Coherent \(\psi(2S)\) photo-production in ultra-peripheral Pb-Pb collisions at \(\sqrt{s_{\rm NN}}\)= 2.76 TeV

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Coherent ψ ( 2S ) photo-production in ultra-peripheral Pb–Pb collisions at √

s _NN = ² . 76 TeV

.ALICE Collaboration

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received23August2015

Receivedinrevisedform14October2015 Accepted14October2015

Availableonline23October2015 Editor:L.Rolandi

Wehaveperformedthefirstmeasurementofthecoherentψ(2S)photo-productioncrosssectioninultra- peripheralPb–PbcollisionsattheLHC.Thischarmoniumexcitedstateisreconstructedviatheψ(2S)→ l⁺l⁻andψ(2S)→^J/ψ

π

⁺

π

⁻decays,wheretheJ/ψdecaysintotwoleptons.Theanalysisisbasedonan eventsamplecorrespondingtoanintegratedluminosityofabout22 μb⁻¹.Thecrosssectionforcoherent ψ(2S)productionintherapidityinterval−⁰.9<y<0.9 isd

σ

_{ψ (}^coh_2S)/dy=⁰.83±⁰.19

stat+^syst mb.The ψ(2S)toJ/ψcoherentcrosssectionratiois0.34⁺₋⁰₀^._.⁰⁸₀₇(stat+^syst).Theobtainedresultsarecomparedto predictionsfromtheoreticalmodels.

©^{2015CERNforthebenefitoftheALICE}Collaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Two-photon and photo-nuclear interactions at unprecedented energies can be studied in heavy-ion Ultra-Peripheral Collisions (UPC) at the LHC. In such collisions the nuclei are separated by impactparameterslargerthanthesumoftheirradiiandtherefore hadronic interactions are strongly suppressed. The cross sections forphotoninducedreactionsremainlargebecausethestrongelec- tromagneticfieldofthenucleusenhancestheintensityofthepho- tonflux,which growsasthesquareofthecharge ofthenucleus.

Thephysics ofultra-peripheral collisions isreviewedin [1,2].Ex- clusivephoto-productionof vectormesons athighenergy, where avector mesonisproduced inaneventwithnoother final state particles, is of particular interest, since it provides a measure of thenucleargluondistributionatlowBjorken-x.

Exclusive production of charmonium in photon–proton inter- actions at HERA [3–5],

γ

+^p→^J

/ψ(ψ(

2S

))

+^{p, has been suc-} cessfully modelled in terms of the exchange of two gluons with nonet-colourtransfer[6].Experimentaldataonthisprocessfrom HERAhavebeenusedtoconstraintheprotongluondistributionat lowBjorken-x[7].Exclusivevectormesonproductioninheavy-ion interactionsisexpectedtoprobethenucleargluondistribution[8], forwhichthereisconsiderableuncertaintyinthelow-xregion[9].

Exclusive

ρ

⁰ [10] and J

/ψ

[11] production has been studied in Au–Au collisions atRHIC. The exclusive photo-production can be eithercoherent,wherethephotoncouplescoherentlytoalmostall thenucleons,orincoherent,wherethephotoncouplestoasingle

E-mailaddress:alice-publications@cern.ch.

nucleon. Coherent production is characterized by low transverse momenta of vector mesons (pT^{60 MeV}

/

c) where the target nucleus normally does not break up. However, the exchange of additionalphotons, radiatedindependently fromthe original one, may leadto the target nucleusbreaking up orde-excite through neutronemission.Simulationmodelsestimatethisoccursinabout 30% ofthe events[12].Incoherentproduction ischaracterized by a somewhat higher transverse momentum of the vector mesons (p_T^{500 MeV}

/

c). In thiscase the nucleus interacting with the photon breaksupbut,apartfromsingle nucleonsornuclearfrag- mentsintheveryforwardregion,nootherparticlesareproduced besidesthevectormeson.

Wepublishedthefirstresultsonthecoherentphoto-production of J

/ψ

in UPC Pb–Pb collisions at the LHC [13] in the rapidity region −³

.

6

<

y

<

−²

.

6, which constrain the nuclear gluon dis- tributionatBjorken-x^{10−2.Shortly}afterwards,ALICEpublished a second paper measuring both the coherentandthe incoherent J

/ψ

vector mesoncrosssection atmid-rapidity[14],allowing the nucleargluondistributionatBjorken-x^{10−3 tobeexplored.The} presentanalysisisperformedinthesamerapidityregionwithre- spect to themeasurement reportedin [14], anditis sensitive to Bjorken-x^{10−3 too.}

Thereareveryfewstudiesofphoto-productionof

ψ(

2S

)

offnu- clei.Incoherentphoto-production,usinga21 GeVphotonbeamoff adeuteriumtarget,hasbeenstudiedin[15];non-exclusivephoto- production,usingbremsstrahlung photonswithanaverageenergy of 90 GeV off a ⁶Litarget, have beenreported in[16]. However, no previous measurements of

ψ(

2S

)

coherent photo-production offnucleartargets havebeenreportedintheliterature.

http://dx.doi.org/10.1016/j.physletb.2015.10.040

0370-2693/©^{2015CERNforthebenefitoftheALICE}Collaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

Inthisletter, resultsfromALICE onexclusive coherentphoto- production of

ψ(

2S

)

mesons at mid-rapidity in ultra-peripheral Pb–Pbcollisionsat√

sNN=²

.

76TeV arepresented.Themeasured coherent

ψ(

2S

)

crosssectionandthe

ψ(

2S

)/

J

/ψ

crosssectionra- tioarecomparedtomodelpredictions[17–22].

