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DOI: 10.1016/j.physletb.2019.134926
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by Elsevier. All rights reserved.
DIRETORIA DE TRATAMENTO DA INFORMAÇÃO
Cidade Universitária Zeferino Vaz Barão Geraldo
CEP 13083-970 – Campinas SP
Fone: (19) 3521-6493
http://www.repositorio.unicamp.br
Physics
Letters
B
www.elsevier.com/locate/physletb
Coherent
J
/ψ
photoproduction
at
forward
rapidity
in
ultra-peripheral
Pb–Pb
collisions
at
√
s
NN
=
5
.
02 TeV
.
ALICE
Collaboration
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received19April2019
Receivedinrevisedform15August2019 Accepted6September2019
Availableonline10September2019 Editor:M.Doser
TheALICEcollaborationperformedthefirstrapidity-differentialmeasurementofcoherentJ/ψ photopro-ductioninultra-peripheralPb–Pb collisions atacenter-of-massenergy√sNN = 5.02 TeV.TheJ/ψ is
detectedviaitsdimuondecayintheforward rapidityregion(−4.0<y<−2.5) foreventswherethe hadronicactivityisrequiredtobeminimal.Theanalysisisbasedonaneventsamplecorrespondingto anintegratedluminosityofabout750 μb−1.ThecrosssectionforcoherentJ/ψ productionispresented
insixrapiditybins.TheresultsarecomparedwiththeoreticalmodelsforcoherentJ/ψphotoproduction. Thesecomparisonsindicatethatgluonshadowingeffectsplayaroleinthephotoproductionprocess.The ratio ofψ to J/ψ coherentphotoproduction crosssections was measuredandfound tobeconsistent withthatmeasuredforphotoproductionoffprotons.
©2019TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Ultra-peripheral collisions (UPC) between two Pb nuclei, in whichtheimpactparameterislargerthan thesumoftheir radii, providea usefulwaytostudyphotonuclear reactions [1–4]. Pho-toproduction of vector mesons in these collisions has an easily identifiableexperimentalsignature:thedecayproductsofthe vec-tormeson,inthecaseofthisanalysisa
μ
+μ
− pair,aretheonly signalsinanotherwiseemptydetector.Thisprocessisakinto ex-clusivevector mesonproductioninelectron–proton collisions, al-readystudiedextensivelyatHERA [5].Theexchangephoton,which carriesamomentumtransfersquaredQ2,istypifiedbyverysmallvaluesofQ2,andmaybedescribedasquasi-real.Theintensityof thephotonfluxscalesasthesquareofnuclearchargeresultingin large crosssections forthe photoproduction ofvector mesons in Pb–Pb collisionsat theCERN LargeHadron Collider(LHC),where themeasurementpresentedinthisLetterwasperformed.
Photoproductionof vectormesons onnucleican beeither co-herent, where the photon couples coherently to the nucleus as a whole, or incoherent, where the photon couples to a single nucleon [2]. Coherent production is characterized by low vector mesontransverse momentum (
pT60 MeV/c) and by thetar-getnucleusnotbreakingup.Incoherentproduction,corresponding to quasi-elastic scattering off a single nucleon, is characterized byasomewhathigheraveragetransversemomentum(
pT500MeV/c).The target nucleusnormallybreaks up inthe incoherent production,but, except for single nucleons or nuclear fragments
E-mailaddress:alice-publications@cern.ch.
in the very forwardregion, no other particles are produced. The incoherentproduction canbe accompanied by theexcitation and dissociationof the target nucleonresulting ineven higher trans-verse momenta of the produced vector mesons, extending well above1 GeV/c [6].
Coherent photoproduction of the J
/ψ
meson, a charm-anti-charm bound state, is of particular interest since, for a leading order QCD calculation [7], its cross section is expected to scale as the square of the gluon parton density function (PDF) in the target hadron. The mass of the charm quark provides an energy scalelargeenough toallowforperturbativeQCD calculations.For thisprocess,a variablecorrespondingtoBjorken-x canbedefined using the mass of the vector meson (mJ/ψ) and its rapidity ( y)asx
= (
mJ/ψ/
√
sNN)
exp(
±
y).Thoughnext-to-leadingordereffectsandscale uncertainties complicate extractionof gluon PDFsfrom J
/ψ
photoproduction data [8], the related uncertainties are ex-pected tolargely cancelin theratioof coherentphotoproduction cross sections off nucleiand off protons [9]. Thus, coherent J/ψ
photoproduction off lead nuclei (
γ
+
Pb→
J/ψ
+
Pb) provides a powerful tool to studypoorly known gluon shadowing effects at low Bjorken-x values ranging from x∼
10−5 to x∼
10−2 at LHC energies [10,11].The ALICE collaboration has pioneered the study of charmo-nium photoproduction in ultra-peripheral Pb–Pb collisionsat the LHCatacenter-of-massenergypernucleonpair
√
sNN=
2.
76 TeV[12–14]. Coherent J
/ψ
photoproduction was studied both at for-wardrapidity (−
3.
6<
y<
−
2.
6) withtheALICEmuon spectrom-eter and at mid-rapidity (|
y|
<
0.
9) with the central barrel. The CMS collaboration studied coherent J/ψ
photoproductionaccom-https://doi.org/10.1016/j.physletb.2019.134926
0370-2693/©2019TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
panied by neutron emission in the semi-forward rapidity range 1
.
