Exploration of jet substructure using iterative declustering in pp and Pb–Pb collisions at LHC energies

(1)

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Exploration of jet substructure using iterative declustering in pp and Pb–Pb collisions at LHC energies

.ALICE Collaboration

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

Articlehistory:

Received13May2019

Receivedinrevisedform10January2020 Accepted13January2020

Availableonline22January2020 Editor: L.Rolandi

TheALICEcollaborationattheCERNLHCreportsnovelmeasurementsofjetsubstructureinppcollisions at√

s =^{7 TeV}^and ^central ^Pb–Pb^collisions^at√

s_NN =².76 TeV. Jetsubstructureoftrack-based jets is explored via iterative declustering and grooming techniques. We present the measurement of the momentum sharingof two-prongsubstructure exposedvia grooming, the zg,and itsdependence on theopeningangle,inbothppandPb–Pbcollisions.Wealsopresentthemeasurementofthedistribution ofthenumber ofbranchesobtainedintheiterativedeclusteringofthejet,whichisinterpretedasthe number ofitshardsplittings.InPb–Pbcollisions,weobserveasuppression ofsymmetricsplittingsat largeopeninganglesandanenhancementofsplittingsatsmallopeninganglesrelativetoppcollisions, withnosigniﬁcantmodiﬁcationofthenumberofsplittings.Theresultsarecomparedtopredictionsfrom variousMonteCarloeventgeneratorstotesttheroleofimportantconceptsintheevolutionofthejetin themediumsuchascolour coherence.

©²⁰²⁰^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Theobjectiveoftheheavy-ionjet physicsprogram attheLHC is to probe fundamental, microscopic properties of nuclear mat- terathighdensitiesandtemperatures.Jetsprovidewell-calibrated probes of the dense medium created in heavy-ion collisions. In pp collisions, the production of jets and their substructurehave been measured extensively and these measurements are well- reproducedby theoreticalcalculationsbasedonperturbative QCD (pQCD) (see Refs. [1–4] and citations therein). Jets are produced inhigh-momentumtransferprocesses,whichoccurontimescales muchshorterthantheformationtimeoftheQuark-GluonPlasma (QGP) generated in heavy-ion collisions; the production rates of jetsinheavy-ioncollisions can thereforebe calculated accurately usingthesamepQCD approachesasforpp collisions,aftertaking intoaccounttheeffectsofnucleargeometryandnuclearmodiﬁca- tionofpartondistributionfunctions(PDFs)[5].

Jets traversing the QGP will interact via elastic and radia- tive processes which modify the reconstructed jet cross section andstructurerelative to jetsinvacuum (“jetquenching”) [6]. Jet quenchingeffectshavebeenextensivelyobservedinnuclearcolli- sions at RHIC and LHC in measurements of inclusiveproduction and correlations of high-pT hadrons and jets, including correla- tionsof high-energytriggers (hadrons,photons, W andZbosons, andjets)andreconstructedjets[7–10] aswell asinthemeasure-

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

ment ofjet shapes[11–16]. Comparisons of thesemeasurements totheoreticaljet quenchingcalculationsenablethe determination ofdynamicalpropertiesoftheQGP,notablythetransportparame- terqˆ [17].

More recently,the modificationof thejet substructuredue to jetquenchinghasbeenexploredinheavy-ioncollisionsusingtools developedforthemeasurementofjetsubstructureinppcollisions forQCDstudiesandBeyondStandardModelsearches[2,18].Akey tool is iterativedeclustering, which subdividesjetsinto branches or splittings that can be projected onto the phase space ofsuch splittings,calledtheLund plane [19–21]. Whilethesplittingmap contains kinematic information of all splittings, techniques like grooming [22,23] canbeappliedtoisolateaspecificregionofthe splittingmap accordingto differentcriteriasuch asmitigation of non-perturbativeeffects,enhancement ofthejet quenchingsignal orsimplificationofperturbativecalculations.