2. Detectordescription

ThemaincomponentsoftheALICEdetectorareacentralbarrel placedinalargesolenoidmagnet(B=⁰

.

5 T),coveringthepseudo- rapidity region |

η

_|

<

0

.

9, and a muon spectrometer at forward rapidity,covering the range −⁴

.

0

< η <

−²

.

5 [23]. Three central barreldetectorsareusedinthisanalysis.TheALICEInternalTrack- ingSystem(ITS) ismadeofsixsiliconlayers,all ofthemusedin thisanalysisforparticletracking.TheSiliconPixelDetector(SPD) makes up the two innermost layers ofthe ITS, covering pseudo- rapidityranges|

η

|

<

2 and|

η

|

<

1

.

4,fortheinner(radius3.9 cm) andouter(averageradius7.6 cm)layers,respectively.TheSPDisa finegranularitydetector,havingabout10⁷ pixels,andisused for triggering purposes. The Time Projection Chamber (TPC) is used fortrackingandforparticle identification[24]andhasan accep- tancecoveringthepseudo-rapidity region|

η

|

<

0

.

9.The Time-of- Flightdetector(TOF) surroundsthe TPCandisa largecylindrical barrel of Multigap Resistive Plate Chambers (MRPC) with about 150,000 readoutchannels, giving very highprecision timing. The TOF pseudo-rapidity coverage matches that of the TPC. Used in combination withthe tracking system, the TOF detector is used forcharged particle identificationup to a transverse momentum ofabout 2.5 GeV/c (pions and kaons)and 4 GeV/c (protons). In addition,theTOFdetectorisalsousedfortriggering[25].

The analysispresented below also makes use of two forward detectors.TheV0countersconsistoftwo arraysof32scintillator tiles each,covering the range 2

.

8

< η <

5

.

1 (V0-A, on theoppo- sitesideof themuon spectrometer)and−³

.

7

< η <

−¹

.

7 (V0-C, on thesame side as the muon spectrometer)and positioned re- spectively at z=^{340 cm and z}= −^{90 cm from the} interaction point.

Finally, two sets of hadronic Zero Degree Calorimeters (ZDC) arelocated at114 m on eitherside ofthe interactionpoint. The ZDCsdetect neutrons emitted inthe very forwardand backward regions (|

η

_|

>

8

.

7),suchasneutronsproducedbyelectromagnetic dissociationofthenucleus[26](seeSection3).

3. Dataanalysis

Theeventsampleconsidered forthepresentanalysiswas col- lectedduringthe2011Pb–Pbrun,usingadedicatedBarrelUltra- PeripheralCollisiontrigger (BUPC), selecting events withthe fol- lowingcharacteristics:

(i) atleasttwohitsintheSPDdetector;

(ii) anumberoffiredpad-OR(N^on)intheTOFdetector[25]inthe range2≤^Non≤^{6,withatleasttwoofthemwithadifference} inazimuth,

φ

,intherange150^◦≤

φ

≤^180◦;

(iii) nohitsintheV0-Aandnohitsinthe V0-C detectors.

Theintegratedluminosityusedinthisanalysiswas 22

.

4⁺₋⁰₁^._.⁹₂ μb⁻¹. Luminosity determination and systematics are discussed in Sec- tion3.1. Inthepresentanalysis,coherent

ψ(

2S

)

photo-production wasstudiedinfourdifferentchannels:

ψ(

2S

)

→^l+l−and

ψ(

2S

)

→ J

/ψ π

⁺

π

⁻,followedbythe J

/ψ

→^{l+l− decay,wherel+l− canbe} eitherae⁺e⁻ or

μ

⁺

μ

⁻pair.

3.1. The

ψ(

2S

)

→^{l+l−channel}

Forthedi-muon anddi-electrondecaychannelsthefollowing selectioncriteriawereapplied:

(i) areconstructedprimaryvertex.Theprimaryvertexpositionis determined fromthe tracksreconstructed intheITSandTPC asdescribedin Ref.[27].Thevertexreconstruction algorithm isfullyefficientforeventswithatleastonereconstructedpri- marychargedparticleinthecommonTPCandITSacceptance;

(ii) only two good tracks with at least 70 TPC clusters and at least1SPDclustereach.Moreover,particlesoriginatedinsec- ondary hadronic interactions or conversions in the detector material, were removed using a distance ofclosest approach (DCA) cut. The tracks extrapolated to the reconstructed ver- tex should have a DCA in the beam direction DCAL≤2 cm, and in the plane orthogonal to the beam direction DCAT ≤ 0

.

0182+⁰

.

0350

/

p¹_T^.01,where pTisthetransversemomentum in (GeV/c)[28];

(iii) at least one of the two good tracks selectedin criterion (ii) should have pT≥^{1 GeV}

/

c; thiscut reducesthe background, while itmarginally affectsthe genuine leptons fromJ

/ψ

de- cays;

(iv) the V0 trigger required no signal within a time window of 25 ns aroundthecollisiontime inanyofthescintillatortiles of both V0-A and V0-C. Signals in both V0 detectors were searchedofflineinalargerwindowaccordingtotheprescrip- tiondescribedin[14];

(v) thespecificenergylossdE

/

dxforthetwotracksiscompatible withthatofelectronsormuons (seebelow);itisworthnoting thattheTPCresolutiondoesnotallowmuonandchargedpion discrimination;

(vi) thetwotrackshaveoppositecharges.