8<
|
y|
<
2.
3 [15]. The ALICE and CMS results on J/ψ
photo-productionwerecomparedwithpredictionsfrommodelsavailable atthat time, andsuggested that moderateshadowing inthe nu-cleus was necessary to describe themeasurements. In particular, thenucleargluonshadowingfactorRg,i.e.theratioofthenuclear gluondensitydistributiontotheprotongluondistribution,was ex-tracted from the ALICE measurements [10], and found to be, at thescaleofthecharmquark mass, Rg(x
∼
10−3)
=
0.
61+−00..0504 andRg
(x
∼
10−2)
=
0.
74−+00..1112.The ALICEcollaboration also measuredthecoherentcrosssectionfor
ψ
photoproductionatmid-rapidity, andtheresults supported, within theexperimental uncertainties, themoderate-shadowingscenario [14].InthisLetter, we presentthefirst measurementof the coher-entJ
/ψ
photoproduction inultra-peripheral Pb–Pb collisionsata center-of-mass energyper nucleon pair√
sNN=
5.
02 TeV. Themeasurement was performedwiththe ALICEmuon spectrometer coveringtherapidityrange
−
4.
0<
y<
−
2.
5.Theresultspresented herearebasedon datatakenin2015andin2018, duringRun 2 of the LHC. The recorded data sample is some 200 times larger thanthedatausedinthe√
sNN=
2.
76 TeVPb–Pb analysis [12].Thenewresultisbasedontheabsoluteluminosity normalization incontrast toprevious measurement based onthe normalization relative to the continuum
γ γ
→
μ
+μ
− cross section predicted by STARlight [16]. Thesetwo improvements implya considerable reduction in the statistical and systematic uncertainties and the possibilitytostudytherapiditydependenceintheforwardregion. 2. DetectordescriptionThe ALICE detector and its performance are described in [17,18]. Muonsfrom J
/ψ
decays are measured in the single-arm muonspectrometer,whileotheractivityisvetoedusingtheSilicon Pixel Detector (SPD), the V0 and ALICE Diffractive (AD) detec-tors. The muon spectrometer covers the pseudorapidity interval−
4.
0<
η
<
−
2.
5.It consistsof a teninteraction length absorber followed by five tracking stations, the third of which is placed inside a dipole magnet with a 3 T·
m integrated magnetic field, a 7.2 interaction length iron wall, and a trigger system located downstreamoftheironwall.Eachtrackingstationismadeoftwo planesofcathodepadchambers,whilethetriggersystemconsists offourplanesofresistiveplatechambersarrangedintwostations. Muon tracks are reconstructed using the tracking algorithm de-scribedin [19].Thecentralregion|
η
|
<
1.4iscoveredbytheSPD consisting of two cylindrical layers of silicon pixel sensors. The V0detectoriscomposed ofthe V0AandV0Csub-detectors, con-sisting of 32 cells each andcovering the pseudorapidity interval 2.
8<
η
<
5.
1 and−
3.
7<
η
<
−
1.
7, respectively. The newly in-stalledADdetectoriscomposedoftheADCandADAsub-detectors locatedat−
19.
5 and+
16.
9 mfromtheinteractionpointcovering thepseudorapidityranges−
7.
0<
η
<
−
4.
9 and 4.
7<
η
<
6.
3, re-spectively [20].TheV0andADdetectorsarescintillatortilearrays withatimeresolutionbetterthan1ns,allowingonetodistinguish betweenbeam-beamandbeam-gasinteractions.3. Dataanalysis
Theanalysispresentedinthispublicationisbasedonasample ofevents collected during the 2015and 2018Pb–Pb data taking periodsat
√
sNN=
5.
02 TeV,characterizedbysimilarbeamcon-ditionsandinteractionrates.Themuonspectrometerperformance wasstableduringthewholeRun 2thusallowingforthemerging ofthetwo datasets.Thetrigger requiredtwooppositely charged tracks in the muon spectrometer, and vetoes on V0A, ADA and ADC beam-beam interactions. The single muon trigger threshold
was set to a transversemomentum pT
=
1 GeV/c [21]. Theinte-grated luminosities of 216 μb−1 in2015 and538 μb−1 in2018, with relative systematic uncertainty of 5%, were estimated from the counts of a reference trigger, based on multiplicity selection intheV0detector.Thereferencetriggercrosssectionwasderived from Glauber-model-based estimatesof the inelastic Pb–Pb cross section [22].
Events with only two tracks with opposite electric charge (unlike-sign)inthemuon spectrometerwereselected offline.The pseudorapidity ofeachtrackwas requiredto bewithin therange
−
4.
0<
η
<
−
2.
5. The tracks hadto fulfill the requirements, de-scribedin [12],ontheradialcoordinateofthetrackattheendof theabsorberandontheextrapolationtothenominalvertex.Track segmentsinthetrackingchambershadtobematchedwith corre-spondingsegmentsinthetriggerchambers.Additional offline vetoes on the V0A, ADA and ADC detector signals were applied to ensure the exclusive production of the muon pair. Exclusivity in the muon spectrometer region was as-suredbyrequiringamaximumof2firedcellsinV0C.Onlineand offline veto requirements may result in significant inefficiencies (denoted as veto inefficiencies) in the exclusive J
/ψ
cross sec-tion measurementsduetoadditional V0andAD detectoractivity induced byindependenthadronicorelectromagneticpile–up pro-cessesaccompanyingthecoherentJ/ψ
photoproduction.The prob-abilityofhadronicpile–updidnotexceed0.
