Evidence for light-by-light scattering and searches for axion-like particles in ultraperipheral PbPb collisions at sNN=5.02TeV

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Physics

Letters

B

www.elsevier.com/locate/physletb

Evidence

for

light-by-light

scattering

and

searches

for

axion-like

particles

in

ultraperipheral

PbPb

collisions

at

√

s

_NN

=

5

.

02 TeV

.

The

CMS

Collaboration



CERN,Switzerland

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received10October2018

Receivedinrevisedform18July2019 Accepted29July2019

Availableonline1August2019 Editor: M.Doser Keywords: Light-by-light CMS UPC Photoproduction PbPb

Evidence for the light-by-light scattering process,

γ γ

→

γ γ

, in ultraperipheral PbPb collisions at a centre-of-mass energy per nucleon pair of 5.02 TeV is reported. The analysis is conducted using a data samplecorrespondingto anintegratedluminosity of390 μb−1 recordedbythe CMSexperiment at the LHC. Light-by-light scattering processes are selected in events with two photons exclusively produced,eachwithtransverseenergyEγ_T>2 GeV,pseudorapidity|

η

γ_|

_<

_{2.4,diphotoninvariantmass}

mγ γ>5 GeV,diphotontransversemomentump_Tγ γ<1 GeV,anddiphotonacoplanaritybelow0.01.After allselection criteriaare applied,14 eventsareobserved,comparedtoexpectationsof9.0_±0.9 (theo) events for the signal and 4.0±1.2 (stat) forthe background processes. The excessobserved indata relative to the background-only expectation correspondsto a significance of 3.7standard deviations, andhaspropertiesconsistentwiththoseexpectedforthelight-by-lightscatteringsignal.Themeasured fiduciallight-by-lightscatteringcrosssection,

σ

fid(

γ γ

→

γ γ

) =120±46 (stat)±28 (syst)±12 (theo) nb,

isconsistentwiththestandardmodelprediction.Themγ γ distributionisusedtosetnewexclusionlimits ontheproductionofpseudoscalaraxion-likeparticles,viathe

γ γ

→a_→

γ γ

process,inthemassrange

ma=5–90 GeV.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Elastic light-by-light (LbL) scattering,

γ γ

→

γ γ

, is a pure quantummechanicalprocessthatproceeds,atleadingorderinthe quantum electrodynamics (QED)coupling

α

, via virtual box dia-grams containing charged particles (Fig. 1, left). In the standard model(SM),theboxdiagram involvescontributionsfromcharged fermions (leptons andquarks) and the W± boson. Although LbL scatteringvia anelectron loophasbeenindirectlytestedthrough thehigh-precisionmeasurements oftheanomalousmagnetic mo-ment ofthe electron [1] and muon [2], its direct observationin thelaboratoryremains elusive becauseofa verysuppressed pro-duction cross section proportional to

α

4

_≈

₃

_×

₁₀−9_{. Out of the}

two closely-related processes—photon scattering in the Coulomb field of a nucleus (Delbrück scattering) [3] and photon splitting inastrongmagneticfield(“vacuumbirefringence”) [4,5]—onlythe former hasbeen clearly observed [6]. However, asdemonstrated inRef. [7],the LbLprocesscanbe experimentallyobserved in ul-traperipheral interactions of ions, with impact parameters larger than twice the radius of the nuclei, exploiting the very large

 _{E-mailaddress:cms-publication-committee-chair@cern.ch.}

fluxes of quasireal photons emitted by the nuclei accelerated at TeVenergies [8].Ionsacceleratedathighenergiesgeneratestrong electromagneticfields,which,intheequivalentphoton approxima-tion [9–11],canbeconsideredas

γ

beamsofvirtuality

Q

2

_<

₁

_/

_R2_,

where R is theeffectiveradiusofthecharge distribution.Forlead (Pb)nucleiwithradius

R

≈

7 fm,thequasirealphotonbeamshave virtualities

Q

2

_<

₁₀−3_GeV2_{,butverylargelongitudinalenergy(up}

to Eγ

=

γ

/

R

≈

80 GeV,where

γ

istheLorentzrelativisticfactor), enablingtheproductionofmassivecentralsystemswithverysoft transversemomenta(pT



0

.

1 GeV).Sinceeachphotonfluxscales

asthesquareoftheioncharge Z2,

γ γ

scatteringcrosssectionsin PbPbcollisionsareenhancedbyafactorof

Z

4

_

₅

_×

₁₀7 _compared

tosimilarproton-protonorelectron-positroninteractions.

Many final states have been measured in photon-photon in-teractions in ultraperipheral collisions of proton and/or lead beams at the CERN LHC, including

γ γ

→

e+e− [12–21],

γ γ

→

W+W− [22–24], andfirstevidenceof

γ γ

→

γ γ

reportedby the ATLAS experiment [25] witha signal significance of4.4standard deviations(3.8standarddeviationsexpected).Thefinal-state signa-tureofinterestinthisanalysisistheexclusive productionoftwo photons, PbPb

→

γ γ

→

Pb(∗)

γ γ

Pb(∗), where the diphoton final stateismeasuredintheotherwiseemptycentralpartofthe detec-tor,andtheoutgoingPbions(withapotentialelectromagnetic

ex-https://doi.org/10.1016/j.physletb.2019.134826

0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Fig. 1. Schematicdiagramsoflight-by-lightscattering(γ γ→γ γ,left),QEDdielectron(γ γ→e+e−,centre),andcentralexclusivediphoton(gg→γ γ,right)productionin ultraperipheralPbPbcollisions.The(∗)_{superscriptindicatesapotentialelectromagneticexcitationoftheoutgoingions.}

citationdenotedbythe(∗)_{superscript)survivetheinteractionand}

escapeundetectedatverylow

θ

angleswithrespecttothebeam direction (Fig. 1, left). The dominant backgrounds are the QED production of an exclusive electron-positron pair (γ γ

→

e+e−) where the e± are misidentified as photons (Fig. 1, centre), and gluon-inducedcentral exclusiveproduction(CEP) [26] of apairof photons(Fig.1,right).

The

γ γ

→

γ γ

processattheLHChasbeenproposedasa par-ticularlysensitivechanneltostudyphysicsbeyondtheSM. Modifi-cationsoftheLbLscatteringratescanoccurif,e.g. newheavy par-ticles,suchasmagneticmonopoles [27],vector-likefermions [28], ordarksector particles [29], contribute tothe virtual corrections oftheboxdepictedinFig.1.Other newspin-evenparticles,such asaxion-likeparticles(ALPs) [30] orgravitons [31],can also con-tributeto the LbL scatteringcontinuum or to newdiphoton res-onances.In addition, light-by-lightcross sectionsare sensitive to Born–InfeldextensionsofQED [32],andanomalousquarticgauge couplings [33].

We report a study of the

γ γ

→

γ γ

process, using PbPb collision data recorded by the CMS experiment in 2015 at

√

sNN

=

5

.

02 TeV and corresponding to an integrated luminosity

of 390 μb−1. A comparison of exclusive diphoton anddielectron yields, with almost identical event selection and reconstruction efficiencies, is provided as a function of key kinematic variables to check of the robustness of the analysis. The ratio of the LbL scattering to QED e+e− production cross sections is reported, so asto reduce thedependence on various experimental correc-tionsanduncertainties.Usingthemeasured

mγ γ distribution,

new exclusion limits are set on ALP production, in the mass range

ma

=

5–90 GeV.