The optimizationofthe selectioncriteriato tagefficiently the

ψ(

2S

)

was tailoredbyusing theSTARLIGHT [17] eventgenerator combinedwiththe ALICEdetectorfullsimulation. About950,000 coherent and incoherent events were simulated for each decay channel. The eventtotal transverse momentum reconstruction is obtained addingthe pT of the two leptons. The selection of co- herent events requires a threshold on the reconstruction of the eventtotal transverse momentum, obtainedby adding the p_T of the two decay leptons. Transverse momentum carried away by thebremsstrahlung photonsreflects ina broadeningoftheevent total pT. Bremsstrahlung effects are more important for the di- electrondecayandthecorrespondingp_T thresholdhastobelarger inthiscase.ConsequentlyapT cut pT

<

0

.

15 GeV

/

cfordi-muons andpT

<

0

.

3 GeV

/

c fordi-electrons:98 (77)%ofthecoherentsig- nal is retained for di-muons and di-electrons respectively. Fig. 1 (top panel) showsthe invariant mass (left) and the pT distribu- tion(right) for thesedecaychannels. The pT distributions clearly showacoherentpeakatlowp_T.Noeventsarefoundwithatrans- versemomentumexceeding1.5 GeV/c,asexpectedforanegligible hadroniccontamination,characterizedbyamuchlargereventpT. Thenumberof

ψ(

2S

)

candidatesareobtainedbyfittingtheinvari- antmassdistributionofbothchannelstoanexponentialfunction describingtheunderlyingcontinuumandtoaCrystalBallfunction toextractthe

ψ(

2S

)

signal.TheCrystalBall

ψ(

2S

)

resonancemass andwidthwereleftfree,whilethetailparameters(

α

andn)were fixedtothevaluesobtainedby MonteCarlosimulation.Themass (width calculatedfromthestandard deviation)value fromthefit is3

.

664±⁰

.

013 GeV

/

c² (22±^9MeV

/

c²)ingoodagreementwith theknownvalueofthe

ψ(

2S

)

massandcompatiblewiththeab- solute calibration accuracy of the barrel. The obtainedyield (see Table 1)was N^yield=

(

18

.

4±⁹

.

3

)

.

Fig. 1.Invariantmass (left)andpT distributions (right)forultra-peripheralPb–Pbcollisionsat√

sNN=2.76TeV and−0.9<y<0.9 foreventssatisfyingtheeventselections inSection3.Thechannelsψ(2S)→l⁺l⁻areshownonthetoppanel(l⁺l⁻=e⁺e⁻andμ⁺μ⁻),theψ(2S)→π⁺π⁻μ⁺μ⁻channelisshowninthecentralandthechannel ψ(2S)→π⁺π⁻e⁺e⁻inthebottomone.Thenumberofeventisobtainedbythefit(toppanel)orbyeventcountinginaselectedinvariantmassregion(centralandbottom panel),seetext.

The product of the acceptance and efficiency correction

(

Acc×

ε )

ψ (2S) was calculated astheratio ofthe numberofsim- ulated events that satisfy the conditions i) to vi), to the num- ber of generated events with the

ψ(

2S

)

in the rapidity interval

−⁰

.

9

<

y

<

0

.

9.Transverse polarization ofthe

ψ(

2S

)

is expected fromhelicityconservationforaquasi-realphoton.Inaddition,for the coherent sample, a reconstructed

ψ(

2S

)

transverse momen-

tumcondition pT

<

0

.

15 GeV

/

c(pT

<

0

.

3 GeV

/

c)wasrequiredfor di-muons (di-electrons)inthefinalstate.Thevaluesforthecom- binedacceptanceandefficiencyarereportedinTable 1.

AccordingtoSTARLIGHTthefraction(fI)ofincoherentoverco- herenteventsinthelow pTregionis4.4%fordi-muonsand16.6%

fordi-electrons.Anothertheoreticalmodel,describedin[22],pre- dicts a muchhighercoherent overincoherentcrosssection ratio,

Table 1

Summaryofthemainexperimentalresultsandcorrectionparametersusedinthecrosssectionevaluation.Thebottomlineshows thecrosssectionforthethreeψ(2S)decaychannels.

ψ(2S)→l⁺l⁻ ψ(2S)→μ⁺μ⁻π⁺π⁻ ψ(2S)→e⁺e⁻π⁺π⁻

Signal counts 18.4±9.3 17±4.1 11.0±3.3

Bkg. counts(N^back) 0 1 0

fI (5.6±¹.8)% (3.4±¹.1)% (13.2±⁴.3)%

(Acc×ε)ψ (2S) (3.65±⁰.16)% (2.35±⁰.14)% (1.33±⁰.08)%

BR (1.56±0.11)% (2.02±0.03)% (2.02±0.03)%

Lint (22.4⁺₋⁰₁^._.⁹₂)μb⁻¹ (22.4⁺₋⁰₁^._.⁹₂)μb⁻¹ (22.4⁺₋⁰₁^._.⁹₂)μb⁻¹

y 1.8 1.8 1.8

dσ_{ψ (}^coh_2S)

dy (mb) 0.76±0.40(stat)±0.13(syst) 0.81±0.22(stat)⁺₋⁰₀^._.⁰⁹₁₀(syst) 0.90±0.31(stat)⁺₋⁰₀^._.¹³₁₂(syst)

resulting in a fI prediction 50% smaller. Taking the average of thesetwopredictions,

(

3

.

3±¹

.

1

)

% fordi-muonsand

(

11

.

1±³

.

