcoefficientqˆtobeusedintheexpressionofωˆ isthegluontransport
coefficientqˆ ≡ qˆ ,independentlyoftheincomingandoutgoingpartoncolorstates[5]. Thelimiting
g
behaviorsof(3)inthefullycoherentdomain,namely,the(logarithmic)‘plateau’atω (cid:28) ωˆ,andthe
1/ω2 suppression at ω (cid:29) ωˆ, are displayed in Fig. 2 (right), where for the sake of illustration the
incomingandoutgoingpartonsarechosenofthesametype,C = C . Withacoloroctett-channel
R R(cid:48)
exchange,C = N ,theheightoftheplateauisthus∝(2C −N ),seeFig.2(right).2
t c R c
Theinducedcoherentradiationassociatedwith1 → 2forwardprocesseswasalsoaddressed(in
theleadinglogarithmandlarge N limits), forg → qq¯ andq → qginthedipoleformalism[6]and
c
forq→qgandg→ggusingtheopacityexpansion[7]. Intheleadinglogarithmapproximation,the
softinducedcoherentradiationdoesnotprobethesizeofthefinaltwo-partonsystem,andthusonly
dependsonitstotalcolorcharge. Hencetheconjecture,proposedandexplicitlycheckedforq → qg
andg → gginRef.[7],thatthespectrumassociatedwith1 → nhardforwardprocessesisgivenby
anincoherentsumofspectraassociatedwith1 → 1processes,weightedbytheprobabilities P for
R(cid:48)
the n-parton state to be produced in color representation R(cid:48) in the hard process. This conjecture is
expectedtoholdforanyfiniteN (butonlyintheleadinglogarithmapproximation)[7].
c
3 Coherent energy loss in p–A collisions
Inducedcoherentradiationarisesintheproductionofasingleforwardparticle[1–5]andinforward
dijetproduction[6,7],suggestingthebroadrelevanceofcoherentenergylossinforwardprocesses.
3.1 Quarkoniumsuppressionfromfixed-targettocolliderenergies
Coherent energy loss is expected in quarkonium production in p–A collisions, where typically (at
√
sufficientlylarge s)ahigh-energygluonfromtheprojectileprotonisscatteredtoacompactcolor
octetheavyQQ¯ pair[1].
1Thecolorfactorin(3)hasaverysimpleexplanation[5]. Theinterferencetermisoftheform∼2TaTa (whereTaand
R R(cid:48) R
Ta arethecolorgeneratorsoftheincomingandoutgoingpartoncolorrepresentationsRandR(cid:48)),whichcanbewrittenas
R(cid:48)
2TRaTRa(cid:48) =(TRa)2+(TRa(cid:48))2−(TRa−TRa(cid:48))2=CR+CR(cid:48)−Ct.
2Intheq→qcase,CR =CF =(Nc2−1)/(2Nc),wehave2CF−Nc <0andtheinducedcoherentenergylossisnegative,
seeRef.[5]foradiscussionandsimpleinterpretationofthisresult.
PhysicsOpportunitiesatanElectron-IonCollider
InRefs.[2,8],coherentenergylossisimplementedasfollows. Thesingledifferentialp–Apro-
ductioncrosssectionasafunctionofthequarkonium(labelledψ)energyreads
1 dσψ (cid:90) εmax dσψ
pA (E)= dε P(ε,E,qˆL) pp (E+ε) , (4)
A dE dE
0
where E (respectively,ε)istheenergy(respectively,energyloss)ofthecompact QQ¯ pairintherest
(cid:16) (cid:17)
frameofthenucleusA.Theupperlimitontheenergylossisεmax =min E,E −E ,whereE isthe
p p
beamenergyinthatframe.Theenergylossprobabilitydistribution,orquenchingweight,P,issimply
related [2] to the induced coherent radiation spectrum for the g → QQ¯ process, which spectrum is
givenbyEq.(3)intheparticularcaseC = C = C = N . Thequenchingweightdependsonthe
(cid:112) R R(cid:48) t c
gluonnuclearbroadening qˆL,withqˆ parametrizedas[2]
(cid:34) 10−2 (cid:35)0.3 1
qˆ ≡qˆ ; x ≡ , (5)
0 min(x ,x ) 0 2m L
0 2 p
√
whereqˆ istheonlyfreeparameterofthemodel,andx = M e−y/ s(withythequarkoniumrapidity
0 2 ⊥
inthecenter-of-massframeofanelementaryproton–nucleoncollision,andM =3GeV(M =9GeV)
for the cc¯ (bb¯) mass in the expression of M ). The parameter qˆ is determined by fitting the J/ψ
⊥ 0 √
suppression measured by E866 [16] in p–W over p–Be collisions ( s = 38.7 GeV), see [2]. The
obtainedvalueisqˆ =0.075+0.015 GeV2/fm. Thep–pproductioncrosssectionappearinginEq.(4)is
0 −0.005
obtainedfromafittop–pmeasurements.