2. TheCMSdetector

The central feature of the CMS apparatus is a superconduct-ing solenoidof6 m internal diameter,providinga magneticfield of3

.

8 T.Withinthesolenoidvolumeare asiliconpixelandstrip tracker,aleadtungstatecrystalelectromagneticcalorimeter(ECAL), andabrass andscintillatorhadroncalorimeter(HCAL),each com-posedofa barrel(EB andHB) andtwoendcap (EEandHE) sec-tions. Forward calorimetry (HF), based on a steel absorber and quartzfibresthatrunlongitudinallythroughtheabsorberand col-lectCherenkovlight, primarilyfromtheelectromagneticparticles, complementsthecoverage providedbythebarrelandendcap de-tectors up to pseudorapidity

|

η

|

=

5

.

2. Muons are measured in gas-ionisation detectors embedded in the steel flux-return yoke outsidethe solenoid. The silicon trackermeasures charged parti-cles within the

|

η

|

<

2

.

5 range. It consists of 1440 silicon pixel and15 148siliconstripdetectormodules.Fornonisolatedcharged particles in the transverse momentum range 1

<

pT

<

10 GeV

and

|

η

|

<

1

.

4, the track resolutions are typically 1.5% in pT and

25–90(45–150) μminthetransverse(longitudinal)impact param-eter [34]. The first level of the CMS trigger system [35], Level-1

(L1), composed ofcustom hardware processors, uses information fromthe calorimetersandmuon detectors toselectthe most in-teresting events in a fixed time interval of less than 4 μs. The high-leveltrigger(HLT)processorfarmfurtherdecreasestheevent rate beforedata storage.A moredetaileddescription ofthe CMS detector,togetherwithadefinitionofthecoordinatesystemused andtherelevantkinematicvariables,canbefoundinRef. [36].

3. Simulationandreconstruction

The light-by-light signal is generated with the MadGraph v5 [37] MonteCarlo(MC) eventgenerator,withthemodifications discussed inRefs. [7,38] toincludethenuclearphoton fluxesand theelementaryLbLscatteringprocess.Thelatterincludesallquark andleptonloopsatleadingorder,butomitstheW boson contribu-tions,whichareonlyimportantfordiphotonmasses

mγ γ

>

2mW.

Next-to-leading order (NLO) quantum chromodynamics and QED corrections increase

σγ γ

_→γ γ by justa few percent [39] and are alsoneglectedhere.Exclusive

γ γ

→

e+e−eventscanbe misiden-tifiedasLbLscatteringifneitherelectrontrackisreconstructedor ifboth electrons undergo hardbremsstrahlung. This QEDprocess is generated using the starlight v2.76 [40,41] event generator, alsobasedontheequivalent-photonfluxes.Sincethecrosssection fortheQEDe+e− backgroundisfourtofiveordersofmagnitude largerthanthatforLbLscattering,anditreliesonphysicsobjects (electrons) that are very similar to thoseof thesignal (photons), the exclusivedielectronbackgroundisanalysed indepthinorder to estimate many ofthe (di)photon efficiencies directlyfrom the data,aswellastodetermineanLbL/(QEDe+e−) productioncross sectionsratiowithreducedcommonuncertainties.Thecentral ex-clusiveproductionprocess,gg

→

γ γ

,issimulatedusing superchic 2.0 [42], wherethecomputed proton-protoncrosssection [26] is conservativelyscaled tothePbPb caseby multiplyingitby A2R4_g, where A

=

208 isthemassnumberofleadand

R

g

≈

0

.

7 isagluon

shadowing correction in the relevant kinematic range [43], and wheretherapiditygapsurvivalprobability,encodingthe probabil-itytoproducethediphoton systemexclusively withoutanyother hadronicactivity,isassumedtobe100%.Giventhelarge theoreti-caluncertaintyoftheCEPprocessforPbPbcollisions,theabsolute normalisationofthisMC contributionisdirectlydeterminedfrom acontrolregioninthedata,asexplainedlater.Allgeneratedevents are passed through the Geant4 [44] detector simulation,andthe events are reconstructed with the same software asfor collision data.Thesimulationdescribesthetrackermaterialbudgetwithan accuracybetterthan10%,asestablishedbymeasuringthe distribu-tion ofreconstructed nuclearinteractionsandphotonconversions inthetracker [34,45].

Photons and electrons are reconstructed using an algorithm based on the particle flow global event description (GED) [46]. The GED algorithm uses information from each subdetector sys-tem to provide charged-particle tracks, calorimeter clusters, and muontracks.Electromagneticshowersfromphotonsandelectrons

deposit97% of their incident energy into an array of 5

×

5 ECAL crystals. The tracker material can induce photon conversion and electronbremsstrahlungand,becauseofthepresenceofthestrong CMSsolenoidalmagneticfield,theenergyreachingthecalorimeter istherebyspreadin

φ

.Thespreadenergyiscapturedbybuildinga clusterofclusters,or“supercluster” [47].TheGEDalgorithmallows foranalmostcompleterecoveryoftheenergyofthephotonsand electrons, even if they initiate an electromagnetic shower in the materialinfrontoftheECAL.Nonetheless,inthecaseofphotons, inordertokeeptoaminimumthee±contamination,we require themtobeunconvertedinthetracker.Thereconstructedenergyof thissuperclusterisusedtodefinetheenergyofthephoton.Since thedefaultCMSphoton reconstructionalgorithm isoptimisedfor

γ

ande± withtransverseenergies

E

T

=

E sin

θ >

10 GeV,whereas

thecrosssectionforphotonsandelectronsfromexclusive produc-tionpeaksinthelower

E

T

≈

2–10 GeV range,aversionoftheGED

algorithmoptimisedforthistransverseenergyrangeisemployed. Thethresholdfortheenergyofphotons,electrons,and superclus-ters,isloweredto1 GeV,insteadofthe10–15 GeVthresholdused in the standard CMS analyses [47]. The full analysis is indepen-dentlyrepeatedusing adifferent “hybrid”photon/electron recon-structionalgorithm [47], obtaining reconstruction efficiencies and final results fully consistent with those derived withthe default GED approach. Additional particle identification (ID) criteria are applied,in order to remove photons(mostly) from high-pT

neu-tralpion decays,based on a shower shape analysisthat requires thewidthoftheelectromagneticshower alongthe

η

directionto bebelow0.02(0.06)unitsintheECALbarrel(endcap).

Electron candidates are identified by the association of a charged-particletrackfromthecollisionvertexwithsuperclusters in the ECAL. The association takes into account energy deposits bothfromtheelectronandfrombremsstrahlungphotonsproduced duringits passagethroughthe innerdetector.Additional electron identificationcriteria(isolation,numberoftrackerhits,HCAL/ECAL energy deposit) are applied, as discussed in Ref. [13]. The elec-tronenergyscaleisverifiedusingasampleof

γ γ

→

e+e−events, comparingtheenergyofthesupercluster E to themomentumof thetrack

p.

Theelectron

E

/

p ratio iswithin5%ofunityinthe bar-reland15% intheendcaps. Agood agreementis foundbetween data andsimulation, both in the energyscale andresolution. In addition, the LbL simulation is also used to validate the photon energyscale.Thereconstructedsuperclusterenergyandgenerated photonenergyagreewithinafewpercent,confirmingthatthe re-constructedsuperclusterenergyiswellcalibrated.