4

)

% fordi-electrons isobtained. The uncertainty was obtainedby re- quiringtheused value to agreewiththe two modelswithin 1

σ

. Thefinal fI (seeTable 1)istheaverageofthe fI fordi-electrons anddi-muons, weighted withthe corresponding acceptance and efficiency(Acc×

ε

). The remaining background (N_back) was esti- matedstudyingthewrong-sign eventsample,obtainedby apply- ingcuts(i)to(v).Fordi-muonanddi-electronchannelsnowrong- signeventswerefoundintheinvariantmassrangeconsideredand thereforeN_back=^0.

Thecoherent

ψ(

2S

)

yieldisobtainedusingtheformula N^coh_{ψ (2S)}

=

^Nyield

−

N^back

1

+

^fI

,

(1)

giving N^coh_{ψ (2S)}=¹⁷

.

5±⁹

.

0.The coherent

ψ(

2S

)

differentialcross sectioncanbewrittenas:

d

σ

_{ψ (}^coh_2S)

dy

=

^N

coh ψ (2S)

(

Acc

× ε )

_{ψ (}2S)

·

Lint

·

^y

·

^BR

(ψ (

2S

) →

^l+l−

) ,

(2) where

(

Acc×

ε )

ψ (2S)correspondstotheacceptanceandefficiency asdiscussed above. BR

(ψ(

2S

)

→^l+l−

)

is the branching ratiofor

ψ(

2S

)

decay into leptons [29], y=¹

.

8 the rapidity bin size, and Lint the total integratedluminosity. These values are listed in Table 1. The systematic uncertainty on the yield for the di- leptonchannelisobtainedbyvaryingthebinsizeandbyreplacing the exponential witha polynomial to fit the

γ γ

process. In ad- dition,the Crystal Ballfunction parameters can be alsoobtained byfittingasimulatedsamplemadeof

ψ(

2S

)

and

γ γ

eventcock- tailand then used to fit the coherent-enriched data sample too.

Byapplyingthedifferentmethods reportedabove, themaximum differenceinthe obtainedyieldis12%: thisvalue isusedassys- tematicuncertainty on the yield. The STARLIGHT model predicts adependenceofthe

ψ(

2S

)

crosssection ontherapidity,givinga

≈10% variation over therapidity range −⁰

.

9

<

y

<

0

.

9. Inorder toevaluate the systematicuncertaintyon the acceptancecoming fromthegeneratorchoice,aflatdependenceofd

σ

_{ψ (}2S)

/

dy inthe interval −⁰

.

9

<

y

<

0

.

9,aspredictedby other models,was used.

Therelativedifferencesin(Acc×

ε

)betweentheinputshapeswas 1.0%,andaretakenintoaccountinthesystematicuncertaintycal- culation.Thesystematicuncertaintyonthetrackingefficiencywas estimatedbycomparing,indataandinMonteCarlo,theITS(TPC) hitmatchingefficiencytotracksreconstructedwithTPC(ITS)hits only.

Thetrigger efficiencywas measured relying on a datasample collected in a dedicated run triggered by the ZDCs only. Events witha topology havingthe BUPC conditions,givenat thebegin- ning of Section 3, were selected. The resulting trigger efficiency was compared to that obtained by the Monte Carlo simulation, showinganagreementwithin⁺₋⁴₉^._.^0%_0%.

Thee

/ μ

separationwasobtainedbyusingtwomethods:

a) a sharpcut inthe scatter plotofthe firstlepton dE

/

dxasa function of the second lepton dE

/

dx, whereall theparticles beyondagiventhresholdareconsideredaselectrons;

b) using theaverage ofthe electron (muon) dE

/

dx andconsid- eringas electrons (muons)the particles within three sigmas fromtheBethe–Blockexpectation.Thedifferencebetweenthe two methods was used asan estimate ofthe systematicun- certainty,giving±^2%.

The systematic uncertainty related to the application of the V0 offline decision (cut iv) on Section 3.1, was evaluated repeating theanalysiswiththiscutexcluded.Thisresultsinamorerelaxed eventselection,increasingthecrosssectionby6%.

Theintegratedluminositywasmeasuredusingatriggerforthe mostcentral hadronicPb–Pb collisions. Thecross section forthis process was obtained with a van der Meer scan [30], giving a cross section

σ

=⁴

.

10⁺₋⁰₀^._.²²₁₃

(

syst

)

b[31]. Theintegrated luminos- ity for the BUPC trigger sample, corrected for trigger live time, was Lint=²²

.

4⁺₋⁰₁^._.⁹₂ μb⁻¹,wheretheuncertaintyisthe quadratic sum ofthe cross section uncertainty quoted above andthe trig- gerdeadtime uncertainty.An alternativemethodbasedon using neutronsdetectedinthetwoZDCswasalsoused.TheZDCtrigger condition required a signal in atleast one of the two calorime- ters, thusselecting single electromagnetic dissociationas well as hadronic interactions. The cross section for this trigger was also measured with a van der Meer scan [26]. The integrated lumi- nosity obtained for the BUPC by this method is consistent with theone quoted abovewithin 2.5%.The sources andthe valuesof the systematic uncertainties are listed in Table 2. As a result in therapidity interval−⁰

.

9

<

y

<

0

.

9 a crosssectiond

σ

_{ψ (}^coh_2S)

/

dy= 0

.

76±⁰

.

40

(

stat

)

⁺₋⁰₀^._.¹²₁₃

(

syst

)

mb isobtained.