InthisworkwefocusontheMassDrop[22] orSoftDrop(SD) grooming [23] withzcut=⁰.1 andβ=^0.^This^technique^selects^the ﬁrstsplittinginthedeclusteringprocessforwhichthesubleading prongcarriesafractionzofthemomentumoftheemittingprong larger than zcut. Note that this criterion selects a subset of the splittings.Thegroomingprocedureremovessoftradiationatlarge anglestoexposeatwo-prongstructureinthejet.Thesharedmo- mentumfractionofthoseprongsiscalledzg,the groomedsubjet momentumbalance.The measurementof zg invacuumisclosely relatedtotheAltarelli-Parisisplittingfunctions[23].

https://doi.org/10.1016/j.physletb.2020.135227

0370-2693/©²⁰²⁰^TheÂuthor(s).^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

(2)

Theoreticalconsiderationsofthein-mediummodiﬁcationofzg can be found in [24–27]. A key physics ingredient in the theo- retical calculationsis colour coherence [28]. Thisis the effectby whicha colour dipolecannot be resolvedby themedium astwo independent colour chargesifthe openingangle ofthe dipole is smallcomparedtoafundamentalmediumscale.Ifthedipolecan- notberesolved,itwillpropagatethroughthemedium asasingle colour charge.Ifcolour coherenceisatwork,therewillbepartsof thejet substructure thatwon’t be resolved, leading to a reduced effectivenumberofcolour chargesandthusareducedamountof energylossinmedium.

Withthegroomingtechniqueweselectahardtwo-prongsubstructure.Thenweinspectthedependenceontheopeningangleof therateofsuchtwo-prongobjectsinmediumrelativetovacuum.

Weareinterested inunderstandingwhetherlarge-anglesplittings are more suppressed relative to vacuum than small-angle splittings, as one would expect if large-angle splittings are resolved bythemedium andradiate inthemediumincoherently.Previous measurements of zg by theCMS collaboration [29] show a mod- iﬁcation in central Pb–Pb collisions relative to the pp reference whilstmeasurementsperformedatRHICbytheSTARcollaboration showed no modiﬁcation [30]. Those measurements did not scan the R dependenceandcoverdifferent intervalsofthe sublead- ingprongenergiesthatcanbiastowardsdifferenttypicalsplitting formationtimes.

ThisworkreportsthemeasurementbytheALICEcollaboration of zg, the shared momentum fractionof two-prongsubstructure, itsdependenceontheopeningangleandnSD,thenumberofsplit- tings satisfyingthegrooming condition obtainedvia the iterative declustering ofthe jet [31], inpp collisions at√

s = ⁷ ^TeV ^and central(0–10%)Pb–Pbcollisionsat√

sNN =².76 TeV.

2. Datasetsandeventselection

AdetaileddescriptionoftheALICEdetectoranditsperformance canbefoundinRefs. [32,33].Theanalysedppdatawerecollected during Run1 oftheLHC in2010 withacollision centre-of-mass energyof√

s =^{7 TeV}ûsingâ^minimum^bias^(MB)^trigger.^The^MB triggerconfigurationisthesameasdescribedinRef. [34].Thedata fromheavy-ioncollisionswere recordedin2011at√

sNN =².76 TeV.Thisanalysisusesthe0–10%most-centralPb–Pbcollisionsse- lectedbytheonlinetriggerbasedonthehitmultiplicitymeasured intheforwardV0detectors [35].Thedatasetsandeventselection areidenticalto Refs. [7,11].Afteroﬄineselection, thepp sample consistsof168millionevents,whilethePb–Pbsampleconsistsof 19millionevents.

The analysis uses charged tracks reconstructed by the Inner TrackingSystem(ITS) [36] andTimeProjectionChamber(TPC) [37]

whichboth coverthe fullazimuth andpseudo-rapidity|

η

|<0.9.

Tracksarerequiredtohavetransversemomentum0.15<pT<100 GeV/c.Thetrackselectionisslightlydifferentintheanalysisofthe 2010andthe2011data.Theformerusesasubclassoftrackswith worsemomentumresolutionthatisexcludedfromthelatter[38].

In pp collisions, the tracking eﬃciency is approximately 80%

fortracks with p_T>1 GeV/c,decreasing toroughly 56% at p_T= 0.15 GeV/c, with a track momentum resolution of 1% for pT= 1 GeV/c and 4.1% for pT=^{40 GeV/c} [33,34,39]. In Pb–Pb collisions, the trackingeﬃciency is about2 to 3% worse than inpp.