2%,howevertherewas a significant pile–up contribution fromthe electromagnetic elec-tron pair production processγ γ
→
e+e−. The veto inefficiency induced by thesepile–up effectsin the V0A,V0C, ADA andADC detectors, was estimated using the events selected with an un-biased trigger based only on the timing of bunches crossing the interaction region. The veto rejection probability, defined as the probability todetect activityinthesesub-detectors, wasfound to scale linearlywith the expected number of collisions per bunch crossingreaching10%inV0A.Thevetoinefficiencycorrection fac-tors were determinedby weightingthe correspondingveto rejec-tion probabilities over periods with different pile–up conditions, taking the luminosity of each period as a weight. The veto in-efficiency of the V0A online and offline selection was found to be pV0A= (
4.
6±
0.
2)
%, where the uncertainty is related to thelimited statistics in the unbiased trigger sample. The veto ineffi-ciencies in ADA (pADA) and ADC(pADC) were found to be about
0
.
2%, because these detectors are far away from the interaction pointandarethusmuchlessaffectedbysofte+e− pairs.Theveto inefficiency inV0C,associatedwiththerequirementofmaximum 2 fired cells, was found to be negligible. The average veto effi-ciency correction factorveto
=
95.
0%, and thisis applied to rawJ
/ψ
yields to account for hadronic and electromagnetic pile–up processes,wascalculatedasaproductofindividualveto inefficien-ciesveto
= (
1−
pV0A)(
1−
pADA)(
1−
pADC)
.The acceptance and efficiency of J
/ψ
andψ
reconstruction were evaluated using a large sample of coherent andincoherent J/ψ
andψ
events generated by STARlight2.2.0 [23] withdecay muonstrackedinamodeloftheapparatusimplementedinGEANT 3.21 [24]. Themodelincludesarealistic descriptionofthe detec-tor performance during datataking as well as its variation with time.Theacceptanceandefficiencyoffeed-downψ
→
J/ψ
+
π π
decays were also evaluated using the STARlight generator under theassumptionthatfeed-downJ/ψ
mesonsinheritthetransverse polarizationoftheirψ
parents,asindicatedbyprevious measure-ments [25]. The same samples were also used for modeling the signalshapeanddifferentbackgroundcontributions.A sample enriched in coherent candidates was obtained by selecting dimuons with transverse momentum pT
<
0.
25 GeV/c.The invariant mass distributions for selected unlike-sign muon pairs are shown in Fig. 1, left, in the full dimuon rapidity range
Fig. 1. Left:invariant massdistributionformuonpairssatisfyingtheeventselectiondescribedinthetext.Thedashedgreenlinecorrespondstothebackground.Thesolid magentaandredlinescorrespondtoCrystalBallfunctionsrepresentingJ/ψandψsignals,respectively.Thesolidbluelinecorrespondstothesumofbackgroundandsignal functions.Right:transversemomentumdistributionformuonpairsintherange2.85<mμμ<3.35 GeV/c2(aroundtheJ/ψmass).
−
4.
0<
y<
−
2.
5 and inFig. 2 insixrapidity subranges. The in-variantmassdistributionsare fittedwithafunctionmodelingthe backgroundandtwoCrystalBallfunctions [26] fortheJ/ψ
andtheψ
peaks.Theshapeofthebackgroundatlargeinvariantmassesis welldescribed by an exponentialdistribution, asexpectedifitis dominatedby theprocessγ γ
→
μ
+μ
−.However, atmasses be-low theJ/ψ
,the distribution isstrongly influencedby the muon trigger condition. In order to model this, the whole background distribution is fitted using a template made from reconstructed STARlighteventscorresponding totheγ γ
→
μ
+μ
− process. The resultsofthefitareparametrizedusingafourth-orderpolynomial, whichturns smoothly into an exponential tailasfrom 4 GeV/c2.Thecoefficientsofthepolynomialarethenkeptfixedinthefitto theexperimentaldata,whiletheslopeoftheexponentialtermand thenormalizationare left free.The fittedslope isfound toagree within 2.5standard deviations withthe value obtained fromthe generatedsample.
TherawinclusiveJ
/ψ
andψ
yields, N(J/ψ)
andN(ψ
)
,were obtained by fitting the dimuon invariant mass spectrum in the range 2.
2<
mμμ<
6 GeV/c2. The slope parameters in theCrys-tal Ball functions were fixed from fits to the respective Monte Carlo sets. The width parameter
σ
J/ψ was left free for the J/ψ
,andwas fixed to
σ
ψ=
σ
J/ψ· (
σ
ψMC/
σ
JMC/ψ)
for theψ
, where theratio
σ
MCψ
/
σ
MC
J/ψ
∼
1.
09 of theψ
totheJ/ψ
widths wasobtainedfromthefitstocorrespondingMonteCarlosets.Themass parame-teroftheCrystalBallfunctionwasleftunconstrainedfortheJ
/ψ
. Duetothe smallψ
statistics,theψ
mass wasfixed sothat the differencewithrespecttotheJ/ψ
massisthesameasquoted by thePDG [27]. The J/ψ
massmJ/ψ=
3.