Quite remarkably, all available J/ψ and Υ suppression measurements from fixed-target experi-
ments(SPS,HERA,FNAL)toRHICcouldbedescribedwithintheabovesimplemodelonabroad
kinematicalrangeinrapidityy(or x )[2].3 ThepredictionsforJ/ψandΥsuppressioninp–Pbcolli-
√ F
sionsat s=5.02TeV[2]areshowninFig.3.Ascanbeseen,themodelpredictsaratherstrongJ/ψ
suppressionatforwardrapidity(say,y (cid:38) 3)andaslightenhancementinthemostbackwardrapidity
bins (y < −4). The suppression predicted in the Υ channel shares the same features, however the
suppression is less pronounced than that of J/ψ, since the (average) coherent energy loss scales as
M−1, see Eq. (2). The latter predictions proved to be in excellent agreement with ALICE [17] and
⊥
LHCb[18]data.
(y)RpPb 11..24 p-Pb s = 5 TeV
1
0.8
0.6
0.4
EE.. lloossss JJ//ψψ
0.2 EE.. lloossss ΥΥ
0-5 -4 -3 -2 -1 0 1 2 3 4 5
y
√
Figure3.J/ψandΥsuppressioninp–Pbcollisionsat s=5.02TeVfrominducedcoherentenergyloss[2].
3Asimpleextensionofthemodel(4)todoubledifferentialcrosssectionsdσψpA/dEd2(cid:126)p⊥similarlyyieldsagooddescription
ofthequarkoniumsuppressiondataasafunctionoftransversemomentum[9].
EPJWebofConferences
3.2 Light-hadronsuppressionattheLHC
Coherent energy loss can also be applied to light-hadron production in p–A collisions. The picture
of light-hadron production we use is as follows [19]. In the target rest frame, a projectile parton
i of high energy E scatters on the target and produces a dijet made of two partons, j and k, with
i
approximatelyback-to-backtransversemomenta,|K(cid:126) | (cid:39) |K(cid:126) | ≡ K ,andenergyfractions E /E =
j⊥ k⊥ ⊥ j i
x andE /E =1−x .Thelabel jischosenforthepartonwhichthenfragments(onalongtimescale)
h k i h
intothedetectedhadroncarryingtransversemomentum p =zK andenergyE (cid:39)zx E,wherezis
⊥ ⊥ h i
thefragmentationvariable. Forsimplicityweshallconsideronlythepartonicprocessg → gg(with
singlegluonexchangeinthet-channel),whichdominatesattheLHCatnottoolarge p .