3.2. The

ψ(

2S

)

→

π

⁺

π

⁻J

/ψ

,J

/ψ

→^l+l−

(

l⁺l⁻=^e+e−

, μ

⁺

μ

⁻

)

channels

The analysis criteriaused to selectthese channelsare similar to those described in Section 3.1, with the requirements on the trackquality slightly relaxedto keep the efficiencyatan accept- able level.Such a cut softening was allowed by the smaller QED background in four track events, compared to the channels de- scribedin Section3.1.Selection(ii) ismodified sothat fourgood tracks with at least 50 TPC clusters each are required. In addi- tiontocutsi)tovi),theinvariantmassofdi-muons(di-electrons) was required to match that expected by leptons from J

/ψ

de- cay, i.e. 3

.

0

<

Mπ⁺π⁻μ⁺μ⁻

<

3

.

2 GeV

/

c² for di-muons (2

.

6

<

Mπ⁺π⁻e⁺e⁻

<

3

.

2GeV

/

c² fordi-electrons).

Theacceptanceandtheefficiencywere estimatedwithsimilar techniques.Duetothecouplingtothephoton,the

ψ(

2S

)

istrans- verselypolarized.Accordingtopreviousexperiments[32],J

/ψ

and

Table 2

Systematicuncertaintiesperdecaychannel.

ψ(2S)→^l+l− ψ(2S)→μ⁺μ⁻π⁺π⁻ ψ(2S)→^e+e−π⁺π⁻

Signal extraction ±^12% <1% <1%

Incoherent contamination (fI) ±¹.8% ±¹.3% ±⁴.8%

(Acc×ε) Generator ^d_dy^σ ±1% ±2% ±2%

Tracking efficiency ±⁴.2% ±⁶.0% ±⁶.0%

Trigger efficiency ⁺₋^4%_9% ⁺₋^4%_9% ⁺₋^4%_9%

e/μseparation ±^2% ±^2% ±^2%

V0 offline decision ⁺₋^6%_0% ⁺₋^6%_0% ⁺₋^9%_0%

Luminosity ⁺₋⁵₄^._.^5%_0% ⁺₋⁵₄^._.^5%_0% ⁺₋⁵₄^._.^5%_0%

Branching ratio ±⁷.1% ±¹.5% ±¹.5%

Uncorrelated sources ±13% ±2% ±5%

Correlated sources ⁺₋^10%_11% ⁺₋^11%_12% ⁺₋^13%_12%

Total ±^{17% +}₋^11%12% +14%

−13%

two pions from

ψ(

2S

)

decay are in s-wave state and thus the

ψ(

2S

)

polarizationfullytransferstotheJ

/ψ

.Whencomputingthe efficiency andacceptance the

ψ(

2S

)

is therefore assumed trans- versely polarized. A coherent-enriched sample can be obtained by selectingappropriate regionson invariantmass and pT,tuned by using a Monte Carlo simulation, as described in Section 3.1.

The same pT cuts used in Section 3 were applied. By selecting invariant mass in the interval 3

.

6

<

Mπ⁺π⁻μ⁺μ⁻

<

3

.

8 GeV

/

c² (3

.

1

<

Mπ⁺π⁻e⁺e⁻

<

3

.

8 GeV

/

c²) for the

ψ(

2S

)

→

π

⁺

π

⁻

μ

⁺

μ

⁻

(

ψ(

2S

)

→

π

⁺

π

⁻e⁺e⁻) channel, 95% (87%) of the signal was re- tained.Thestripedareaintheinvariantmass(left)plotsonFig. 1 (centralandbottom panels) showsthe

ψ(

2S

)

candidates satisfy- ingthe p_Tcutforthetwochannels.Toextractthecoherent

ψ(

2S

)

yield, thecontribution from incoherent

ψ(

2S

)

was subtracted as shown in Eq. (1). The background was estimated by looking at eventswithallthepossiblecombinationofwrong-signtracks.One event was found in the di-muon sample and no events in the di-electronsample.Thefractionoftheincoherentsamplecontam- inatingthecoherentsample was estimatedasinSection 3.1,and was found tobe 3.4% inthe

ψ(

2S

)

→

π

⁺

π

⁻

μ

⁺

μ

⁻ channel and 13.2% in the

ψ(

2S

)

→

π

⁺

π

⁻e⁺e⁻ channel. The systematic un- certainty on the yield was obtained by using an alternative set of cuts. According to the kinematics of the

ψ(

2S

)

→

π

⁺

π

⁻J

/ψ

decaychannel,pions arecharacterized by asmalltransverse mo- mentum(pT

<

0

.

4 GeV

/

c),whiletheleptontransversemomentum exceeds1.1 GeV/c.Insteadofselectingeventswherethedi-lepton invariantmassisclosetothatoftheJ

/ψ

,eventswereselectedac- cordingtothekinematicsofthedecayproductsofthe

ψ(

2S

)

.All the other cutswere kept as described in Section 3.1. Two alter- nativeselectionswereconsidered:(i) asamplewherebothleptons haveatransversemomentumlargerthan1.1 GeV/c;and(ii) asam- plewithoutanydecayproductwithtransversemomentuminthe range0

.

4

<

pT

<

1

.

2 GeV

/

c.The

ψ(

2S

)

yield was unchangedfor both theseselectionswhile a smallchange applies tothe accep- tance and efficiency in the

π

⁺

π

⁻J

/ψ

decay, giving a negligible systematicuncertainty.Therelativedifferencein(Acc×

ε

)between the STARLIGHT rapidity shape and a flat rapidity one was 2.0%

for

ψ(

2S

)

→

π

⁺

π

⁻J

/ψ

channel,andistakenintoaccountinthe systematicuncertainty calculation.As a resultthe obtainedcross sectionsintherapidityinterval −⁰

.

