Measurement of prompt ${\mathrm{D^0}}$ and ${\mathrm{\overline{D}}{}^0}$ meson azimuthal anisotropy and search for strong electric fields in PbPb collisions at $\sqrt{s_\mathrm{NN}} =$ 5.02 TeV

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Measurement of prompt D ⁰ and D ⁰ meson azimuthal anisotropy and search for strong electric fields in PbPb collisions at √ _s

NN

= ⁵ . 02 TeV

.The CMSCollaboration

CERN,Switzerland

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

Articlehistory:

Received29September2020

Receivedinrevisedform21February2021 Accepted25March2021

Availableonline29March2021 Editor:M.Doser

Keywords:

CMS Heavy-flavor Charm

Electromagneticfields

ThestrongCoulombfieldcreatedinultrarelativisticheavyioncollisionsisexpectedtoproducearapidity- dependentdifference(v2)inthesecondFouriercoefficientoftheazimuthaldistribution(ellipticflow, v2)betweenD⁰(uc)andD⁰ (uc)mesons. Motivatedbythesearchforevidenceofthisfield,theCMS detectoratthe LHCisused toperformthe firstmeasurementofv2.Therapidity-averagedvalue is foundtobev2=⁰.001±⁰.001 (stat)±⁰.003 (syst) inPbPbcollisionsat√_s

NN=⁵.02 TeV.Inaddition, theinfluenceofthecollisiongeometryisexploredbymeasuringtheD⁰andD⁰mesonsv2andtriangular flowcoefficient(v3)asfunctionsofrapidity,transversemomentum(pT),andeventcentrality(ameasure oftheoverlapofthetwo Pbnuclei).Aclear centralitydependenceofprompt D⁰ meson v2 valuesis observed,whilethev3islargelyindependentofcentrality.Thesetrendsareconsistentwithexpectations offlowdrivenbytheinitial-stategeometry.

©^{2021TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The observation of a strongly-coupled quark-gluon plasma (QGP), astate ofmattercomposed ofdeconfinedquarks andglu- ons, was established by experiments investigatingultrarelativistic heavy ioncollisions at the BNL RHIC [1–4] and CERN LHC [5,6].

The azimuthal particle correlationsconstitute an effectivetool to probethe propertiesoftheQGP [1–9].Thesecorrelationsare pa- rameterized by aFourier expansion [10–12],with themagnitude of the Fourier coefficients, vn, providing information about the initial collision geometry and its fluctuations [12]. The second- (v2) and third- (v3) order Fourier coefficients are referred to as

“elliptic”and“triangular”flow harmonics,respectively.Measuring thesecoefficientsforparticlespecieswithdifferentquarkcompo- sition provides additional information about this hot and dense medium [13]. Because of their large mass, charm and bottom quarksareproducedearlierinthecollisions thanthelightquarks (upanddown) [14,15].Inaddition,thecharmandbottomquarks have massesmany timeslarger than the typical temperatures in theQGP [16].Theseheavyquarksexperiencethefullevolutionof themedium untilthehadronizationphase.Asaconsequence,the v_n of charmedD⁰ (uc)and D⁰ (uc) mesons (henceforthreferred toasD⁰mesons,exceptwhereexplicitlystatedotherwise)areex-

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

pected to receive important contributions from medium energy lossandcoalescenceeffects [17,18].

In ultrarelativistic heavy ion collisions, very strong and tran- sient (∼^{10−1 fm}/c) magnetic andelectric fields are expected to beinduced bythecollision spectatorsandparticipants [19].Such electromagnetic(EM)fieldsare predictedto producea difference in the vn harmonics for positively and negatively charged parti- cles [19].Insuchapicture,themagneticfieldismainlyresponsible for splitting the rapidity (y)-odd directed flow (v₁) [19,20]. The electricfieldispredictedtoinduceacharge-dependentsplittingin thev2 coefficientandintheaveragetransversemomentum(^pT⁾ valuesoftheemittedparticles [19].Ascharmquarksareexpected tobecreatedveryearlyinthecollision,theyhaveahigherproba- bilityofinteractingwiththisstrongEMfield thanthelightflavor quarks [20,21].