⊥
The dijet may be produced in different color states R. Since in p–A collisions the amount of
inducedcoherentradiationdependsonR(viatheglobalchargeC ), itisconvenienttofirstexpress
R
thep–pproductioncrosssectionofahadronwithenergyEasanincoherentsumovercolorstates,
dσh (E) (cid:88) (cid:90) dσh (E,x )
pp = dx P (x ) pp h , (6)
dE h R h dEdx
R h
whereweintroducedtheprobabilityP forthedijettobeincolorstateR(whichingeneraldependson
R
theenergyfractionx )andused(cid:80) P (x )=1.InEq.(6),thequantitydσh (E,x )/dEdx isformally
h R R h pp h h
thecrosssectiontofindahadronwithenergyE inagluondijetwithenergyfractions x and1−x .
h h
For N = 3,theprobability P (x )fortheg → ggchannelvanishesinthedecuplet, P (x ) = 0,
c R h 10⊕1¯0 h
andtheggdijetcanthusbecolorsinglet,octetorvigintiseptuplet(R=1,8≡8 ⊕8 ,27)[19].
a s
In p–A collisions, the medium-induced coherent radiation does not probe the dijet [7], and thus
leaves unchanged the dijet internal structure, implying that the light-cone energies of the dijet and
its constituents are simply scaled down by a common factor 1+εˆ (with transverse momenta of the
constituents and the dijet invariant mass being unchanged), where εˆ ≡ ε/E is the dijet fractional
i
(light-cone)energyloss. Thus,foreachdijetcolorstateR,thep–Aandp–phadronproductioncross
sectionsarerelatedsimilarlytoEq.(4)inthequarkoniumcase. Using(6)weget
1 dσhpA(E) =(cid:88)(cid:90) dεˆ Pˆ (εˆ)(cid:90) dx P (x )dσhpp(E(1+εˆ),xh), (7)
A dE R h R h dEdx
R h
wherethequenchingweightPˆ (εˆ)isrelatedtotheinducedcoherentradiationspectrumcorresponding
R
totheg→ggprocesswiththefinalcompactgluonpairincolorstateR. Thelatterspectrumisgiven
bytheexpression(3), withC → N ,C → N ,C → C (whereR = 1,8, or27), M → K [7],
R c t c R(cid:48) √ R ⊥ ⊥
andqˆ stillgivenby(5)butwithnow x2 = p⊥e−yg/(xh s)themomentumfractionofthetargetgluon
inthegg→ggsubprocess(viewedintheproton–nucleoncenter-of-massframe,y beingtherapidity
g
inthisframeofthegluonfragmentingintothehadron).
Dividing(7)by(6)givesthenuclearattenuationfactorRh . SinceP (x )isaratherflatfunction
pA R h
ofx [7,19],weapproximateitasaconstantintheintegrandof(7),andwilleventuallyvaryx within
h h
arealisticrangeinordertoevaluatetheassociatedtheoreticaluncertainty. Thus,
1 dσh (E)/dE (cid:88) (cid:90) dσh (E(1+εˆ))/dE
Rh (E)≡ pA (cid:39) P (x )RR(E); RR(E)≡ dεˆ Pˆ (εˆ) pp , (8)
pA A dσh (E)/dE R h R dσh (E)/dE
pp R pp
whereRR(E)isthenuclearsuppressionfactorofahadronproducedfromaparentdijetincolorstate
R. As anticipated in [7], the hadron suppression factor Rh(E) is the average of the RR’s over the
accessibledijetcolorrepresentations,weightedbythecorrespondingprobabilitiesP (x ).
R h
PhysicsOpportunitiesatanElectron-IonCollider
Reloss11..46 h– y=0 z=0.7 xh=0.5 s = 5.02 TeV Rbroad1.28 h– y=0 z=0.7 xh=0.5 s = 5.02 TeV RpPb 11..46 h– y=0 s = 5.02 TeV
1.6
1.2 1.2
1.4
1 1.2 1
0.8 1 0.8
0.6 0.8 0.6
00..24 RRRRe1e8e2elll7loooossssssss 000...246 RRRRb1b8b2brrr7rooooaaaadddd 00..24 ACEL.M IloCSs E(s1 (+51 04b20ro.50a.52d37. 83(707).)6 < z < 0.8, 0.2 < xh < 0.8)
01 2 3 4 5 6 7 8 9 10 01 2 3 4 5 6 7 8 9 10 01 2 3 4 5 6 7 8 9 10
p (GeV) p (GeV) p (GeV)
T T T
√
Figure4. Nuclearattenuationfactorofchargedhadronsinp–Pbcollisionsat s = 5TeVincludingtheeffect
ofcoherentenergylossonly(left)andnuclearbroadeningonly(middle)fordifferentdijetcolorrepresentations,
andincludingbotheffects(right)aspredictedinthemodel(band)andmeasuredbyALICE[20]andCMS[21].