Thetrack p_T resolution isabout1% at p_T=^{1 GeV/c} ^and^2.5%^for pT=^{40 GeV/c.}

As a vacuum reference for the Pb–Pb measurements we use simulatedppcollisionsat√

s =².76 TeV,calculatedusingPYTHIA 6.425(PerugiaTune2011)[27]andembeddedintorealcentralPb–

Pbeventsatthedetectorlevel,totakeintoaccountthesmearing bythebackgroundﬂuctuations.WeusetheembeddingofPYTHIA-

generated eventsinstead ofthe embedding ofreal pp datamea- suredat√

s =².76 TeVduetothelimitedsizeofthedatasample.

ThePYTHIAMCdescribeswellvacuumintrajetdistributions[2].In thispaper,wevalidate thePYTHIAcalculationbycomparing itto jetsubstructuremeasurementsinppcollisionsat√

s =^{7 TeV.}

3. Jetreconstruction

Jets are reconstructed from charged tracks using the anti-kT algorithm [40] implemented in FastJet [41] with a jet resolution parameter of R=⁰.4. The four-momenta oftracks are combined usingtheE-schemerecombination [41] wherethepionmassisas- sumed forall reconstructedtracks.In orderto ensurethat alljet candidates are fully contained within the ﬁducial volume of the ALICE detectorsystem, accepted jetswere required to havetheir centroidconstrainedto|

η

jet|<0.5.

The jet finding efficiency is 100% in the measured kinematic ranges.Thejetenergyinstrumentalresolutionissimilarforppand Pb–Pb collisions,varying from15% atp^ch_T_,_jet =^{20 GeV/c} ^to^25%ât p^ch_T_,_jet=^{100 GeV/c.}^The^JetÊnergy^Scale^(JES)uncertaintyisdomi- natedbythetrackingefficiencyuncertaintywhichis4%.

In pp collisions, no correction forthe underlying eventis ap- plied. In Pb–Pb collisions, the jet energyis partially adjusted for the effectsofuncorrelatedbackgroundusingthe constituentsub- traction method [42]. Constituent subtraction corrects individual jet constituentsbymodifyingtheir four-momentum.Themomen- tumthat is subtractedfromthe constituentsisdetermined using the underlyingeventdensity,

ρ

,which iscalculatedbyclustering theeventintoR=⁰.2 jetsusingthekTalgorithm [43,44] andtak- ing the median jet pT density in the event. The two leading kT jets are removedbefore calculating the median, to suppress the contribution of true hard jetsin the background estimation. The correctionisappliedsuchthatthetotalmomentumremovedfrom thejetisequalto

ρ

×^Aj,whereA_jisthejetarea.Thisbackground subtractionis appliedboth tothe measureddata andto theem- beddedPYTHIAreference.

4. Observables

Jet constituentsare reclustered using thephysical Cambridge/

Aachen (CA)metric[45],leading toanangle-orderedshower.The declustering process consistsof unwinding the clustering history stepbystep,alwaysfollowingthehardestbranch.Thefirstdeclus- tering step identifies the final subjet pair or branch that was merged.Theseconddeclusteringstepidentifiesthesubjetpairthat was mergedinto theleadingsubjetofthe finalstep,etc. Theco- ordinates of the subleading prong in the Lund Plane (log(zR), log(1/R)) are registered at each declustering step, where z is the fraction of momentum carried by the subleading prong z=

min(pT,1,pT,2)

pT,1+^pT,2 ,withpT,1andpT,2 beingthemomentaoftheleading andsubleadingprongs,respectively,andR theopeningangleof thesplitting.

The observable n_SD is obtained by counting the number of splittingsinthedeclusteringprocessthatsatisfytheSoftDropse- lection z>zcut, zcut=⁰.1. The observable zg corresponds to the subjetmomentumbalance,z,oftheﬁrstsplittingsatisfyingtheSD selection.JetswithnSD=^{0 are}^labelled^“untagged^jets”.^The^zgdis- tribution is absolutelynormalised, includingthe untagged jetsin thenormalisation.Thischoice ofnormalisation,usedhereforthe ﬁrst time, provides crucial information for quantitative comparison ofjet substructuremeasurements in Pb–Pband ppcollisions since it allows theresults to beinterpreted in termsof not only achangeofshapeinthedistributionbutalsointermsofneten- hancement/suppressionoftheyield ofsplittingssatisfyingtheSD conditioninagivenjettransversemomentumrange.