4. Eventselectionandbackgroundestimation

The exclusive diphoton candidates are selected at the trigger levelwithadedicatedL1algorithmthatrequiresatleasttwo elec-tromagnetic clusters (L1 EG) with ET above 2 GeV and at least

oneoftheHFdetectorswithtotalenergybelowthenoise thresh-old. No additional selection is applied in the HLT. Data are also recordedwith single-photontriggers with ET thresholds above 5

and10 GeV,andusedinthisanalysistoestimatetheefficiencyof thefirst trigger via atag-and-probe procedure [48],as described below.Intheofflineanalysis,eventsareselectedwithexactlytwo photons,each with ET

>

2 GeV and

|

η

|

<

2

.

4,thatsatisfy further

selection requirementsdescribed below. Neutraland charged ex-clusivityselection criteriaareapplied toreject eventshavingany additionalactivity over therange

|

η

|

<

5

.

2. First, all events with reconstructed charged-particle tracks with pT

>

0

.

1 GeV are

re-movedfromfurther analysis.Second, eventsare requiredtohave no activity in the calorimeters, above energy noise thresholds (rangingbetweenabout 0

.

6 GeV inthe barrel, to 4

.

9 GeV inthe HF),outsidearegion

η

<

0

.

15 and

φ <

0

.

7 inthebarrel(

η

<

Fig. 2. Acoplanaritydistributionofexclusivee+e−eventsmeasuredindata(circles), comparedtotheexpectedQEDe+e−spectruminthe starlight MCsimulation (his-togram),scaledasdescribedinthetext.Thecurveshowsa

χ

2_{fittothesumoftwo}

exponentialdistributionscorrespondingtoexclusivee+e−plusanyresidual (nona-coplanar)backgroundpairs.Errorbarsaroundthedatapoints indicatestatistical uncertainties,andhashedbandsaroundthehistogramincludesystematicandMC statisticaluncertaintiesaddedinquadrature.Thehorizontalbarsaroundthedata symbolsindicatethebinsize.

0

.

15 and

φ <

0

.

4 inthe endcap) around the two photons. The noise thresholds are determined fromno- or single-bunch cross-ing events. To eliminate nonexclusive backgrounds, characterised by afinal statewithlarger pT andlargerdiphoton acoplanarities,

Aφ

= (

1

− φ

γ γ

/

π

)

, thanthe back-to-back exclusive

γ γ

events,

thetransversemomentumofthediphotonsystemisrequiredtobe

pγ γ_T

<

1 GeV,andtheacoplanarityofthepairtobeAφ

<

0

.

01.The

chosen valuesof the pair pT andacoplanarity selections, similar

to those originally suggested in Ref. [7], are motivatedby previ-ousCMSstudiesofexclusivedileptonproduction [12–14].Thetwo dominant exclusive background sources potentially remaining in the LbLscattering signal region,

γ γ

→

e+e− andCEPgg

→

γ γ

, arestudiedindetailnext.

4.1. QED e+e−background

Inordertohaveafull controloftheQEDe+e− backgroundin theLbLscatteringsignalregion, thesameanalysiscarriedout for the LbLevents isdone on exclusivedielectron candidates, apply-ingthesamecriteriaasdescribedabovefordiphotonevents,with the exception thatexactly two opposite-signelectrons are recon-structed, instead ofexactly two photons, and noadditional track with

p

T

>

0

.

1 GeV shouldbepresentinadditiontothetwotracks

correspondingtotheelectrons.Fig.2showstheacoplanarity distri-butionmeasuredinQEDe+e− eventspassingallselectioncriteria comparedtotheMCexpectation.

The curve is a binned

χ

2 _{fit of the data to the sum of two}

exponential functionsrepresenting the exclusive QED e+e− pro-ductionplusanyresidualbackgroundinthehigh-acoplanaritytail. In the region of acoplanarity below 0.01, 9570 dielectron events are reconstructed with a purity of

P =

0

.

960

±

0

.

002 (stat), ob-tainedfromthe ratioofamplitudes ofthetwo exponential func-tions fitted to the data. The yellow histogram shows the same distribution obtained directly fromthe starlight MC simulation, scaled to the total number of events in data, multiplied by the purity. The corresponding kinematic distributions of the selected

γ γ

→

e+e− events inthe Aφ

<

0

.

01 region are showninFig. 3,

togetherwiththecorrespondingMCpredictionsnormalisedinthe samemanner.ThehashedbandaroundtheMChistogramsinclude the systematic uncertainties (trigger, electron reconstruction and identification, and MC statistical uncertainties added in quadra-ture) discussed in Section 6, estimatedas a function ofelectron

Fig. 3. Comparisonofdata(circles)and starlight MCexpectation(histogram,scaledasdescribedinthetext)fortheexclusivee+e− eventspassingallselectioncriteria, asafunctionofdielectronacoplanarity(topleft),mass(topright),pT(bottomleft),andrapidityy (bottomright).Errorbarsaroundthedatapointsindicatestatistical

uncertainties,andhashedbandsaroundthehistogramsincludesystematicandMCstatisticaluncertaintiesaddedinquadrature.Thehorizontalbarsaroundthedatasymbols indicatethebinsize.TheratioofthedatatotheMCexpectationisshowninthebottompanels.

ET and

η

.Agooddata-to-simulationagreement isfound,thereby

confirming thequality oftheelectromagneticparticle reconstruc-tion,andoftheexclusiveeventselectioncriteria,aswellasofthe MCpredictions [7,41] forexclusiveparticleproductionin ultrape-ripheral PbPb collisions at the LHC. Small systematic differences between the central values of the exclusive dielectron data and the MC predictionare seen in tails of some of the distributions (atincreasingacoplanarityand

p

T)duetothepresenceofslightly

acoplanar events in data, likely from

γ γ

→

e+e− events where one (orboth)electrons radiate an extrasoftphoton, thatare not explicitlysimulated by the MC eventgenerator. These small dis-crepancies have no impact on the final extracted cross sections integratedoverthewholerangeofdistribution(s).

TheQEDdielectronbackgroundisthendirectlyestimatedfrom the starlight MC simulation by counting the number of such e+e− events that pass all LbL scattering selection criteria. The chargedexclusivitycondition,requiringnotrackintheeventabove the pT

=

0

.

1 GeV threshold, is successfulin removing this

back-ground almost entirely. This tracking efficiency is controlled in events with exactly two reconstructed photons and exactly one track, finding good data-MC agreement. The QED background in the signal region is estimated to be Nee,data

=

1

.

0

±

0

.

3 (stat) events,where the assigneduncertainty corresponds to the event countinthesimulatedsamples.

4.2. Central exclusive diphoton background

Although the LbL and CEP processes share an identical final state, their kinematic distributions are different. Diphotons from quasireal

γ γ

fusionprocesses areproduced almostatrestinthe

transverse plane and, thus, the final-state photons are emitted back-to-back with balanced pair transverse momentum pγ γ_T

≈

0. On the other hand, typical CEP photon pairs are produced in diffractive-like gluon-mediated processes [26,42] withlarger mo-mentum exchangesleading to a diphoton transverse momentum distribution peakingat pT

≈

0

.

5 GeV, after selectioncriteria, and

moderately large tails in the azimuthal acoplanarity distribution. Thus, the requirement ondiphoton acoplanarity(Aφ

<

0

.