InsteadofthevariablesE andεˆ,wecanequivalentlychoosethehadronrapidityy(inthecenter-
of-mass frame of the proton–nucleon collision) and the rapidity shift δ ≡ ln(1+εˆ). Making the
dependenceonthehadrontransversemomentum p explicit,wecanrewrite(8)as
⊥
Rh (y,p )(cid:39)(cid:88) P (x )RR(y,p ); RR(y,p )=(cid:90) δmaxd(yδ) Pˆ (x)dσhpp(y+δ,p⊥)/dydp⊥ . (9)
pA ⊥ R h ⊥ ⊥ R dσh (y,p )/dydp
R 0 pp ⊥ ⊥
√
Here,x≡eδ−1andδ (y)=min(ln2,y −y)wherey =ln( s/p ).
max max max ⊥
The sole effect of parton energy loss is encoded in Eq. (9). In addition to energy loss, p -
⊥
broadening can be simply implemented by shifting (cid:126)p by the nuclear broadening ∆(cid:126)p when ex-
⊥ ⊥
pressing the double differential p–A cross section in terms of that in p–p, as was done in Ref. [9].
When |∆(cid:126)p | (cid:28) K , nuclear broadening cannot resolve the dijet, and is thus transferred to the dijet
⊥ ⊥
as a whole. Consequently, all dijet constituents undergo the same rotation of ‘angle’ ∆(cid:126)p /E. The
⊥ i
fragmenting gluon and the tagged hadron respectively acquire a transverse momentum shift x ∆(cid:126)p
h ⊥
andzx ∆(cid:126)p . Takingintoaccounttheeffectof p -broadeningmodifies(9)to
h ⊥ ⊥
Rh (y,p )(cid:39)(cid:88) P (x )RR(y,p ); RR(y,p )=(cid:90) δmaxd(yδ) Pˆ (x)(cid:90) dϕ dσhpp(y+δ+dδy(cid:48),d|(cid:126)pp⊥⊥−zxh∆(cid:126)p⊥R|) , (10)
pA ⊥ R R h ⊥ ⊥ 0 R 2π dσhpp(y,p⊥)
dydp⊥
where∆(cid:126)pR (ofazimutalangleϕ)isthebroadeningofthedijetincolorstateR,andtherapidityshift
⊥
δ(cid:48)inducedbythebroadeningreadsδ(cid:48) ≡ln(p /|(cid:126)p −zx ∆(cid:126)pR|).4
⊥ ⊥ h ⊥
InordertocomputeRh forchargedhadronproductionattheLHC,wedeterminedσh /dydp
pPb pp ⊥
from a fit to 7 TeV p–p data. The fragmentation variable z and the dijet momentum fraction x are
h
chosen as z = 0.7 and x = 0.5 in average (based on estimates from perturbative calculations) but
h
allowedtovaryintherange0.6<z<0.8and0.2< x <0.8.
h
Wedefinetheattenuationfactors R andR obtainedfrom(10)andcorrespondingrespec-
eloss broad
tively to the effect of energy loss only, and of nuclear broadening only. In Fig. 4 (left) we compute
√
RR inp–Pbcollisionsat s=5TeV,fortheaccessiblerepresentationsRoftheparentdijet,aswell
eloss
4Thebroadening∆(cid:126)pRisgivenby,inaverage,(∆(cid:126)pR)2 = Nc+CR(qˆL−qˆ L ). Thecolorfactorarisesfromtheaveragedijet
colorchargeinthenucle⊥us(Nc+CR)/2(sincethedije⊥tenters2tNhcenucleuspwipthchargeNcandexitswithchargeCR)andafter
normalizationbythegluonchargeNc(recallthatqˆisthegluontransportcoefficient).