(3)

Thetrackingsystem enablesthemeasurement ofsubjetswith angularseparation smallerthan 0.1 radians anda scan ofthe zg distributioninrangesofR:R<0.1,R>0.1 andR>0.2.

Fordata frompp collisions, the correction of thedetector ef- fectswasperformedviaunfolding.Theresultsarepresentedinthe jet momentum interval of 40<p^ch_T_,_jet<60 GeV/c,chosen to bal- ancestatisticalprecision anddetectoreffects. InPb–Pb collisions, theresults are presented atdetector-level,with the uncorrelated backgroundsubtracted onaverage from the jet pT and fromthe substructureobservable.Thevacuumreferenceisthussmearedby background ﬂuctuations and instrumental effects. The Pb–Pb re- sultsarepresentedinthejetmomentumrangeof80<p^ch_T_,_jet<120 GeV/c,whereuncorrelatedbackgroundisnegligible.

5. Correctionsandsystematicuncertainties

Fordata frompp collisions, the unfolding ofinstrumental effects is carried out using a four-dimensional response matrix that encodes the smearing of both jet p^ch_T and the substructure observable (shape^part^,^ch, p^part_T_,_jet^,^ch, shape^det^,^ch, p^det_T_,_jet^,^ch), where

“shape”denoteseitherzgornSD.Theupperindex“part”refersto particle-leveland“det”referstodetector-levelquantities,obtained fromsimulationsinwhich ppcollisions are generatedbyPYTHIA (particle-level)and then passed through a GEANT3-based model [46] oftheALICEdetector.Wenotethattheparticle-leveljetﬁnd- ing isperformedusing thetrue particlemasses sothe unfolding correctsforthepionmassassumptionatdetectorlevel.

Togenerate vacuumreference distributions forcomparison to Pb–Pb results, which are not fully corrected, we superimpose detector-levelPYTHIAeventsontorealPb–Pbevents.Consequently, notwo-trackeffects are present, howevertheir impactin datais negligibleduetothelarge requirednumberofclusterspertrack.

Thematchingofparticle-levelandembeddedjetsisperformedas describedin[11].Thematchingeﬃciencyisconsistentwithunity forjetswithpTabove30GeV/c.

Forppcollisions, Bayesianunfoldingintwo dimensionsasim- plementedintheRooUnfoldpackage [47] isused.Theprior isthe two-dimensionaldistribution(p^part_T_,_jet^,^ch,shape^part^,^ch)generatedwith PYTHIA.The defaultnumber of iterations chosen for z_g andn_SD is 4, which corresponds to the ﬁrst iteration for which the re- foldeddistributionsagreewiththecorrespondingrawdistributions within5%.Aclosuretestwasalsocarriedout,inwhichtwostatis- ticallyindependentMonteCarlo(MC)samplesareusedtoﬁllthe responseandthepseudo-data.Forthistest,theunfoldedsolution agreeswiththeMCtruth distributionwithinstatisticaluncertain- ties.

Unfolding of the distributions was attempted for the Pb–Pb case,butnoconvergenceona mathematicallyconsistentsolution wasobtained,duetothelimitedstatisticsofthedatasampleand dueto thefact thatthe responseisstrongly non-diagonaldueto the presence of sub-leading prongs at large angles that are not correlated to particle-level prongs andthat arise due to ﬂuctua- tionsof theuncorrelatedbackground.Strategiesto suppresssuch secondaryprongsarebeyondthescopeofthisanalysis.

Thesystematicuncertaintiesaredeterminedbyvaryingkeyas- pectsofthe correction procedures forinstrumental response and backgroundfluctuations. The mostsignificant components of the systematicuncertainties for zg and nSD are tabulated in Table 1 and2.Forppcollisions,thetrackingefficiencyuncertaintyis±^4%

[15]. The effectofthis uncertaintyon the substructuremeasure- mentisassessedbyapplyinganadditionaltrackrejectionof4% at detector-levelpriortojetﬁnding.Anewresponseisbuiltandthe unfoldingisrepeated,withtheresultingvariationintheunfolded solutionsymmetrisedandtakenasthesystematicuncertainty.This

isthe largestcontributionto theJESuncertainty. Toestimate the regularisationuncertainty,thenumberofBayesianiterationsisvar- ied by ±^{1 with} ^respect ^to ^the ^default ^analysis ^value. ^The ^prior is varied by reweighting the response such that its particle-level projection(PYTHIA)matchesHERWIG7.1.2[48].Thedetector-level intervals in p_T and the substructureobservables are modiﬁed to determine what in the table is referred to as truncation uncertainty.Theuncertaintylabelled“Binning”inthetablescorresponds toavariationinbinningofboth pT andsubstructureobservables, subjecttotheconstraintofatleast10countsintheleastpopulous bintoensurethestabilityoftheunfoldingprocedure.