01) also

significantlyreducesthegg

→

γ γ

background.SincetheMC pre-diction forCEP gg

→

γ γ

haslarge theoretical uncertainties, and inordertoaccountforanyotherremainingbackgroundsresulting in photons that are not back-to-back (such as

γ γ

→

e+e−

γ

(

γ

)

eventspassing theanalysisselection criteria),forwhichnoevent generatoriscurrentlyavailable,theCEPbackgroundisnormalised tomatchthedataintheregionAφ

>

0

.

02,wherethecontribution

from

γ γ

→

γ γ

is negligible(Fig. 4). The background normalisa-tionfactoristhenobtainedfrom

f_nonacoplanarnorm

=



Ndata

(

Aφ

>

0

.

02

)

−

NMCLbL

(

Aφ

>

0

.

02

)

−

N_QEDMC

(

Aφ

>

0

.

02

)



NMC_CEP

(

Aφ

>

0

.

02

)



,

(1)

andfound to be f_nonacoplanarnorm

=

1

.

06

±

0

.

35 (stat).The numberof eventsduetoCEPplusanyresidualbackgroundsisthusestimated to be 3

.

0

±

1

.

1 (stat). The statisticaluncertainties quotedin both valuesaredrivenbythesizeofthedatasampleremainingathigh acoplanarities,afterallselectioncriteriahavebeenapplied.

Table 1

Numberofdiphotoncandidatesmeasured indataandexpectedfromMCsimulationfor LbLscattering,QED e+e−production,andfromtheCEP+othercontributions,aftereacheventselectionstep(cumulative)described inthetext.Theyieldsofthesimulatedprocessesarescaledaccordingtotheirtheoreticalcrosssectionsandthe integratedluminosityoftheanalyseddataset.TheCEP+othervaluesarenormalisedfromthehigh-acoplanarity tailwithascalefactorestimatedfromthedataasdescribedinthetext.TheLbLscatteringsimulationuncertainty quotedisthatofthetheoreticaluncertaintyoftheprediction,whereastheuncertaintiesintheQEDe+e−and CEP+othersyieldsarestatistical.

Selection criteria Data LbL MC QED e+e−MC CEPMC+other (normalisedtodata) Charged exclusivity 648 11.1±1.2 (theo) 10.3±1.0 (stat) 24.3±8.1 (stat) Neutral exclusivity 108 10.8±1.1 (theo) 10.1±1.0 (stat) 23.6±7.9 (stat) Diphoton pT<1 GeV 39 10.2±1.1 (theo) 7.7±1.0 (stat) 19.5±6.5 (stat)

Diphoton acoplanarity<0.01 14 9.0±0.9 (theo) 1.0±0.3 (stat) 3.0±1.1 (stat)

Fig. 4. Diphotonacoplanaritydistributionforexclusiveeventsmeasuredinthedata afterselection criteria(squares),comparedtothe expectedLbLscatteringsignal (orangehistogram),QEDe+e− (yellowhistogram),andthe CEP+other(lightblue histogram,scaledtomatchthedataintheAφ>0.02 regionasdescribedinthe text)backgrounds.SignalandQEDe+e−MCsamplesarescaledaccordingtotheir theoreticalcrosssectionsandintegratedluminosity.Theerrorbarsaroundthedata pointsindicatestatisticaluncertainties.Thehorizontalbarsaroundthedatasymbols indicatethebinsize.

4.3. Light-by-light signal distributions

The exclusive diphoton signal is extracted after applying all selection criteria described above and estimating the amount of residual QED e+e− and CEP+other backgrounds. Table 1 shows thenumberofeventsremainingaftereachselectioncriterion.The mainselectionrequirementcorrespondstotwophotonseachwith

ET

>

2 GeV,

|

η

|

<

2

.

4 (excluding photonsfalling inthe

η

≈

0

.

1

gap region between the EB and EE, 1

.

444

<

|

η

|

<

1

.

566), and diphoton invariant mass greater than 5 GeV. The numbers of events measured in data and expected from the sum of all MC contributionsinthefirsttworowsdonotmatchbecausethese se-lectionrequirementsacceptafractionofnonexclusivebackgrounds that are not includedin the simulation.Once thefull exclusivity selectioncriteriaareapplied, thedata-to-simulationagreementis very good.We observe14 LbL scatteringcandidates, to be com-paredwith9

.

0

±

0

.

9 (theo) expectedfromtheLbLscatteringsignal, 3

.

0

±

1

.

1 (stat) fromcentral exclusive plusany residualdiphoton backgrounds, and 1

.

0

±

0

.

3 (stat) from misidentified QED e+e− events.

An extra selection criterion has been also studied by further requiring that the candidate LbL scattering events have no sig-nal above the noise threshold in the pixel tracker layers. This more stringent selection is sensitive to charged particles down to

∼

40 MeV,and resultsina number ofreconstructed LbL scat-tering signal counts (and even more reduced QED backgrounds) consistentwiththe MCpredictions. However,since theefficiency ofsuchatightselectionisdifficulttoassessfromacontrolregion

indata,thedefaultanalysisiskeptwiththecharged-particletrack

pT

>

0

.

1 GeV exclusivityrequirement.

Fig. 5 showsthe comparison of the measured and simulated photon transversemomentum,photonpseudorapidity, photon az-imuthal angle, diphoton invariant mass, diphoton rapidity, and diphoton transversemomentum distributions. Both themeasured yields andkinematic distributions are in accord withthe combi-nation oftheLbLscatteringsignalplus QEDe+e− andCEP+other backgroundexpectations.

5. Crosssectionextraction

Given the low signal yield available for an extraction of dif-ferential cross section distributions, an integrated fiducial cross section for LbL scattering above a diphoton mass mγ γ

=

5 GeV iscalculatedinstead.Theratio R of crosssectionsofthe light-by-lightscatteringovertheQEDe+e−processesismeasured,thereby reducing the uncertainties related to trigger and reconstruction efficiencies,andintegratedluminosity.Efficiencyuncertainties par-tially cancel in the ratio, as described later, thanks to a similar selection appliedto photonsandtoelectrons; andthe integrated luminositydependencefullycancelsout.Theratio

R is

definedas

R

=

σ

fid

(

γ γ

→

γ γ

)

σ

(

γ γ

→

e+e−

,

me+e−

_>

_{5 GeV}

₎

=

Nγ γ,data

−

Nγ γ,bkg Cγ γ CeeAccee Nee,data

_P

.

(2)

Here

σ

fid

(

γ γ

→

γ γ

)

is the LbL scattering fiducial cross

sec-tion (i.e. passing all the aforementioned pT,

η

, mγ γ kinematic

selection criteria for the single photons and for the photon pair);

σ

(

γ γ

→

e+e−

,

me+e−

>

5 GeV

)

is the total cross section for the QED e+e− process for masses above 5 GeV; Accee

₌

Ngen

₍

_pgen

T

>

2 GeV

,

|

η

gen

|

<

2

.

4

,

me

+_e−

>

5 GeV

)/

Ngen

₍

_me+e−

_>

5 GeV

)

=

0

.

058

±

0

.