0993±
0.
0009 GeV/c2,ob-tainedfromthefit inthefull rapidity range
−
4.
0<
y<
−
2.
5,is inagreementwiththePDGvaluewithin3standarddeviations.TherawinclusiveJ
/ψ
yields obtainedfrominvariant massfits containcontributionsfromthecoherentandincoherentJ/ψ
pho-toproduction,whichcanbeseparatedintheanalysisoftransverse momentumspectra.The pT distributionsfordimuonsintherange2
.
85<
mμμ<
3.
35 GeV/c2 are shownin Fig. 1,right, in the full dimuon rapidity range−
4.
0<
y<
−
2.
5 and in Fig. 3 in six ra-piditysubranges.ThesedistributionswerefittedwithMonteCarlo templates produced using STARlight, corresponding to different productionmechanisms:coherentJ/ψ
,incoherentJ/ψ
,feed-down J/ψ
fromcoherentψ
decays,feed-downJ/ψ
fromincoherentψ
decaysandcontinuumdimuonsfromthe
γ γ
→
μ
+μ
−process.Inorder to describe the high-pT tail, the incoherentJ
/ψ
photopro-ductionaccompanied bynucleon dissociationwasalso takeninto accountinthefitswiththetemplatebasedontheH1 parametriza-tionofthedissociativeJ
/ψ
photoproduction [28] (denotedas dis-sociativeJ/ψ
inthefollowing):dN dpT
∼
pT 1+
bpd npd p2T −npd.
(1)The H1 collaboration provided two sets of measurements corre-spondingtodifferentphoton–protoncenter-of-massenergyranges: 25 GeV
<
W γp<
80 GeV (low-energy data set) and 40 GeV<
W γp
<
110 GeV (high-energy dataset). The fit parametersbpd=
1
.
79±
0.
12(
GeV/c)
−2andnpd
=
3.
58±
0.
15 fromthehigh-energydata set were used by default, while the corresponding uncer-taintiesandthelow-energyvaluesbpd
=
1.
6±
0.
2(
GeV/c)
−2 andnpd
=
3.
58(
fixed)
wereusedforsystematicchecks.The templates were fitted to the data leaving the normaliza-tion free for coherent J
/ψ
, incoherent J/ψ
and dissociative J/ψ
production.Thenormalizationofthe
γ γ
→
μ
+μ
− spectrumwas fixed to the one obtainedfrom the invariant mass fits. The nor-malization of the coherent and incoherent feed-down J/ψ
tem-plates was constrained to thenormalization ofprimary coherent and incoherent J/ψ
templates, according to the feed-down frac-tions extractedfrom the measurement ofraw inclusive J/ψ
andψ
yields,asdescribed below.The extractedincoherentJ/ψ
frac-tion fI=
NN(incoh J(coh J/ψ )/ψ ) forpT<
0.
25 GeV/c rangesfrom(
4.
9±
0.
6)
%to
(
6.
4±
0.
8)
% depending on the rapidity interval andis consis-tent withbeingconstant within theuncertainties ofthe fits.The contributionofincoherentJ/ψ
withnucleondissociationwas also takenintoaccountinthisfraction.4. Resultsanddiscussion
4.1. Ratioofcoherent
ψ
andJ/ψ
crosssectionsTheobtaineddimuoninvariantmassspectracanbeusedto ex-tract theratio of coherent
ψ
andJ/ψ
cross sections R=
σσ((ψJ/ψ ))andthefractionoffeed-downJ
/ψ
fromψ
decaysintherawJ/ψ
yields.Thefitstotheinvariantmassdistributionsfordimuonswith pair pT
<
0.
25 GeV/c in thefull rapidity range−
4.
0<
y<
−
2.
5resultinthefollowingratioofthemeasuredrawinclusive
ψ
and J/ψ
yields:Fig. 2. Invariant mass distributions in six rapidity bins for muon pairs satisfying the event selection described in the text.
RN
=
N
(ψ
)
N
(
J/ψ )
=
0.
0250±
0.
0030(
stat.),
(2) The rawψ
and J/ψ
yields in thisratiocontain contributions both fromcoherentandincoherentψ
and J/ψ
photoproduction. However, according to the dimuon pT fits, the fraction fI ofin-coherentJ
/ψ
inthe rawJ/ψ
yields doesnot exceed 6% and, ac-cordingtoSTARlight [23] andcalculationswithinthecolordipole approach [29],thefractionofincoherentψ
intherawψ
yieldsis expectedtobesimilar.TheRN ratiocanthereforebeconsideredas agoodestimate oftheratioofcoherentJ/ψ
andψ
yields,since theincoherentfractionsofψ
andJ/ψ
yieldslargelycancelintheratio. Besides, the raw J
/ψ
yields contain significant feed-down contributioncomingfromψ
→
J/ψ
+
anything decays.Takinginto account thisfeed-downcontribution,one can expressthe RN ra-tiointermsofprimarycoherentψ
andJ/ψ
photoproductioncross sectionsσ
(ψ
)
andσ
(
J/ψ)
integratedoveralltransversemomenta intherapidityrange−
4.
0<
y<
−
2.