In the case of Pb–Pb collisions, the evaluation of the uncertainty due to tracking eﬃciency is carried out similarly to the pp case. The zg measurement is done differentially in ranges of R. The limits of the R ranges were varied by ±^10%, ^which corresponds approximatelytothewidthofthedistributionofthe relativedifferenceofparticle-levelandembedded-levelR inPb–

Pbcollisions.ThedifferencesbetweenPYTHIAandtheunfoldedpp distributions aretakenintoaccount whenusingPYTHIAasa ref- erenceforPb–Pb measurements. Thisisdone by reweighting the embedded PYTHIA reference so that its particle-level projection matchestheunfoldedpp p_T_,_jet vsz_g (or p_T_,_jet vsn_SD) correlation.

Thedifferencebetweenthereferencesmearedwiththedefaultand the reweighted response isassigned asthe corresponding uncertainty.

InboththeppandPb–Pbanalyses,theuncertaintiesareadded in quadrature. All the contributions to the overall uncertainty produce changes in a given interval of the distribution that are strongly anti-correlated with changes in a different interval, i.e., theyinducechangesintheshapeoftheobservable.

6. Results

Figs. 1 and 2 show fully corrected distributions of zg and n_SD measured in pp collisions at √

s=^{7 TeV} ^for ^charged^jets ⁱⁿ the interval 40<p^ch_T_,_jet< 60GeV/c.The results are compared to distributions obtained from PYTHIA6 (Perugia Tune 2011), from PYTHIA6+POWHEG [49],toconsider theimpactofNLO effects, andfromthenewerPYTHIA8(Tune4C)[50].

Thezgdistributioniswell-describedwithinsystematicandsta- tisticaluncertainties by all theMC generatorsconsidered. As dis- cussedabove,untaggedjetscontributetothenormalisationofthe distributions. The untagged contribution is not shown in Fig. 1, dueto the suppressed zero onthe horizontal axis,butis shown inFig.2inthebinrepresentingn_SD=^0.^Table³^shows^the^tagged fractionfordata andsimulations.Forpp (rightmostcolumn),the untagged fraction is about 2%. The Monte Carlo distributions in Fig.2disagreewiththedatainthe tailsofthedistribution.They haveasigniﬁcantlylowerfractionofjetswithnosplittings(nSD = 0) thanobservedindata.TheadditionofPOWHEGcorrectionsto PYTHIA6inducesasmallshiftofthedistributiontowardsalarger numberofsplittings.

Fig.3 shows zg distributions measuredin central Pb–Pbcolli- sionsforvariousrangesofangularseparationR.The resultsare presented in the uncorrected transverse momentum range 80≤ p^ch_T_,_jet<120 GeV/candcomparedtothedistributionofPYTHIAjets embeddedintoreal0–10%centralPb–Pbevents.

Fig.3 showsa larger difference betweenthemeasured Pb–Pb andembeddedreferencedistributions forlargervaluesofR,in- dicating arelative suppressionintherateofsymmetricsplittings (zg≈⁰.5) incentralPb–Pb collisions.However,duetothesteeply falling zg distribution,thefractionofalljetsthatexhibitsymmet- ricsplittingsissmall,andthisstrongsuppressioncorrespondstoa suppressionofonlyafewpercentinthetotalrateofjetspassing

(4)

Table 1

Relativesystematicuncertaintiesonthemeasureddistributionsinppcollisionsforthreeselectedjet shapeintervalsinthejet p^ch_T_,_jetintervalof40–60 GeV/c.DuetotheshapeofthenSDdistribution,the systematicvariationsleadtoacrossingatcentralvalueswhichartiﬁciallyreducestheevaluatedsystem- aticuncertainty.Toimprovethiswesmooththetotalsystematicuncertaintybyinterpolatingbetween neighbouringbins.