9

<

y

<

0

.

9 ared

σ

_{ψ (}^coh_2S)

/

dy= 0

.

81±⁰

.

22

(

stat

)

⁺₋⁰₀^._.⁰⁹₁₀

(

syst

)

mb forthe

ψ(

2S

)

→

π

⁺

π

⁻J

/ψ

,J

/ψ

→

μ

⁺

μ

⁻ channel andd

σ

_{ψ (}^coh_2S)

/

dy=⁰

.

89±⁰

.

31

(

stat

)

⁺₋⁰₀^._.¹³₁₂

(

syst

)

mb forthe

ψ(

2S

)

→

π

⁺

π

⁻J

/ψ

,J

/ψ

→^{e+e−channel.}

Fig. 2. Measured differentialcross section of ψ(2S) photo-productionin Pb–Pb ultra-peripheralcollisionsat√

sNN=2.76TeV at−0.9<y<0.9 inthreedifferent channels.Thesquarerepresentsthesystematicuncertaintieswhilethebarrepre- sentsthestatisticuncertainty.Thecombinedcrosssectionuncertainty(shadedarea) wasobtainedusingtheprescriptionfromreference[33].

3.3. Combiningthecrosssections

The

ψ(

2S

)

coherentproduction crosssectionsreported inthe Sections 3.1 and 3.2 (Fig. 2) were combined, using the statisti- cal and the uncorrelated systematic uncertainty as a weight. Fi- nallythecorrelatedsystematicuncertaintywasadded.Asymmetric uncertaintys were combined according tothe prescriptions given in [33].The average crosssection inthe rapidityinterval −⁰

.

9

<

y

<

0

.

9 isd

σ

_{ψ (}^coh_2S)

/

dy=⁰

.

83±⁰

.

19

stat+^syst mb.

3.4. Coherentproductionwithnuclearbreakupornucleus de-excitationfollowedbyneutronemission

InUPConeorbothnucleimaygetexcitedduetotheexchange of additional photons. This excitation may lead to break up of the nucleusvia emission of one or more neutrons. The neutron emission wasmeasured byusingtheZDCdetector,fortheevents studied in thedecay channel,

ψ(

2S

)

→^l+l−

π

⁺

π

⁻.We found 20 events

(

71⁺₋⁹₁₁

)

% withnoneutronsoneitherside (0n,0n),8events

(

29⁺₋¹¹₉

)

% withat leastone neutronon eitherside (Xn), 7events

(

25⁺₋¹⁰₈

)

% with no neutron on one side and atleast one neutron on the other one (0n Xn) and 1 event

(

4⁺₋⁸₃

)

% with at least one neutron on both sides (Xn Xn). Uncertainties onthe fraction are obtained assuminga binomial distribution.These fractionsare in agreement with predictions by STARLIGHT [12] and RSZ [8], as showninTable 3.

Table 3

Numberofeventsfordifferentneutronemissionsintheψ(2S)→^l+l−π⁺π⁻pro- cess.

Data Fraction STARLIGHT RSZ

0n 0n 20 (71⁺₋⁹₁₁)% 66% 70%

Xn 8 (29⁺₋¹¹₉)% 34% 30%

0n Xn 7 (25⁺₋¹¹₉)% 25% 23%

Xn Xn 1 (4⁺₋⁸₃)% 9% 7%

3.5.The

ψ(

2S

)

toJ

/ψ

crosssectionratio

In orderto comparethe coherent

ψ(

2S

)

cross section to the previously measured J

/ψ

cross section [14], we report on the

ψ(

2S

)/

J

/ψ

crosssection ratio.Manyofthesystematicuncertain- tiesof thesemeasurements are correlated andcancel out in the ratio.Sincetheanalysisreliesonthesamedatasampleandonthe sametrigger,thesystematicuncertaintiesfortheluminosityeval- uation,trigger efficiency,anddead time were consideredasfully correlated.Severaluncertainties,correspondingtothesamequan- tity,measured atslightlydifferentenergies(corresponding tothe differentmasses), are partiallycorrelated, while theuncorrelated partis small.Namely, thesystematicuncertainties fore

/ μ

sepa- rationandthe measurement oftheneutron numberare strongly correlatedandhencecanbeneglectedintheratio.Thesystematic uncertaintiesconnectedtothesignalextractionandthebranching ratioareconsidereduncorrelatedbetweenthetwomeasurements.

The quadratic sum of these sources together with the statistic uncertaintywas usedtocombinedifferentchannelsinboth mea- surements. For the combination of asymmetric uncertainties the prescriptionfromreference[33]wasused.Thevalueoftheratiois

(

d

σ

_{ψ (}^coh_2S)

/

dy

)/(

d

σ

_J^coh_/ψ

/

dy

)

=⁰

.

34⁺₋⁰₀^._.⁰⁸₀₇

(

stat+^syst

)

.

4. Discussion

We have previously measured the coherent photo-production crosssectionfortheJ

/ψ

vectormesonatmidandforwardrapidi- ties[13,14]. The results showedthat the measured cross section wasingoodagreementwithmodelsthatincludeanuclear gluon shadowingconsistentwiththeEPS09parametrization[9].Models basedonthe colourdipole modelorhadronicinteractions ofthe J

/ψ

withnuclearmatterweredisfavoured.The

ψ(

2S

)

issimilarto theJ

/ψ

initscomposition (cc)andmass,butithasamorecom- plicated wave function as a consequence of it being a 2S rather thana1Sstate,andhasalargerradius.Thereisaconsensusview aboutthepresenceofanodeinthe

ψ(

2S

)

wavefunction:fewau- thorspointedoutthatthisnodegivesanaturalexplanationofthe

ψ(

2S

)

smallercrosssectioncomparedtotheJ

/ψ

one;inaddition itwas arguedthat the nodemaygive strong cancellationsinthe scatteringamplitudein

γ

-nucleusinteractions[34,35].