In this letter, measurements of the v2 and v3 coefficients as functionsofD⁰ mesonrapidity, pT,andlead-lead (PbPb)collision centralityare presented.Thecollision centralitybins aregivenin percentagerangesofthetotalinelastichadroniccrosssection,with the 0–10% centrality bin corresponding to the 10% of collisions havingthe largestoverlapof thetwo nuclei. Theflow harmonics aremeasuredusingthescalarproductmethod [22,23].Inthisanal- ysis, the selection of D⁰ mesons uses multivariate methods [24]

forselectingD⁰ candidatesandtheirantiparticles.Thecontamina- tionfromnonpromptD⁰candidates,arisingfromBmesondecay,is consideredasasystematicuncertainty.Usingthedatarecordedin PbPbcollisions duringthe2018LHCrunperiod,correspondingto

https://doi.org/10.1016/j.physletb.2021.136253

0370-2693/©^{2021TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

0.58 nb⁻¹ ofintegratedluminosity,theflowcoefficientsaremea- suredwithintherapidity range|^y|<2,whichistwiceaslargeas achievedinpreviousCMSmeasurements [25].Theextensionofthe measurements tothislargerrapidity range,together withsmaller statisticaluncertainties provided bya larger dataset,furnish im- portantinputsforabetterunderstandingofthethree-dimensional evolutionoftheQGPformedinheavyioncollisions.Measurements ofthe v₂ difference betweenD⁰ andD⁰ mesons,v₂,asa func- tionofrapidityarepresentedasamethodtoprobepossibleeffects originatingfromtheCoulombfields.

2. Experimentalapparatusanddatasample

The central feature of the CMS apparatus is a superconduct- ing solenoidof6 m internal diameter,providinga magneticfield of 3.8 T. Within the solenoid volume, there are four primary subdetectors including a silicon pixel and strip tracker detector, a lead tungstate crystalelectromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrel andtwoendcapsections.Ironandquartz-fiberCherenkovhadron forward (HF) calorimeters cover the pseudorapidity range 2.9<

|η_|<5.2.TheHFcalorimetersaresegmentedtoform0.175×⁰.175 (η×φ^{) towers. Muons are measured in} gas-ionization detec- tors embedded inthesteelflux-returnyokeoutsidethesolenoid.

The silicon tracker measures charged particles within the range

|η_|<2.5.AdetaileddescriptionoftheCMSdetector,togetherwith a definitionofthecoordinatesystemusedandtherelevantkine- maticvariables,canbefoundinRef. [26].

Theanalysispresentedinthisletterusesapproximately4.27× 10⁹minimumbias(MB)PbPbcollisioneventscollectedbytheCMS experimentduringthe2018LHCrun.TheMBeventsaretriggered byrequiringsignalsinbothforwardandbackwardsidesoftheHF calorimeters [27]. Further selections are applied offline to reject eventsfrombackgroundprocesses(beam-gasinteractionsandnon- hadroniccollisions),seeRef. [28] fordetails.Eventsarerequiredto have atleast one interaction vertex, reconstructed basedon two tracks ormore,andwithadistance oflessthan15 cm fromthe centerof thenominalinteraction pointalong thebeamaxis.The primary interaction vertex is defined as the one with the high- est track multiplicity in the event. The shapesof the clusters in thepixeldetectorhavetobecompatiblewiththoseexpectedfrom particles producedattheprimary vertexlocation. ThePbPb colli- sioneventsarealsorequiredtohaveatleasttwocalorimetertow- ersineachHFdetectorwithenergydepositsofmorethan4 GeV pertower.Thesecriteriaselect(99±²)%ofinelastichadronicPbPb collisions.The possibilitytohavevalueshigherthan100% reflects the possible presence of ultra-peripheral (nonhadronic)collisions intheselectedeventsample.

Events fromMonte Carlo (MC) simulations are used to study both promptandnonpromptD⁰ mesonprocesses.The eventsare generated using an embedding procedure, in which D⁰ mesons generatedbypythia8.212 [29] (tuneCP5 [30])areembeddedinto MB eventsfromhydjet 1.9 [31]. Afull simulationoftheCMSde- tectorisperformedusingGeant4 [32].ThepromptD⁰ mesonMC simulationisemployedtodefinesignalselectionsandmeasureef- ficiencycorrections,whilethenonpromptD⁰ mesonMCsampleis usedtoestimatesystematicuncertaintiescomingfromnonprompt D⁰contamination.