5:RN
=
σ(ψ)B R(ψ→μμ)(ψ)σ(J/ψ )B R(J/ψ→μμ)(J/ψ )+σ(ψ)B R(ψ→J/ψ )(ψ→J/ψ )B R(J/ψ→μμ)
Fig. 3. Transverse momentum distributions in six rapidity intervals for muon pairs satisfying the event selection described in the text. where
(
J/ψ)
=
12.
0%,(ψ
)
=
15.
8% and(ψ
→
J/ψ)
=
7.
2%are the efficiency corrections for primary coherent J
/ψ
,ψ
and feed-downJ/ψ
fromcoherentψ
decaysestimatedwithSTARlight, whileB R(J/ψ
→
μμ
)
= (
5.
961±
0.
033)
%, B R(ψ→
μμ
)
= (
0.
80±
0.
06)
%, B R(ψ→
J/ψ
+
anything)
= (
61.
4±
0.
6)
% are the corre-spondingbranchingratios [27].Equation (3) canbeusedtoexpress theratio of primary coherentψ
andJ/ψ
photoproductioncross sections,R,intermsofthemeasuredyieldratioRN:R
=
RNB R(J/ψ→μμ)(J/ψ )B R(ψ→μμ)(ψ)−RNB R(ψ→J/ψ )(ψ→J/ψ )B R(J/ψ→μμ)
(4)
Substituting the measured RN value from Eq. (2) and the corre-spondingefficiencyvaluesandbranchingratios,onegets:
R
=
0.
150±
0.
018(
stat.)
±
0.
021(
syst.)
±
0.
007(
BR),
(5)where the uncertainties on branching ratios B R(J
/ψ
→
μμ
)
andB R(ψ
→
μμ
)
were addedinquadrature,whilethemainsources of systematic uncertainties are the variation of the fit range, of the signal andbackground shapes, andofthe dimuon transverse momentumcut.The measured ratio ofthe
ψ
and J/ψ
cross sectionsis com-patiblewiththeexclusivephotoproductioncrosssectionratio R=
Table 1
J/ψyields,efficiencies, fIand fDfractionsandcoherentJ/ψcrosssections.
Rapidity range NJ/ψ fD fI dσJcoh/ψ/d y (mb)
(−4.00,−2.50) 21747±190 0.120 0.055 0.055±0.001 2.549±0.022(stat.)+−00..209237(syst.) (−4.00,−3.75) 974±36 0.051 0.055 0.064±0.008 1.615±0.060(stat.)+0.135 −0.147(syst.) (−3.75,−3.50) 3217±70 0.140 0.055 0.058±0.004 1.938±0.042(stat.)+−00..166190(syst.) (−3.50,−3.25) 5769±98 0.204 0.055 0.060±0.003 2.377±0.040(stat.)+−00..212229(syst.) (−3.25,−3.00) 6387±105 0.191 0.055 0.052±0.002 2.831±0.047(stat.)+0.253 −0.280(syst.) (−3.00,−2.75) 4229±85 0.119 0.055 0.049±0.003 3.018±0.061(stat.)+−00..259294(syst.) (−2.75,−2.50) 1190±47 0.029 0.054 0.049±0.006 3.531±0.139(stat.)+−00..294362(syst.)
H1collaborationinep collisions [30] andwiththeratio R
≈
0.
19 measured by the LHCb collaboration in pp collisions [31]. The measured ratio also agrees with predictions based on the Lead-ing Twist Approximation [32] for Pb–Pb UPC ranging from 0.13 to 0.18 depending on the model parameters. Theψ
-to-J/ψ
co-herentcross section ratioisexpectedtohavea mild dependence onthecollisionenergyandvectormesonrapidity [32] (at mosta few percent). Therefore the measured ratio can be directly com-pared to the unexpectedly largeψ
-to-J/ψ
coherent cross sec-tion ratio 0.
34+−00..0807, measured by ALICE in theψ
→
l+l− andψ
→
l+l−π
+π
− channels at central rapidity in Pb–Pb UPC at√
sNN
=
2.
76 TeV [14].Theratioatcentral rapidityismorethana factortwo larger butstill stays compatiblewithin 2.5standard deviationswiththe forwardrapiditymeasurement, owingmainly tothelargeuncertaintiesofthecentralrapiditymeasurementthat willbeimprovedbytheanalysisofthemuchlargerUPCdata sam-plecollectedwiththeALICEcentralbarrelinRun2.
ThemeasuredcrosssectionratioR wasusedtoextractthe frac-tionoffeed-downJ
/ψ
fromψ
relativetotheprimaryJ/ψ
yield:fD
=
N(
feed-down J/ψ )
N(
primary J/ψ )
=
R(ψ
→
J/ψ)
(
J/ψ )
B R(ψ
→
J/ψ )
(6)The fraction fD
=
8.
5%±
1.
5% was obtained forthe full rapidityrangewithoutanypTcut,wherestatistical,systematicand
branch-ingratiouncertainties wereaddedinquadrature.Thefraction re-ducesto fD
=
5.
5%±
1.
0% forpT<
0.