001 (stat) is the dielectron acceptance for the fiducial single-electronkinematicselections determined from the starlight MC generator; Nγ γ,data _{is the number of}

dipho-toneventspassingtheselectionindata; Nγ γ,bkg istheestimated numberofbackgroundeventspassingallselectioncriteria;

N

ee,data

isthenumberofdielectroneventspassingourselectionindata;

P

isthepurityoftheestimatedfractionofQEDe+e−signal among thesedielectronevents;and

C γ γ and C

ee_{aretheoverallefficiency}

correction factors, for the

γ γ

and e+e− selections, respectively, thataredeterminedasdiscussedinthenextsection.

5.1. Diphoton analysis efficiencies

The C γ γ correction factor in Eq. (2) is obtained through the factorisedexpression

Fig. 5. DistributionsofthesinglephotonET,

η

,andφ,aswellasdiphotonpT,rapidity,andinvariantmassmeasuredforthefourteenexclusiveeventspassingallselection

criteria(squares),comparedtotheexpectationsofLbLscatteringsignal(orangehistogram),QEDe+e−MCpredictions(yellowhistogram),andtheCEPplusotherbackgrounds (lightbluehistogram,scaledtomatchthedatainthe Aφ>0.02 region).SignalandQEDe+e−MCsamplesarescaledaccordingtotheirtheoreticalcrosssectionsand integratedluminosity.Theerrorbarsaroundthedatapointsindicatestatisticaluncertainties.Thehorizontalbarsaroundthedatasymbolsindicatethebinsize.

where the diphoton efficiency

εγ γ is

determined using the LbL scattering MC simulation. This efficiency receives contributions fromtriggering,photonreconstructionandidentification,and neu-tral and charged exclusivitycriteria that are directly determined from the data via independent data-to-simulations scale factors, SF

=

ε

data

_/

_ε

MC_{,asexplainedbelow.}

ThediphotonefficiencyisfirstderivedfromtheLbLscattering simulationvia:

ε

γ γ

=

Nreco

(

ET

>

2 GeV

,

|

η

reco

| <

2

.

4

,

ID, trigger, excl.

)

Ngen

₍

_E

T

>

2 GeV

,

|

η

gen

| <

2

.

4

)

,

(4)

wheretheselectioninthenumeratoranddenominatorappliesto exactlytwophotonsrequiredineachevent,whicharealsowithin the fiducial kinematic region in diphoton pT, mass, and

acopla-narity. It is found to be

ε

γ γ

_{= (}

₂₀

_.

₇

_±

₀

_.

₄

₎

_{%, mostly driven by}

the inefficiencies of the single photon reconstruction and

identi-fication, andofthetrigger (εγ,reco+ID

_,

_ε

γ γ,trig.

_≈

_{70%).The quoted}

uncertaintyhereisstatisticalonly,reflecting thefinitesizeofthe LbLscatteringMCsample.

ThesecondtermofEq. (3),thephotonreconstructionand iden-tification efficiencycorrection

(

SFγ,reco+ID

₎

_{, isextractedfromdata}

by selecting

γ γ

→

e+e−

(

γ

)

events,where one of the electrons emits a hard bremsstrahlung photon dueto interaction with the materialofthetracker.The

p

Tofthetwoelectronsin

γ γ

→

e+e−

eventsbeingapproximately equal,ifoneofthe electrons emitsa hardbremsstrahlungphoton,itmaynotreachtheECALtobe iden-tifiedasanelectronbutitcanstillbereconstructedinthetracker asachargedparticle.

Ina firststep,hard-bremsstrahlungeventsareselectedamong events passing a trigger requiring one L1 EG cluster with ET

>

5 GeV, that have exactly two oppositely charged particle tracks and exactly one electron reconstructed. Among those events,

we then look for exactly one photon compatible with a hard bremsstrahlung, asdescribed below. Such eventsare used to es-timatetheefficiencyinatag-and-probeprocedure,via

ε

γ_data,reco+ID, hard-brem

=

N

reco+ID,hard-brem probe

Nreco+ID, hard-brem_passing

,

(5)

wheredenominatorandnumeratoraredefinedasfollows:

•

Nreco+ID, hard-brem_passing : Electrons are selected if (i) their direction

matcheswithoneofthetworeconstructedtrackswithina ra-dius

R

=

√

(

η

)

2

_{+ ( φ)}

2

_<

₁

_.

_{0 (where}

_η

_and

_φ

_{are those}

oftheelectrontrack),(ii)they have

E

T above5 GeV,and(iii)

theirassociatedECALsuperclusterismatchedwithin

R

<

0

.

1 toanL1EGclusterwith

E

T

>

5 GeV.The

p

Tofthetrackthatis

not matchedwiththeelectron shouldbe below2 GeV,since we assume that trackto be generated by the electron after bremsstrahlungemission.The punmatched track

T

<

2 GeV

require-ment ensures that thislow-pT chargedparticle issufficiently

bentbythemagneticfield,andthustheexpectedphoton (ex-trapolatedtotheECAL)andthesecondelectronaresufficiently separated.Eventsenteringthedenominatorarenotrequiredto haveareconstructedphoton.

•

Nreco+ID, hard-brem_probe : Events from the denominator are also in-cludedinthenumeratorifaphotonisfoundwith

E

T

>

2 GeV

thatpassestheidentificationcriteria.

The efficiencyis extractedusing a fit to the acoplanarity dis-tribution between the electron and the charged-particle track, and amounts to

ε

_dataγ,reco+ID, hard-brem

= (

86

.

5

±

7

.

0

)

%, to be com-paredwith

ε

γMC,reco+ID, hard-brem

= (

82

.

5

±

2

.

0

)

% in the MC

simula-tion, where uncertainties are statistical(as well as all other un-certaintiesquotedinthissection).Theratiooftheseefficienciesis usedtodefinethecorrespondingSFγ,reco+ID, hard-brem

=

1

.

05

±

0

.

09 scalefactor. Wenote that thisprocedure checksnot only the re-construction and identification efficiency in data, but also effec-tivelyincludesbinmigrationsoutsidethefiducial

p

Trangedueto

the effectsof photon energy scale andresolution. The impact of binmigrations in the final diphotoncross section is found to be belowthe1%level.

Events in the study above comprise exactly two charged-particle tracks, corresponding to the two electrons. They do not probethe possibility that thephoton, reconstructed in theECAL, haspreviously alsointeracted in the trackergenerating an e+e− pairthathasbeenalsoreconstructedasoneortwoadditional dis-placedlow-pTcharged-particletracks.InthecaseofanLbL

scatter-ingevent,sucha genuinesignaleventwouldbediscarded bythe strictchargedexclusivitycriterion,whichisappliedindependently oftheproximityofthetrackstothephoton,inordertokeepthe QED e+e− background to a minimum. The modeling of this ef-ficiencyloss in simulation is checked using hard-bremsstrahlung eventswithasimilarselectionasabove,exceptthatuptotwo ad-ditionalcharged-particle tracksarenowallowed intheevent. We checkthefractionofevents wherenoadditionaltrack, more dis-placed than the one with pT

<

2 GeV required in the selection,

is found in a window

|

η

|

<

0

.

15,

| φ|

<

0

.

7 around the pho-ton. This efficiencyamounts to

ε

_dataγ,tk veto

= (

89

.

9

±

1

.

7

)

% in data, and

ε

_MCγ,tk veto

= (

91

.

1

±

1

.

2

)

% intheMCQEDe+e−simulation.The ratiooftheseefficiencies gives SFγ,tk veto

₌

₀

_.