3. ReconstructionandselectionofD⁰mesons

Prompt D⁰ mesons are reconstructed from the decay D⁰→ π⁺₊K⁻ andD⁰→π⁻₊K⁺withabranchingfractionof(3.94± 0.04)%,usingselected trackswith p_T>1.0 GeV/c andwithin the acceptanceof|η_|<2.4.Candidatesareformedbycombiningpairs

of tracks from oppositely charged particles andrequiring an in- variantmass(minv) withina ±^{200 MeV/c2 windowoftheworld-} averageD⁰mesonmassof(1864.83±⁰.05)MeV/c²[33].Foreach pair of selected tracks, two possible candidates for D⁰ and D⁰ mesonsareconsideredbyassumingoneofthetrackshasthepion mass, while the other track has the kaon mass, and vice versa.

Kinematicvertexfits are performedto reconstructthe secondary verticesofD⁰ candidatedecays.

After the D⁰ candidate reconstruction, a selection using a boosted decision tree (BDT) algorithm from the tmva pack- age [24] isemployed.FortheBDTtraining,misidentifiedD⁰ candi- datesindataevents,wherepionandkaonhavethesamecharge, areusedtomimicthecombinatorialbackground.Thesignalcandi- datesaretakenfromMCsimulationsofpromptD⁰ mesonsandare requiredtomatchD⁰ particlesatthegeneratorlevel.Thevariables related to D⁰ mesons used to discriminate the signal from the backgroundare: χ² probability fortheD⁰ vertexfit, 3D distance betweenthe secondaryand primary verticesand its significance, the decay length significance projected in the xy-plane, and the angleintwoandthreedimensionsbetweenthemomentumofthe D⁰ mesoncandidateandthelineconnectingtheprimary andthe secondaryvertices(pointingangle).Relatedtothedecayproducts oftheD⁰mesoncandidate,thevariablesusedare:theuncertainty in pT returned by thetrack fittingprocedure, the significanceof thezandthexydistancesofclosestapproachtotheprimaryver- tex,andthenumberofhitsinthetrackerdetector.Thesevariables are chosen by analyzing their BDT ranking (variables more fre- quentlyused in the decisiontree) and correlation matrixamong all variables. Different BDT boost algorithms are tested, choosing theadaptive boost algorithm [24] asdefault. Overtrainingchecks aredone forall analysisbins bycomparing theBDT distributions fromtrainingandtestingD⁰mesonsamples.Inaddition,aBDTcut optimization is performedin bins of centrality, pT, and rapidity, doingascanindifferentBDTscoresandfindingtheoneresulting in maximal D⁰ mesons signal significance for each analysis bin.

Comparedto acutoff-based procedure, thisBDT selection almost doublesthe signalsignificancefor D⁰ mesonsin1<|^y|<2,and increasesthesignal significanceby30%forD⁰ mesonsin|^y|<1, for events with collision centrality in the range 0–30%. For the remaininganalysisbins asimilar performance ofBDTandcutoff- basedmethodsisobserved.

4. Analysistechnique

The elliptic andtriangular flow coefficientsof D⁰ mesons are extractedusingthescalarproduct(SP) method,similarly towhat wasdone inapreviousCMSpublication [25].Inthismethod,the vn coefficientsofD⁰ candidates(includingbackgrounds)aremea- suredusing

v_n{^SP} ≡ ^Qn^D0Q_nA^{∗ Q}nAQ_nB^∗QnAQ^∗_nC

QnBQ_nC^∗

, (1)

with the Q-vectors expressed as Qn≡M

j=¹w_je^inφj, where the sumis over the total number(M) of HF towers above a certain energy threshold (with the weights wj taken as the energy de- positedintheHFtoweratazimuthalangle φj),oftrackswith pT aboveacertainthreshold(with wj takenastrackpT inφjangle), orofselectedD⁰ mesoncandidates(withwjtakenequalto1).