25 GeV/c becausefeed-downJ
/ψ
are characterized by wider transverse momentum distribu-tionscomparedtoprimaryJ/ψ
.4.2. CoherentJ
/ψ
crosssectionThecoherentJ
/ψ
differentialcrosssectionisgivenby:d
σ
Jcoh/ψdy
=
N
(
J/ψ)
(
1+
fI+
fD)
(
J/ψ)
BR(
J/ψ
→
μμ
)
vetoLint
y (7)
TherawJ
/ψ
yieldvalues,efficiencies, fI and fD fractionsandco-herent J
/ψ
cross sectionswithrelevantstatistical andsystematic uncertainties are summarized in Table 1. The associated system-aticuncertaintiesarebrieflydescribedinthefollowing.Thefirstsourceofsystematicuncertaintyisrelatedtothe sep-arationofperipheral andultra-peripheral collisions.Coherent-like J
/ψ
photoproduction, observed in peripheral collisions of heavy ions [33],maycontributeafew percenttotherawJ/ψ
yields in casehadronicactivityisnotdetectedbytheV0andADdetectors. In order to reduce a possible contamination from J/ψ
produced inperipheral hadronicevents, theanalysiswas repeatedwithan additionalrequirementthattherebenotrackletsdetectedat mid-rapidity in theSPD (where a trackletis a segment formedby at leastonehitineachofthetwodetectorlayers),resultingin12.6% to 15.0% lower J/ψ
yields depending on the rapidity range. The vetoinefficiency associated withthis additionalSPD requirementwasestimatedwithunbiasedtriggerssimilartowhatwasdonefor the V0and AD vetoinefficiencies. The averagefraction ofevents withatleastoneSPDtrackletwasfoundtobe pSPD
=
9.
4±
0.
2%.TheyieldscorrectedfortheadditionalSPDvetoinefficiencyof9.4% resultincrosssections3.6%to6.0%lowerthantheonesobtained without the SPD veto. This cross section difference is taken into accountinthesystematicuncertainty.
The systematic uncertainties on the efficiencies obtained by variationofthegeneratedrapidityshapesrangefrom0.1%to0.8%, depending on therapidity interval. The trackingefficiency uncer-taintyof3%wasestimatedbycomparingthesingle-muontracking efficiencyvalues obtainedinMC anddata, witha procedure that exploitstheredundancyofthetracking-chamberinformation [34]. The systematic uncertainty on the dimuon trigger efficiency has two origins: the intrinsic efficiencies of the muon trigger cham-bersandtheresponse ofthetrigger algorithm.Thefirst onewas determined byvarying thetriggerchamberefficiencies intheMC byanamountequaltothestatisticaluncertaintyontheir measure-mentwithadata-drivenmethodandamountsto1.5%.Thesecond onewasestimatedbycomparingthetriggerresponsefunction be-tweendataandMC,resultinginefficiencydifferencesrangingfrom 5% to6%depending ontherapidityinterval.Finally,thereisa1% contributionrelatedtothe precisionrequiredtomatchtrack seg-mentsreconstructedinthetrackingandtriggerchambers.
Severaltestswereperformedtoestimatetheuncertaintyonthe raw J
/ψ
signal extraction. These include the uncertainty on the J/ψ
signalshapeestimatedbyfittingtheCrystalBallslope param-eters instead of fixing them fromMonte-Carlo templates andby replacing the single-sided Crystal Ball witha double-sided Crys-talBallfunction.Thevariationofthecontinuumbackgroundshape duetothe uncertaintyonthetriggerresponse function,variation oftheinvariantmassintervalsby±
0.
1 GeV/c2 andofthedimuonpT selectionby
±
0.
05 GeV/c werealsoconsidered.Thesystematicuncertaintyon therawJ
/ψ
yield, estimatedasrootmeansquare oftheresultsobtainedfromalltests,isabout2%withaslight ra-piditydependence.Severalsources ofsystematicuncertainties areassociatedwith different contributions to the pT spectrum: the fractionof
feed-down J
/ψ
,theshape andcontributionoftheγ γ
→
μ
+μ
− tem-plate, the shape for the coherent J/ψ
andthe shape for the in-coherent J/ψ
with nucleon dissociation. These contributions are shortly detailed in the following. First, the fraction fD offeed-downJ
/ψ
withpT below0.25GeV/c wasvariedintherangefrom4.4to6.4%correspondingtothetotalsystematicuncertaintyofthe measured
ψ
-to-J/ψ
crosssection ratio.Second, theshape oftheγ γ
→
μ
+μ
− pTtemplatefromSTARlightdoesnotincludepossi-blecontributions fromincoherentemission ofphotons, character-izedbymuchwidertransversemomentumdistributionsextending well above 1 GeV/c. In order to account for these contributions, the shape of the
γ γ
→
μ
+μ
− pT template was changed fromSTARlight to that obtained from the side-bands surrounding the J
/ψ
peakintheinvariant massspectra,resultingin1%systematicSource Value Lumi. normalization ±5.0% Branching ratio ±0.6%
SPD, V0 and AD veto from−3.6% to−6.0% MC rapidity shape from±0.1% to±0.8% Tracking ±3.0% Trigger from±5.2% to±6.2% Matching ±1.0% Signal extraction ±2.0% fDfraction ±0.7% γ γyield ±1.2%
pTshape for coherent J/ψ ±0.1%
bpdparameter ±0.1% Total from+−89..32% to+
8.9
−10.3%
uncertaintyonthemeasured coherentcrosssection. Third,a0.2% systematicuncertaintywasdeterminedviathevariationofthe
γ γ
contribution according to the statistical uncertainty in the back-groundtermcalculatedfromtheinvariantmassfits.Amodification ofthetransversemomentumspectraforthecoherentJ
/ψ
accord-ing to the model [35], results in a 0.1% systematic uncertainty. Finally,the template shape for the incoherent J/ψ
with nucleon dissociationwasvariedbyexchangingtheH1high-energyrun pa-rametersforthosedetermined fromthe low-energyrunresulting ina0.1%systematicuncertaintyonthecoherentcrosssection.The systematic uncertainties are summarized in Table 2. The totalsystematicuncertaintyisthequadraticsumofallthesources listed in the table. Luminosity normalization, veto efficiencyand branchingratiouncertainties are fullycorrelated. Theuncertainty onthesignalextractionisconsideredasuncorrelatedasafunction ofrapidity.Finally,allother sourcesofuncertaintyare considered aspartiallycorrelatedacrossdifferentrapidityintervals.