EPJWebofConferences
as for the color average R = (cid:80) P (x )RR , for z = 0.7 and x = 0.5. As can be seen, energy
eloss R R h eloss h
loss leads to a moderate suppression at low p for R = 8 and slightly more pronounced for R = 27
⊥
duetothelargerCasimirfactor. (ThereisnocoherentenergylossinthesingletchannelR = 1.) An
opposite trend is reported in Fig. 4 (middle) regarding RR : the higher the color representation R,
broad
the stronger the enhancement at small p . Energy loss and nuclear broadening effects thus tend to
⊥
balance each other. In this respect, the rapidity dependence of Rh for charged hadrons (inclusive
pPb
in p ≥ pcut ∼ 1GeV)wouldbeinteresting,sinceitisexpectedtobemostlydrivenbyenergyloss.
⊥ ⊥
TheattenuationfactorRh includingbothcoherentenergylossandnuclearbroadeningisshownin
pPb
Fig.4(right). Althoughthetheoreticaluncertainty,resultingfromthevariationofqˆ , x andzonthe
0 h
one hand and from the shape of the p–p cross section on the other hand, is rather large, the model
predictioniscompatiblewithALICE[20]andCMS[21]data.
Moredetailsonthepresentapproachwillfollowinaforthcomingpublication.
4 Outlook
Investigating further coherent energy loss in p–A collisions, in addition to its theoretical interest,
should also help disentangling hot from cold nuclear effects in nucleus-nucleus (A–A) collisions.
Indeed, the sole effect of coherent energy loss in cold nuclear matter, when extrapolated to A–A
collisions,hasbeenshowntoyieldasignificantJ/ψnuclearsuppression[22]. Thisstressestheneed
to fully understand quarkonium/hadron nuclear suppression in p–A collisions before extracting the
additionalhoteffectsexpectedinA–Acollisions.
References
[1] F.Arleo,S.PeignéandT.Sami,Phys.Rev.D83,114036(2011).
[2] F.ArleoandS.Peigné,JHEP1303,122(2013).
[3] N.Armestoetal.,Phys.Lett.B717,280(2012).
[4] N.Armestoetal.,JHEP1312,052(2013).
[5] F.Arleo,R.KolevatovandS.Peigné,Phys.Rev.D93,014006(2016).
[6] T.LiouandA.H.Mueller,Phys.Rev.D89,no.7,074026(2014).
[7] S.PeignéandR.Kolevatov,JHEP1501,141(2015).
[8] F.ArleoandS.Peigné,Phys.Rev.Lett.109,122301(2012).
[9] F.Arleo,R.Kolevatov,S.PeignéandM.Rustamova,JHEP1305,155(2013).
[10] S.GavinandJ.Milana,Phys.Rev.Lett.68,1834(1992).
[11] S.PeignéandA.V.Smilga,Phys.Usp.52,659(2009)[Usp.Fiz.Nauk179,697(2009)].
[12] R.Baieretal.,Nucl.Phys.B483,291(1997).
[13] B.G.Zakharov,JETPLett.65,615(1997).
[14] B.G.Zakharov,JETPLett.73,49(2001)[PismaZh.Eksp.Teor.Fiz.73,55(2001)].
[15] M.Gyulassy,P.LevaiandI.Vitev,Nucl.Phys.B594,371(2001).
[16] M.J.Leitchetal.[NuSeaCollaboration],Phys.Rev.Lett.84,3256(2000).
[17] B.B.Abelevetal.[ALICECollaboration],JHEP1402,073(2014).
[18] R.Aaijetal.[LHCbCollaboration],JHEP1402,072(2014).
[19] F.Arleo,R.KolevatovandS.Peigné,workinprogress.
[20] B.B.Abelevetal.[ALICECollaboration],Eur.Phys.J.C74,no.9,3054(2014).
[21] V.Khachatryanetal.[CMSCollaboration],Eur.Phys.J.C75,no.5,237(2015).
[22] F.ArleoandS.Peigné,JHEP1410,73(2014).