The Q-vectorsrelatedtoHFandthetrackeraremeasuredand correctedfordetectorirregularitiesbyapplyingaflattening anda recenteringprocedure [12,34].The QnAandQnBaredefinedusing the event-planemeasurements fromthe negative (−⁵<η<−^3, HF−^{) and thepositive (3}<η<5, HF+^{) sidesofHF, and Q}nC is measuredusingthetrackerinformationintheregionof|η_|<0.75,

allowing to minimize the correlations among the three regions, with a gap of more than two units of rapidity. The Q_n^D0 vector is definedforeach D⁰ mesoncandidate.The averages ^QnAQ_nB^{∗ , Q}nAQ_nC^{∗ ,andQ}nBQ_nC^{∗ aremade}consideringallselectedevents, while the average ^Qn^D0Q_nA^{∗ is made} considering all D⁰ meson candidates in all selected events. To avoid autocorrelations, the terms^Qn^D0Q_nA^{∗ andQ}nAQ_nB^{∗ useA}=^HF−^(HF+^)whentheD0 mesoncandidateisatpositive(negative)pseudorapidity.

One goal of this analysis is to measure the difference (vn) between D⁰ and D⁰meson flow coefficients, vn, as a function of rapidity, to probe effects from EM fields. The difference vn is measuredas:

v_n{^SP} ≡Q_n^D0Q_nA^∗ − Q_n^D0Q_nA^∗ QnAQ_nB^∗QnAQ_nC^∗

QnBQ_nC^∗

. (2)

The v_n and v_n of D⁰ meson candidates are first measured as a function oftheir minv. The extraction of the D⁰ mesons signal vn (vn), v^sign (v^sign ), is performed via a simultaneous binned

χ² fit of them_inv distribution and of v_n (v_n). The m_inv distri- bution is fitwith threecomponents: a third-order polynomial to modelthecombinatorialbackground,B(minv);twoGaussianswith the same meanbut differentwidths to describe the m_inv indif- ferent kinematic regions for the D⁰ mesons signal, S(m_inv); and oneadditionalGaussiandistributionfortheswapcomponentcor- respondingtotheincorrectmassassignmentfortheassumedpion andkaonparticles,S W(m_inv).Thewidthof S W(m_inv)andthera- tiobetweenthe yieldsof S W(minv)and S(minv)are fixedby the values extractedfromMC simulations. Inthiscase, the following expressioncanbeusedforextractingv^sig_n :

v^sig_n ^+bkg(m_inv)=α(m_inv)v^sig_n + [¹−α(m_inv)]^vbkgn (m_inv). (3) The α(m_inv)parameter, whichcharacterizes thesignal fractionas afunctionofmass,isdefinedasfollows:

α(m_inv)

= [S(minv)+S W(minv)]/[S(minv)+S W(minv)+B(minv)]

=α^signal(m_inv)+α^swap(m_inv). (4)

Forextractingthedifferencev^sig_n ,thefollowingexpressionisem- ployed:

v^sig_n ^+bkg(m_inv)=v^sig_n (α^signal(m_inv)−α^swap(m_inv))+^const. (5)

Thetermv^bkg_n (m_inv)fromEq. (3) ismodeledwithalinearfunction, whiletheconstantparameterconst inEq. (5) isaddedtoaccount forpossiblefluctuationsinthebackgroundvncomponent.Therel- evance ofthis const parameter was investigated by redoing v_n measurements in MC simulation (without azimuthal correlations oreffectsfromEMfields),indicatingthatthisparameterimproves the fit quality anddoes not introduce artificial signals. A cross- check is performedby redoing the measurements using a linear function insteadofa constant.No significantchanges inthecen- tralvaluesof v2 andon theiruncertainties are observed.Fig.1 showsanexampleofasimultaneousfitforv₂ andv₂.