4.3.Discussion
The measured differential cross section of coherent J
/ψ
pho-toproductionin the rapidity range−
4.
0<
y<
−
2.
5 is shownin Fig. 4 and compared with various models. The covered rapidity range corresponds to a Bjorken-x of gluons either in the range 1.
1·
10−5<
x<
5.
1·
10−5or0.
7·
10−2<
x<
3.
3·
10−2 dependingonwhich nucleusemitted the photon.According to models [32], the fraction of high Bjorken-x gluons(x
∼
10−2) is dominantatforwardrapiditiesandrangesfrom
∼
60% at y= −
2.
5 to∼
95% aty
= −
4.TheImpulseApproximation,takenfromSTARlight [16],isbased on the data from the exclusive J
/ψ
photoproduction off protons andneglects all nuclear effects except forcoherence. The square rootof theratioofexperimental pointsandthe Impulse Approx-imation cross section is about 0.8, reflecting the magnitude of the nuclear gluon shadowing factor at typical Bjorken-x values around10−2,undertheassumptionthatthecontributionfromlowBjorken-x
∼
10−5canbeneglected [10].STARlightisbasedontheVectorMesonDominancemodeland aparametrizationoftheexistingdataonJ
/ψ
photoproductionoff protons [23].AGlauber-likeformalismisusedtocalculatetheJ/ψ
photoproductioncross section inPb–Pb UPC accountingfor mul-tipleinteractionswithinthenucleusbutnot accountingforgluon shadowingcorrections.TheSTARlightmodeloverpredictsthedata, indicatingtheimportanceofgluonshadowingeffects,butthe dis-crepancyismuchlowerthanfortheImpulseApproximation.
Guzey,KryshenandZhalov[32] providetwocalculations(GKZ), one based onthe EPS09 LOparametrization of theavailable nu-clear shadowing data [42] and the other on the Leading Twist
Fig. 4. MeasuredcoherentdifferentialcrosssectionofJ/ψphotoproductionin ultra-peripheralPb–Pb collisionsat√sNN = 5.02 TeV.Theerrorbarsrepresentthe sta-tisticaluncertainties,theboxesaroundthepointsthesystematicuncertainties.The theoreticalcalculations [10,16,23,32,36–41] describedinthetextarealsoshown. ThegreenbandrepresentstheuncertaintiesoftheEPS09LOcalculation.
Approximation (LTA) of nuclear shadowing based on the combi-nationoftheGribov-GlaubertheoryandthediffractivePDFsfrom HERA [43].Both theLTAmodelandtheEPS09curve, correspond-ingtotheEPS09LOcentralset,underpredictthedatabutremain compatiblewithitatthemostforwardrapidities.Thedatatends tofollowtheupperlimitofuncertainties oftheEPS09calculation corresponding to the upper bound of uncertainties on the gluon shadowingfactorintheEPS09LOframework.
Severaltheoreticalgroupsprovidedpredictionswithinthecolor dipoleapproachcoupledtotheColorGlassCondensate(CGC) for-malismwithdifferentassumptionsonthedipole-protonscattering amplitude.PredictionsbyGonçalves,Machadoetal.(GM)basedon IIMand b-CGCmodels forthe scatteringamplitude underpredict thedata [36,37]. PredictionsbyLappi andMäntysaari(LM) based ontheIPsat model [38,39] givereasonable agreementthough the rangeofpredictionsdoesnotspanalltheexperimentalpoints. Re-cent predictions by Luszczak and Schafer (LS BGK-I) within the color-dipole formulation of the Glauber-Gribov theory [44] are in agreement with data at semi-forward rapidities,
|
y|
<
3, but slightlyunderpredictthedataatmoreforwardrapidities.Cepila, Contreras and Krelina (CCK) provided two predic-tions based on the extension of the energy-dependent hot-spot model [40] tothenuclearcase:usingthestandardGlauber-Gribov formalism (GG-HS) and using geometric scaling (GS-HS) to ob-tain the nuclear saturation scale [41]. The GG-HS model agrees withdataatmostforwardrapiditiesbutunderpredictsitat semi-forwardrapidities.The GS-HSmodel(notshown)strongly under-predictsthedata.
5. Conclusions
The first rapidity-differential measurement on the coherent photoproductionofJ
/ψ
inthe rapidityinterval−
4<
y<
−
2.
5 in ultra-peripheral Pb–Pb collisions at√
sNN=
5.