₉₉

_±

₀

_.

_{02.The final}

overallscale factorfor reconstruction andidentification, account-ingforthemodelingofphoton conversionsinthe MCsimulation andtheefficiencytoreconstructtheassociateddisplacedtracks,is thenSFγ,reco+ID

₌

_SFγ,reco+ID, hard-brem_SFγ,tk veto

₌

₁

_.

₀₄

_±

₀

_.

_09.

ThethirdtermofEq. (3) accountsforthetriggerselection effi-ciency. Exclusivediphotoneventsareselected usingan L1trigger requiring two electromagnetic clusters with ET

>

2 GeV, and no

activity(abovenoisethresholds)inatleastoneoftheHF calorime-ters. These two components of the trigger, the electromagnetic cluster selection and the HF energy veto, are verified indepen-dently indata. The efficiencyforreconstructing an L1EG cluster with ET

>

2 GeV is verified using a tag-and-probe technique on

QED e+e− events, where the dielectron acoplanarity is fitted to extract thesignal andmeasure theefficiency.The sameselection criteriausedinthemainanalysisareapplied,includingthe exclu-sivityrequirements.Eventsarefurtherselectedusingasupporting triggerrequiringoneL1EGclusterwith

E

T

>

5 GeV withthesame

HF energyvetoastheanalysistrigger. The L1EG clusterused in thetriggerismatched(usingthesamecriterionmentionedabove) to one of the two electrons reconstructed offline, called the tag. The otherelectron intheeventistheprobe,anditqualifies asa passingprobeifitismatchedtoanL1EGclusterwith

E

T

>

2 GeV.

The efficiencyisthenthefractionofprobes that arealsopassing probes,anditisinthe45–100%range,withthelowestefficiency found close to the ET

=

2 GeV threshold andat high

|

η

|

. Scale

factors are determined from the data-MC differences, as a func-tion of ET,intwo

|

η

|

bins.Applying them tothe LbLsimulation,

we findanintegratedscale factorof1

.

12

±

0

.

31 (stat).The same QED e+e− sample isused to test the HFveto componentofthe analysis trigger. This time, we apply the nominal dielectron se-lection, including exclusivityrequirements,butfor a datasample collected with a trigger requiring a single-EG object in the HLT with

E

T

>

10 GeV and

|

η

|

<

1

.

5 plusasmallamountofenergyin

theHFs corresponding to about50% ofthe mostperipheralPbPb events.Bothelectronsintheeventarethenmatchedtoan L1EG cluster with ET

>

2 GeV. We find that

(

100+₋0₃

)

% of the selected

eventsalsopasstheanalysistrigger,i.e. satisfytheHFvetointhe trigger,inperfectagreementwiththeresultpredictedfromtheMC simulation. Combiningthe results ofthe studies above, thescale factorSFγ γ,trig.

=

1

.

12

±

0

.

31 isobtainedfortheratioofthe prod-uct of trigger efficiencies in data to that obtained from the MC simulation.

The last two terms of Eq. (3) account for the efficiency of the exclusivityselections. Thefraction ofeventspassing the QED dielectron selection, withthe exception of the charged and neu-tral exclusivity criteria, are analysed. Using the acoplanarity dis-tribution to extract the signal, we find that

(

92

.

5

±

0

.

3

)

% of the events feature no additional track in the event, to be compared to

(

99

.

3

±

0

.

1

)

% in simulation. We deduce that the correspond-ing scale factor is SFch.excl.

=

0

.

93

±

0

.

01. A similar strategy is usedfortheneutralexclusivityselection,thistimeinevents pass-ing the corresponding requirements. This efficiency is found to be

(

89

.

9

±

1

.

4

)

% in data, and

(

96

.

9

±

1

.

3

)

% in simulation. This scale factor isthen SFneut.excl.

=

0

.

93

±

0

.

02.Differences between the exclusivity efficiencies in data and MC simulation are likely dueto thepresence ofnonexclusive events,such as

γ γ

→

e+e− processes witha small hadronic overlapof the lead ions, whose modelingiscurrentlynotavailable intheMonteCarlogenerators. Theincorporationofsuchnonexclusive eventsinthedefinitionof thesignalisirrelevant,becausebothSFch.excl.andSFneut.excl.cancel outintheRratio,asexplainedinSection6.

5.2. Dielectron analysis efficiencies

Fortheexclusivedielectronanalysis,theefficiencyisestimated usingthe starlight MCsimulationvia

ε

ee

₌

Nreco

(

precoT

>

2 GeV

,

|

η

reco

| <

2

.

4

,

ID, trigger, excl.

)

Ngen

₍

_pgen

T

>

2 GeV

,

|

η

gen

| <

2

.

4

)

Table 2

Summaryofthe overallcrosssection measurementefficiencies Cγ γ ,ee_{, efficienciesfrom simulation}

εγ γ ,ee_{,andindividualdata-to-simulationscalefactorsSF}γ γ ,ee_{,obtainedforthediphotonand}

dielec-tronanalyses.“Reco.andID”standsforreconstructionandidentification.Allquoteduncertaintiesare systematic.

Diphoton global efficiency, Eq. (3) Cγ γ = (21.5±6.5)% Diphoton efficiency (from simulation) εγ γ _{= (20.7±0.4)%}

γreco. and ID data-to-simulation scale factor SFγ ,reco+ID _{= 1.04±0.09}

Diphoton trigger selection data-to-simulation scale factor SFγ γ ,trig. _{= 1}

.12±0.31 Dielectron global efficiency, Eq. (7) Cee ₌

(9.4±1.5)% Dielectron efficiency (simulation) εee _{= (10.4±0.1)%}

e±reco. and ID data-to-simulation scale factor SFe, reco+ID _{= 0}

.98±0.04 Dielectron trigger selection data-to-simulation scale factor SFe e,trig. _{= 1.09±0.16}

Charged exclusivity data-to-simulation scale factor SFch.excl. = 0.93±0.01 Neutral exclusivity data-to-simulation scale factor SFneut.excl. _{= 0}

.93±0.02

where the kinematic criteria in the numerator and denominator areappliedtoexactlythetwoelectronsrequiredintheevent.The differentcomponentsofthe electronefficiencyare againchecked usingdata,via a factorised expressionforthe corresponding cor-rectionfactors:

Cee

=

ε

ee

(

SFe,reco+ID

)

2

(

SFee,trig.

) (

SFch.excl.

) (

SFneutral excl.

).

(7)

Most of the scale factors are common with those used in the diphotonanalysis(sincetheyarecomputedusingthelarger statis-ticalsampleofelectronsindata),exceptforthereconstructionand identification efficiency, which we check again for electrons. For thelatter,atag-and-probetechniqueusingafittotheacoplanarity distribution inQED e+e− events isused, asdone for the dipho-ton case, except that now the probe is a charged-particle track thatisapassingprobeifitismatchedtoanelectronpassingthe reconstruction andidentificationcriteria. We findanefficiencyof

(

89

.

4

±

1

.

2

)

% indata,consistentwith

(

90

.

4

±

1

.

3

)

% intheMC sim-ulation,correspondingtoascalefactorofSFe, reco+ID

₌

₀

_.

₉₉

_±

₀

_.

_02.

The scale factor for the trigger efficiency is also recomputed usingthe pT spectrumintheQEDe+e−MCsimulation,usingthe

same pT- and

|

η

|

-dependentscalefactors asforSFγ γ,trig.,leading

toSFee,trig.