After performing the fits forextractingthe signal vn,there is stillasizablefractionofnonpromptD⁰ mesonsembeddedinv^sig_n . Theextractedv_ncanbewrittenas

v^sig_n =^fpromptv^prompt_n +(1−^fprompt)v^nonprompt_n . (6)

ThenonpromptD⁰mesoncontaminationistakenintoaccountasa systematicuncertainty,bycheckingthatthenonpromptD⁰ meson fraction is always smaller than 12% (i.e., comparable to the un- certaintiesinthereconstructedD⁰ mesonyield).Thisimpliesthat thecentral valuesof vn willnot be considerablyaffected bythis component,beingcompatiblewithin statisticaluncertainties.Such alowfractionarisesfromtheuseofpromptD⁰ mesonsignalsin theBDTtraining,togetherwithvariablesthatarehighlycorrelated withthe distance ofclosest approach (DCA) to theprimary ver- tex,whichisdefinedastheflightdistanceoftheD⁰particletimes thesineofthepointingangleinthreedimensions.AdditionalDCA selectionanddedicatedtraining,involvingpromptandnonprompt D⁰ mesonsignals,donotbringconsiderableimprovementsinper- formance.ThepromptandnonpromptD⁰ mesonfractionsareob- tainedusingtheDCA variable.ForpromptD⁰mesons,thenonzero DCA correspondstothedetectorresolution,andisexpectedtobe concentrated around zero.Fornonprompt D⁰ mesons, largerval- uesofDCA resultfromtheBmesondecay.Toextracttheprompt andnonpromptD⁰ mesonfractions,afittotheDCA distributions isperformedindataconsideringDCA shapesfromMCsimulations forpromptandnonpromptD⁰mesoncomponents.Thenonprompt D⁰ mesonvnisestimatedbyconsideringtworegionsintheDCA:

one withvery low fraction (2.7–8.0%) ofnonprompt D⁰ particles (DCA<0.012 cm), and one witha highfraction (62.0–88.0%) of nonpromptD⁰ particles(DCA>0.012 cm).Usingthisinformation togetherwithEq. (6),itispossibletoestimate v^nonprompt_n bysolv- ing asystemof two equationsfromthe two DCA regions.Inthe currentanalysisthisprocedurecanonlybe doneinwide pT,cen- trality, andrapidity bins, because ofthe limitedamount of data availableintheregionwithDCA>0.012 cm.

5. Systematicuncertainties

Thesources of systematicuncertainties includethe D⁰ identi- fication requirements(BDTselection); theprobability distribution function(PDF)formodelingthebackgroundintheinvariantmass fit;theimpactofacceptanceandefficiencyoftheD⁰ mesonyield;

thevariationofthePDFformodelingthebackgroundvn;andthe remainingnonpromptD⁰contamination.Withtheexceptionofthe last component, the uncertainties are quoted as absolute values ofvnandvnaftercomparing thedefaultanalysisconfiguration withthevariations.Todiminishtheinfluenceofstatisticalfluctua- tions,afterobservingnospecialtrendsinthedeviationsfromthe defaultmeasurements, the systematicuncertainties are evaluated byaveragingthedeviationswithaconstantfitasafunctionofthe analysisbins.

Inordertotakeintoaccountthesystematicuncertaintyassoci- atedwiththeBDTselection,theBDTcutisvariedupanddownby themaximaldeviationbetweentheBDToptimizedselectionbased onMCsimulationsanddata.TheBDTcuts(andvariationsforsys- tematicuncertainties)aredefinedinbinsofcollisioncentrality,pT, and rapidity, ranging from 0.28 to 0.47 (±0.02–0.03). Regarding theeffectofthebackgroundmassmodeling,eitheranexponential functiontogetherwithasecondorderpolynomial,orjustasecond orderpolynomial,areconsideredinsteadofthedefaultfitfunction usingathird-orderpolynomial.Tofitvnasafunctionofmass,the defaultconfigurationusingalinearfunction isreplaced byeither aconstantora secondorderpolynomial.Althoughthe D⁰ meson selectionefficiencyessentiallycancelsin vnmeasurements,asys- tematicuncertaintyisassignedbycomparingtheresultswithand withoutapplyingcorrections basedon MC simulationsin binsof p_T and rapidity.The D⁰ meson selection efficiency times accep- tancevaries from0.5 to 12.5% inthe pT rangeof 1.0–8.0 GeV/c, reachingaplateauofapproximately17.0%forpT>15.0 GeV/c.

The systematic uncertainties regarding contamination from nonpromptD⁰ mesonsareestimatedbymeasuringnonpromptD⁰