02 TeV has beenpresentedandcomparedwithmodelcalculations.TheImpulse Ap-proximationandSTARlightmodelsoverpredictthedata,indicating the importance of gluon shadowing effects. The model basedon thecentralsetoftheEPS09gluonshadowingparametrization, the LeadingTwist Approximation,andthehot-spotmodelcoupledto
the Glauber-Gribov formalism underpredict the data but remain compatiblewithitatmostforwardrapidities.Themajorityofcolor dipolemodelsunderpredictthedata.
The nucleargluon shadowing factorof about0.8at Bjorken-x values around 10−2 and a hard scale around the charm quark mass was estimated from the comparison of the measured co-herent J
/ψ
cross section withthe Impulse Approximation under theassumption that the contributionfromlow Bjorken x∼
10−5 can be neglected. Future studies on coherent heavy vector me-sonphotoproduction accompaniedbyneutron emissionmayhelp to decouplelow-x andhigh-x contributions andprovidevaluable constraints on poorly known gluon shadowing effects at Bjorkenx
∼
10−5 [45].The ratio of the
ψ
and J/ψ
cross sections is in reasonable agreement both withthe ratio ofphotoproduction cross sections offprotonsmeasuredbytheH1andLHCbcollaborationsandwith LTApredictionsforPb–Pb UPC.Acknowledgements
The ALICE Collaboration would like to thank all its engineers andtechnicians fortheir invaluablecontributionstothe construc-tion of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collab-oration gratefully acknowledges the resources and support pro-videdbyall GridcentresandtheWorldwide LHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the followingfundingagencies fortheirsupport inbuildingand run-ningtheALICEdetector: A.I. AlikhanyanNationalScience Labora-tory(YerevanPhysicsInstitute)Foundation(ANSL),State Commit-teeofScienceandWorldFederationofScientists(WFS),Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung,Austria; MinistryofCommunicationsandHigh Tech-nologies, National Nuclear Research Center, Azerbaijan; Conselho NacionaldeDesenvolvimentoCientíficoeTecnológico(CNPq), Uni-versidadeFederal doRioGrande doSul(UFRGS), Financiadorade Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), National Natural Science Founda-tionof China(NSFC) andMinistryof EducationofChina (MOEC), China; Croatian Science Foundation and Ministry of Science and Education, Croatia; Centro de Aplicaciones Tecnológicas y Desar-rolloNuclear(CEADEN),Cubaenergía,Cuba;MinistryofEducation, YouthandSportsoftheCzechRepublic,CzechRepublic;The Dan-ish Councilfor IndependentResearch NaturalSciences, the Carls-bergFoundationandDanishNationalResearchFoundation(DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commis-sariat à l’Energie Atomique (CEA), Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre Na-tional de la Recherche Scientifique (CNRS) andRlégion des Pays de laLoire,France; Bundesministeriumfür Bildung,Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum fürSchwerionenforschungGmbH,Germany;GeneralSecretariatfor ResearchandTechnology,MinistryofEducation,Researchand Re-ligions, Greece; National Research, Development and Innovation Office,Hungary;DepartmentofAtomicEnergy,Governmentof In-dia (DAE), Department of Science and Technology, Government ofIndia (DST), University Grants Commission,Government of In-dia(UGC)andCouncil ofScientific andIndustrialResearch(CSIR), India; Indonesian Institute ofScience, Indonesia;Centro Fermi – MuseoStoricodellaFisica e CentroStudi eRicercheEnrico Fermi andIstitutoNazionalediFisicaNucleare(INFN),Italy;Institutefor Innovative Science and Technology, Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS)
KAKENHIandJapaneseMinistryofEducation,Culture, Sports, Sci-enceand Technology (MEXT),Japan; Consejo Nacionalde Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Interna-cional enCiencia yTecnología(FONCICYT)andDirección General deAsuntosdelPersonalAcademico(DGAPA),Mexico;Nederlandse OrganisatievoorWetenschappelijkOnderzoek(NWO),Netherlands; The ResearchCouncil ofNorway, Norway;CommissiononScience andTechnology forSustainable Developmentin theSouth (COM-SATS),Pakistan;PontificiaUniversidadCatólicadelPerú,Peru; Min-istry of Science andHigher Education and NationalScience Cen-tre, Poland; Korea Institute of Science and Technology Informa-tion and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education andScientific Research,Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research(JINR), MinistryofEducationandScience oftheRussian Federation, National ResearchCentre KurchatovInstitute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministryof Education,Science, ResearchandSport ofthe Slovak Republic, Slovakia; NationalResearch Foundation of South Africa,SouthAfrica;SwedishResearchCouncil(VR)andKnut& Al-iceWallenbergFoundation(KAW),Sweden;EuropeanOrganization for Nuclear Research, Switzerland;National Science and Technol-ogy Development Agency (NSDTA), Suranaree University of Tech-nology(SUT)andOfficeoftheHigherEducationCommissionunder NRU projectofThailand,Thailand;TurkishAtomicEnergy Agency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine; ScienceandTechnologyFacilitiesCouncil(STFC),UnitedKingdom; NationalScienceFoundationoftheUnitedStatesofAmerica(NSF) andUnitedStatesDepartmentofEnergy,OfficeofNuclear Physics (DOENP),UnitedStatesofAmerica.
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