=

1

.

09

±

0

.

16.

5.3. Summary of the efficiencies

Theoverall crosssection measurement efficiencies,efficiencies in simulation, as well as the individual data-to-simulation scale factors,obtainedforthediphotonanddielectronanalysesare sum-marisedinTable 2.Since thedata-to-simulation scalefactors are consistentwithunity,theyarenotincludedinthenumberslisted inTable1norintheresultsplottedinFigs.2–5,buttheyareused toobtainthe resultsinSection7.Theoverall diphotoncross sec-tionefficiency,Eq. (4),isabout20%comparedwithabout10%for dielectrons,Eq. (6). Thedielectronanalysisis afactoroftwo less efficientthan thediphoton one, becauseeach single electronhas a relatively largerprobability of losingenergy by bremsstrahlung before reaching the ECAL,andtherefore their probability to pass thetriggerselectionthresholdand/ortheirenergybeproperly re-constructedissmaller.Suchefficiencylossesarefurtherenhanced asthey entersquaredfortwo electrons to passthe triggerorbe concurrentlyreconstructedabovethe

p

Tandmassthresholds.

6. Systematicuncertainties

ThemainsourcesofuncertaintyintheLbLscatteringandQED e+e−productionmeasurementsarerelatedtothetriggerand sin-gle

γ

,

e± reconstruction efficiencies (Table 2).The uncertainty in

Table 3

SummaryofthesystematicuncertaintiesintheratioofthefiducialLbLscattering tototalQEDe+e−crosssections.

Photon reconstruction and identification (SFγ ,reco+ID_{) (2×9)%}

Electron reconstruction and identification (SFe, reco+ID₎

(2×2.5)%

Trigger 12%

Size of simulated background samples 6%

Total 23%

the latter is doubled in the total cross section, since we con-sider diphoton and dielectron final states. No additional uncer-tainty in the photon energy scale and resolution is considered, since possibledata-simulation differencesarealreadyincluded in the derivation of the reconstruction and identification scale fac-tors.Systematicuncertaintieshavebeenestimatedforthedifferent terms defining the ratio R of the LbL scattering over QED e+e− productioncrosssectionsgivenbyEq. (2),andaresummarisedin Table 3. Because the scale factors used for the trigger efficiency arecommontothediphotonanddielectronanalyses,their associ-ateduncertaintycancelspartiallyintheratio.However,becauseof differentreconstructionandidentificationefficiencies,the

E

T

spec-trum of photons is different from that of the electrons, leading to only incomplete cancellationofthe uncertainty. Assuming the uncertaintyineachindividual

p

T-binnedscalefactorisfully

corre-latedbetweenthephotonandelectroncases,butwithno correla-tionbetweenthescalefactorsfordifferentpT,wepropagatethese

uncertaintiessimultaneouslytothenumeratoranddenominatorof the ratio SFγ γ,trigger

/

SFee,trigger, resulting in a 12% uncertainty in that ratio.Thechargedandneutralexclusivityscalefactors, com-mon to the diphotonand dielectronmeasurements, are assumed tocancelintheratio R. TherestoftheSFtermslistedinTable2

havesmall statisticaluncertaintiesfromthe finitesize oftheMC samplesusedtoderivethem,whichpropagateintopercent uncer-taintiesinthefinalcrosssection,andareneglectedhere.

AmongtheotherparametersinEq. (2),thenormalisationofthe CEP and QED e+e− backgrounds in the signal region propagates intoa16% uncertaintyinthebackgroundyield(resultinginan6% uncertaintyinthecrosssection measurement),accountingforthe finite size of the MC samples. An additional uncertainty of 25% (10% inthefinalcrosssection),reflectingthefinitesizeofthedata sample athighacoplanaritiesusedfortheabsolutenormalisation of the CEPplus residual nonexclusive backgrounds, is considered asastatisticaluncertaintyratherthanasystematicone.

The final systematic uncertainty is obtained from adding in quadraturetheindividualuncertaintiesandislistedinthelastrow ofTable3.

7.Results

7.1. Light-by-light cross section

Thecompatibilityofthedatawiththebackground-only hypoth-esis has been evaluated from the measured acoplanarity distri-bution (Fig. 4), using a profile-likelihood ratio as a test statistic, includingallsystematicuncertaintiesasnuisanceparameterswith log-normalpriors [49,50].Theuncertaintyduetothefinitesizeof theMCsamplesisalsoincludedasanadditionalnuisance param-eterforeach binofthe histogram.The significanceof theexcess atlowdiphotonacoplanarityindata,estimatedfromtheexpected distributionoftheteststatisticforthebackground-onlyhypothesis obtainedwithpseudo-experiments, is3.7standarddeviations(3.5 standard deviations expected). If using only the total number of eventsobserved andexpectedintheregion Aφ

<

0

.

01,weobtain

asignificanceof3.4 standarddeviations(3.2 expected).

The final ratio of the fiducial LbL scattering to the total QED e+e−crosssectionsisobtainedfromEq. (2),andamountsto

R

= (

25

.

0

±

9

.

6 (stat)

±

5

.

8 (syst)

)

×

10−6

,

(8)

wherethestatisticaluncertaintyincludesthenormalisation uncer-tainties of the CEP and QED backgrounds, added in quadrature. Thefiducialcrosssection isobtainedfromthetheoretical predic-tionof

σ

(

γ γ

→

e+e−

,

mee

_>

_{5 GeV}

₎

₌

₄

_.

₈₂

_±

₀

_.

_{48 (theo) mb from}

starlight,where the10% uncertainty is derived fromalternative approaches [51] to computethenonhadronic-overlapconditionin thesimulation:

σ

fid

(

γ γ

→

γ γ

)

=

120

±

46 (stat)

±

28 (syst)

±

12 (theo) nb

,

(9)

ingood agreementwith thetheoretical LbL prediction [7] inthe fiducialregion,definedinSection5,of

σ

fid

(

γ γ

→

γ γ

)

=

116

±

12 nb

.

(10)

The10%uncertaintyintheLbLtheoreticalpredictioncovers differ-ent implementations of the nonhadronic-overlap condition com-puted with a Glauber model [52] for varying Pb radius and nucleon-nucleon cross section values, as well as neglected NLO corrections.

7.2. Exclusion limits on axion-like particle production

Themeasured invariant massdistribution(Fig. 5,centerright) isusedtosearchforpossiblenarrowdiphotonresonances,suchas pseudoscalaraxion-like particles produced in the process

γ γ

→

a

→

γ γ

[30].The LbL,QED, andCEP+othercontinuum processes are considered as backgrounds in this search. Fully simulated starlightsamplesforvarious ALPmasses,

m

_a,rangingfrom5to 90 GeV arereconstructed with the same code used for the LbL analysisinordertoestimatetheALPacceptanceandefficiency,as wellastheexpectedreconstructeddiphotonmasstemplate distri-butions.CorrectionstotheefficiencyestimatedintheMC simula-tionare derived basedon data, andapplied in thesame wayas fortheLbLanalysis.Abinnedmaximumlikelihoodfitofthesignal andbackgroundcontributionsisperformedonthedata,where sys-tematicuncertaintiesare includedasnuisanceparameters witha log-normalprior.TheCLscriterion [53,54],withaprofilelikelihood

ratioasteststatistic [55],isusedtoextractexclusionlimitsinthe

σ

(

γ γ

→

a

→

γ γ

)

crosssectionat95%confidencelevel(CL). Lim-itson

σ

(

γ γ

→

a

→

γ γ

)

crosssectionforaxion-likeparticleswith masses5–90 GeV aresetinthe1500–20 nb range(Fig.6).The68 and95%CL bandsaround theexpected limitsare obtainedusing pseudo-experiments.