In Pb–Pb collisions the poor knowledge of the

ψ(

2S

)

wave function as a function of the transverse quark pair separation d makesitdifficulttoestimatethenuclearmattereffects.

There are predictions by five different groups for coherent

ψ(

2S

)

production in ultra-peripheral Pb–Pb collisions; some of them published several different calculations (see Fig. 3). The modelbyAdeluyiandNguyen (AN)isbasedonacalculationwhere the

ψ(

2S

)

crosssection isdirectly proportional tothegluon dis- tribution squared [18]. It is essentially the same model used by AdeluyiandBertulani[36]tocalculatethecoherentJ

/ψ

crosssec- tion, which was found to be in good agreement withthe ALICE data,whencoupledto theEPS09shadowingparametrization. The calculations are done for four different parameterizations of the nucleargluondistribution:EPS08[37],EPS09[9],HKN07[38],and

Fig. 3. Measured differential cross section ofψ(2S) photo-production in ultra- peripheralPb–Pbcollisionsat√

sNN=².76TeV at−⁰.9<y<0.9.Theuncertainty wasobtainedusingtheprescriptionfromreference[33].Thetheoreticalcalculations describedinthetextarealsoshown.

MSTW08[39].Thelast one(MSTW08)correspondstoascalingof the

γ

p crosssection neglecting anynuclear effects (impulseap- proximation).Itisworthnotingtheyusedforthe

ψ(

2S

)

thesame wave functionusedforthe J

/ψ

.The modelbyGay Ducati,Griep, and Machado (GDGM) [19] is based on the colour dipole model andissimilar tothemodelbyGoncalvesandMachadoforcoher- entJ

/ψ

production[20].Thelattercalculationcouldnotreproduce the ALICE coherent J

/ψ

measurement. The new calculation has, however,beentuned tocorrectlyreproducethe ALICEJ

/ψ

result.

The modelby Lappi andMantysaari (LM) is basedon the colour dipole model [21]. Theirpredictionfor theJ

/ψ

was abouta fac- toroftwoabovethecrosssectionmeasuredbyALICE.Thecurrent

ψ(

2S

)

crosssectionhasbeenscaleddowntocompensateforthis discrepancy.ThemodelbyGuzeyandZhalov(GZ)isbasedonthe leading approximation of perturbative QCD [22]. They used dif- ferent gluon shadowing predictions, using the dynamical leading twist theory orthe EPS09fit.Finally,STARLIGHT uses the Vector Meson Dominance model and a parametrization of the existing HERA data to calculate the

ψ(

2S

)

cross section from a Glauber modelassumingonlyhadronicinteractionsofthe

ψ(

2S

)

[17].This modeldoesnotimplementnucleargluonshadowing.

ItisworthnotingthatremovingallnucleareffectsinSTARLIGHT gives a cross section for J

/ψ

production almost identical to the Adeluyi–Bertulanimodel,ifthe MSTW08parametrizationisused.

The last one corresponds to a scaling of the

γ

–p cross section neglecting any nuclear effects, i.e. considering all nucleons con- tributing to the scattering (impulse approximation). Conversely, when applying the same procedure to the

ψ(

2S

)

vector meson production, the comparison shows that STARLIGHT cross section is 50% smaller with respect to the Adeluyi–Nguyen one. This resultmay indicate that the

γ

₊p→

ψ(

2S

)

+^{p cross section is} parametrized in a different way in the two models, due to the limitedexperimental data,makingitdifficultto tunethemodels.

ForJ

/ψ

,awealthof

γ

+^p→^J

/ψ

+^{pcrosssectiondatahasbeen} obtainedby ZEUSandH1,while theprocess

γ

₊p→

ψ(

2S

)

+^p wasmeasuredbyH1atfourdifferentenergiesonly.Thismakesit much harder toconstrain the theoreticalcross section tothe ex- perimentaldata.Sincetheeffectofgluonshadowingdecreasesthe vector mesonproductioncrosssection, thismayexplain whythe

ψ(

2S

)

STARLIGHT cross section is close to the AN-EPS09 model, whileitisafactoroftwolargerforJ

/ψ

.

The coherent

ψ(

2S

)

photo-production cross section is com- paredtocalculationsfromtwelvedifferentmodelsinFig. 3.Since acomprehensivemodeluncertaintyisnotprovidedby themodel authors, thecomparison withthe experimental results isquanti- fiedbydividingthedifferencebetweenthevalueofeachmodelat y=^{0 andthe}experimentalresult,bytheuncertaintyofthemea-

Fig. 4.Ratiooftheψ(2S)toJ/ψcrosssectionforppandγp interactionscompared totheoreticalpredictions.TheALICEratiomeasuredinPb–Pbcollisionsisshownas well.Theuncertaintywasobtainedusingtheprescriptionfromreference[33].