Fig. 6. Observed(fullline)andexpected(dottedline)95%CL limitsonthe pro-ductioncross section σ(γ γ→a→γ γ) as afunctionof the ALPmass ma in

ultraperipheral PbPbcollisions at√sNN=5.02 TeV.Theinner (green)andouter

(yellow)bandsindicatetheregionscontaining68and95%,respectively,ofthe dis-tributionoflimitsexpectedunderthebackground-onlyhypothesis.

The cross section limits shown in Fig. 6 are used to set ex-clusion limitsin the gaγ vs, ma plane, where gaγ

≡

1

/

is the

ALPcouplingtophotons(with

beingtheenergyscaleassociated withthe underlyingU(1) symmetry whosespontaneousbreaking generatestheALPmass).Twoscenariosare consideredwherethe ALP couples to photons F μν alone, or also to hypercharge Bμν

withoperators:a F



F

/

4

andaB



B

/(

4

cos2

_θ

W

)

(where

θ

W is the

Weinbergangle),respectively [30].Thederived constraintsonthe ALP massand its coupling tophotons are compared in Fig. 7 to those obtained [30,56] from various experiments [13,57–59], as-suming a 100% ALP decay branching fraction to diphotons. For an ALP sensitive to the electromagnetic current alone (left plot), our exclusionlimits are thebest so far over the

m

a

=

5–50 GeV

mass range. In the case of extra ALP couplings to electroweak currents (right plot), our result provides new constraints in the

ma

=

5–10 GeV region.

8. Summary

Evidenceforlight-by-light(LbL)scattering,

γ γ

→

γ γ

,in ultra-peripheralPbPb collisionsatacentre-of-massenergypernucleon pairof 5

.

02 TeV has beenreported,basedon a datasample cor-responding to an integratedluminosity of390 μb−1 recordedby the CMSexperimentat theLHC in 2015. FourteenLbL-scattering candidateeventspassingallselectionrequirementshavebeen ob-served, withphoton transverseenergy above 2 GeV and pseudo-rapidity

|

η

|

<

2

.

4, diphoton invariant mass greater than 5 GeV, diphoton transverse momentum lower than 1 GeV, and dipho-ton acoplanarity below 0.01. Both the measured total yields and kinematic distributions are in accord with the expectations for theLbLscatteringsignalplus smallresidual backgroundsthatare mostly frommisidentified exclusive dielectron(γ γ

→

e+e−) and gluon-induced central exclusive (gg

→

γ γ

) processes. The ob-served (expected) significance of the LbL scattering signal over the background-only expectationis 3.7(3.5) standard deviations. The ratio of the fiducial LbL scattering to the total QED dielec-tron cross sections is R

= (

25

.

0

±

9

.

6 (stat)

±

5

.

8 (syst)

)

×

10−6_.

Fromthetheoretical

γ γ

→

e+e−crosssection prediction,we de-rive a fiducial light-by-light scattering cross section,

σ

fid

(

γ γ

→

γ γ

)

=

120

±

46 (stat)

±

28 (syst)

±

12 (theo) nb, consistentwith the standard model expectation. The measured exclusive dipho-toninvariantmassdistributionisusedtosetnewexclusionlimits on theproduction ofpseudoscalaraxion-like particles (ALPs),via theprocess

γ γ

→

a

→

γ γ

,overthe

m

a

=

5–90 GeV massrange.

Fig. 7. Exclusionlimitsat95%CL intheALP-photoncouplinggaγ versusALPmassmaplane,fortheoperatorsa FF/4 (left,assumingALPcouplingtophotonsonly)and

a BB/(4 cos2

θW)(right,includingalsothehyperchargecoupling,thusprocessesinvolvingtheZ boson)derivedinRefs. [30,56] frommeasurementsatbeamdumps [60],in

e+e−collisionsatLEP-I [56] andLEP-II [57],andinpp collisionsattheLHC [13,58,59],andcomparedtothepresentPbPblimits.

For ALPs coupling to the electromagnetic (and electroweak) cur-rent,the derived exclusion limitsare currentlythe best overthe

ma

=

5–50 GeV (5–10 GeV)massrange.

Acknowledgements

WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technicalandadministrativestaffs atCERN andatother CMS in-stitutes for their contributions to the success of the CMS effort. Inaddition,wegratefullyacknowledgethecomputingcentresand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructureessential to ouranalyses. Finally, we acknowledge the enduring support for the construc-tionandoperation oftheLHCandthe CMSdetectorprovidedby thefollowingfunding agencies:BMBWFandFWF(Austria); FNRS andFWO (Belgium); CNPq,CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIENCIAS (Colombia); MSESand CSF (Croatia); RPF (Cyprus); SENESCYT(Ecuador);MoER,ERCIUT,andERDF(Estonia);Academy ofFinland,MEC,andHIP(Finland);CEAandCNRS/IN2P3(France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NKFIA (Hun-gary);DAEandDST(India);IPM(Iran);SFI(Ireland);INFN(Italy); MSIPandNRF (RepublicofKorea);MES (Latvia);LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, andUASLP-FAI(Mexico);MOS(Montenegro);MBIE(NewZealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna);MON,ROSATOM,RAS,RFBR,andNRCKI(Russia);MESTD (Serbia);SEIDI,CPAN,PCTI,andFEDER(Spain);MoSTR (SriLanka); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU andSFFR(Ukraine); STFC (United Kingdom);DOE andNSF (USA).

Individuals have received support from the Marie-Curie pro-gramme and the European Research Council and Horizon 2020 Grant,contract No. 675440 (EuropeanUnion);theLeventis Foun-dation;the Alfred P. Sloan Foundation; the Alexander von Hum-boldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie etdans l’Agriculture (FRIA-Belgium); the Agentschapvoor Innovatie door Wetenschap enTechnologie(IWT-Belgium); theF.R.S. - FNRS and FWO (Belgium) under the “Excellence of Science - EOS” - be.h projectn.30820817; theMinistryofEducation,Youth andSports (MEYS) of the Czech Republic; the Lendület (“Momentum”) Pro-gramme and the János Bolyai Research Scholarship of the Hun-garian Academy of Sciences, the New National Excellence

Pro-gram ÚNKP, the NKFIA research grants 123842, 123959, 124845, 124850 and 125105 (Hungary); the Council of Science and In-dustrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund,the MobilityPlus programmeofthe Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/ 02861,Sonata-bis2012/07/E/ST2/01406;theNationalPriorities Re-search Program by Qatar National Research Fund; the Programa Estatalde Fomentode laInvestigación CientíficayTécnica de Ex-celencia María de Maeztu, grant MDM-2015-0509 and the Pro-grama Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF; theRachadapisekSompotFundforPostdoctoralFellowship, Chula-longkornUniversityandtheChulalongkornAcademic intoIts2nd CenturyProject AdvancementProject(Thailand);theWelch Foun-dation,contractC-1845;andtheWestonHavensFoundation(USA).

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