Fig. 5.Ratiooftheψ(2S)toJ/ψ crosssectionmeasuredbyALICEinPb–Pbcolli- sions.Theuncertaintywasobtainedusingtheprescriptionfromreference[33].The predictionsfromdifferenttheoreticalmodelsarealsoshown.

surement itself. The present measurement disfavours the EPS08 parametrization when implemented in the AN model and the GDGMmodelswithastrongshadowing.Similarlythemodelsthat neglect anynuclear effectare disfavoured at a levelbetween 1.5 and 3 sigmas. The systematic uncertainties on the cross section parametrization andthe experimental statistical uncertainties do notallowapreferencetobegivenbetweenthemodelsimplement- ing moderate nuclear gluon shadowing (as AN-EPS09) andthose takingintoaccountGlaubernucleareffectsonly(asSTARLIGHT).

Fig. 4showsthe

ψ(

2S

)

to J

/ψ

crosssection ratiomeasured in Pb–Pb collisions by ALICEandthose obtainedin pp collisions¯ by CDF[40],andinpp collisionsby LHCb[41].BothSTARLIGHT and the GDGM model predict correctly the experimental pp results.

Thefigure alsoshowstheratiomeasured byH1 in

γ

p collisions.

TheH1resultiscompatiblewiththeppmeasurements,whilethe ALICEpointis2

σ

largerthantheaverageoftheppmeasurements, althoughstillwithsizableuncertainties.Thisdifferencemayindi- catethat the nuclear effects and/or thegluon shadowing modify theJ

/ψ

andthe

ψ(

2S

)

productioninadifferentway,sinceother effects,asthedifferentphotonflux,duetothelarger

ψ(

2S

)

mass, couldnotexplainsuchadifference.

Fig. 5showsthecomparisonofthe

ψ(

2S

)

toJ

/ψ

crosssection ratiobetweenmeasurements andpredictionsinPb–PbUPC. Most modelspredict a

ψ(

2S

)

toJ

/ψ

crosssection ratioinPb–Pbcolli- sions smaller by 2–2

.

5

σ

than the one measured by ALICE. It is worthnotingthesamemodelswhichreproducedcorrectlythepp

ratio,failindescribingthePb–Pbratio.ItissurprisingthattheAN model,althoughitassumesa

ψ(

2S

)

wavefunctionidenticaltothe J

/ψ

one,describesinasatisfactorywaythisratio.

5. Conclusions

We performed the first measurement of the coherent

ψ(

2S

)

photo-production cross section in Pb–Pb collisions, obtaining d

σ

_{ψ (}^coh_2S)

/

dy=⁰

.

83±⁰

.

19

stat+^syst

mb in the interval −⁰

.

9

<

y

<

0

.

9. This result disfavours models considering all nucleons contributing to the scattering and those implementing strong shadowing, as EPS08 parametrization. The ratio of the

ψ(

2S

)

to J

/ψ

crosssection ratio inthe rapidity interval −⁰

.

9

<

y

<

0

.

9 is 0

.

34⁺₋⁰₀^._.⁰⁸₀₇

(

stat+^syst

)

. Most of the models underpredict this ra- tio by 2–2

.

5

σ

. The currentmodels of the

ψ(

2S

)

production in ultra-peripheral collisions require furtherefforts; the datashown inthepresentanalysismayhelp toimprovetheunderstandingof this processand torefine thetheory behind the exclusive vector mesonphoto-production.

Acknowledgements

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by all Grid centresandthe WorldwideLHC ComputingGrid (WLCG) Collaboration. The ALICE Collaboration acknowledges the follow- ing funding agencies for their support in building and running the ALICEdetector:State CommitteeofScience,WorldFederation of Scientists (WFS) and Swiss Fonds Kidagan, Armenia, Conselho Nacional de Desenvolvimento Científico e Tecnológico(CNPq), Fi- nanciadora de Estudose Projetos(FINEP),Fundaçãode Amparoà PesquisadoEstadodeSãoPaulo(FAPESP);NationalNaturalScience Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) andthe Ministryof Science and Technology of the Peo- ple’sRepublicofChina (MSTC);MinistryofEducationandYouthof the CzechRepublic; DanishNatural ScienceResearchCouncil, the Carlsberg Foundation and the Danish National Research Founda- tion;TheEuropeanResearchCouncilundertheEuropeanCommu- nity’sSeventhFrameworkProgramme;HelsinkiInstituteofPhysics andtheAcademyofFinland;FrenchCNRS-IN2P3,the‘RegionPays de Loire’,‘RegionAlsace’,‘Region Auvergne’andCEA,France;Ger- man BundesministeriumfurBildung,Wissenschaft,Forschungund Technologie (BMBF)and theHelmholtz Association; General Sec- retariat for Research and Technology, Ministry of Development, Greece; HungarianOrszagos Tudomanyos KutatasiAlappgrammok (OTKA) andNationalOfficefor ResearchandTechnology (NKTH);

Department of Atomic Energy and Department of Science and TechnologyoftheGovernmentofIndia;IstitutoNazionalediFisica Nucleare (INFN) and Centro Fermi – Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Italy; MEXT Grant-in- Aid for Specially Promoted Research, Japan; Joint Institute for Nuclear Research, Dubna; National Research Foundation of Ko- rea (NRF); Consejo Nacional de Ciencia yTecnología (CONACYT), Direccion General de Asuntos del Personal Academico (DGAPA), México,AmeriqueLatineFormationacademique–EuropeanCom- mission (ALFA-EC) and the EPLANET Program (European Particle PhysicsLatinAmericanNetwork);StichtingvoorFundamenteelOn- derzoek derMaterie(FOM)andtheNederlandseOrganisatievoor WetenschappelijkOnderzoek(NWO),Netherlands;ResearchCoun- cil ofNorway(NFR); NationalScienceCentre, Poland; Ministryof