Observable zg nSD

Interval 0.1–0.175 0.25–0.325 0.4–0.5 0 3 6

Tracking eﬃciency (%) 1.9 0.2 1.0 16.1 1.1 18.3

Prior (%) ⁺₋⁰₃^._.⁰₉ ⁺₋⁷₀^._.⁶₀ ⁺₋⁰₉^._.⁰₄ ⁺₋⁰₁^._.⁰₆ ⁺₋⁰₉^._.⁰₂ ⁺₋⁰₂₁^.⁰_.₃ Regularisation (%) ⁺₋⁰₀^._.⁸₅ ⁺₋⁰₀^._.²₂ ⁺₋⁰₀^._.⁴₅ ⁺₋⁰₁^._.⁴₄ ⁺₋¹₁^._.⁴₁ ⁺₋¹₃^._.⁷₀ Truncation (%) ⁺₋²₀^._.²₀ ⁺₋¹₀^._.⁸₀ ⁺₋²₀^._.⁴₀ ⁺₋⁰₀^._.⁰₀ ⁺₋⁰₀^._.⁰₁ ⁺₋⁴₀^._.⁴₀

Binning (%) 0.5 4.5 1.2 N/A N/A N/A

Total (%) ⁺₋³₄^._.⁰₄ ⁺₋⁸₃^._.²₀ ⁺₋²₉^._.⁶₆ ⁺₋¹⁶₁₆^._.¹₂ ⁺₋⁷₆^._.⁸₂ ⁺₋¹⁸₂₈^._.⁹₂

Table 2

RelativesystematicuncertaintiesonthemeasureddistributionsinPb–Pbcollisionsforthreese- lectedjetshapeintervalsandoneRselectioninthejetp^ch_T_,_jetintervalof80–120 GeV/c.

Observable zg(R>0.1) nSD

Interval 0.1–0.175 0.25–0.325 0.4–0.5 0 3 6

Tracking eﬃciency (%) 4.9 2.8 11.4 11.2 7.9 11.1 Angular cutoff (%) ⁺₋²₃^._.³₈ ⁺₋²₀^._.⁸₀ ⁺₋¹⁰₀_.₀^.⁰ N/A N/A N/A Reference (%) ⁺₋⁰₀^._.⁰₀ ⁺₋¹²₀_.₀^.⁴ ⁺₋¹⁰₀_.₀^.¹ ⁺₋³⁰₀_.₀^.¹ ⁺₋⁰₅^._.⁰₂ ⁺₋⁵₀^._.³₀ Total (%) ⁺₋⁵₆^._.⁴₂ ⁺₋¹³₂_.₈^.¹ ⁺₋¹⁸₁₁^._.²₄ ⁺₋³²₁₁^._.¹₂ ⁺₋⁷₉^._.⁹₅ ⁺₋¹²₁₁^._.³₁

Fig. 1.Fullycorrectedzg distributioninpp collisionsfor40≤^p^chT,jet<60GeV/c comparedwithpredictionsfromPYTHIAsimulations.Thestatisticaluncertainties areshownasverticalbarsandthesystematicuncertaintiesarerepresentedbya shadedarea.

boththeSDandangularcuts(cf.Table3).Conversely,inthesmall R limitasmallexcessofsplittingsisobservedinthedata.

Fig. 3also showscomparisons to predictions from the JEWEL event generator [51] and Hybrid model [52] calculations. The JEWELsimulationsincludethemediumresponsefromjet-medium interactions [53]. The theoreticalpredictions must besmeared to accountforthedetectoreffectsaswellasfluctuationsduetoun- correlated background.This smearing is performedby construct- ing a 6-dimensional response matrix by superimposing PYTHIA events atdetector level to real 0–10% centralPb–Pb events.The 6-dimensionalmatrixmapseveryembedded jetfroma givenbin of(z^part_g ,R^part,p^part_T_,_jet)to(z^det_g ,R^det, p^det_T_,_jet).Thesmearingofthe distributionssignificantlymodifiesthepredictionsandisessential forquantitativecomparisonofthemeasurementsandcalculations.

Themodels capturethequalitative trends ofthedata, namely theenhancementofthenumberofsmall-anglesplittings andthe

Fig. 2.FullycorrectednSDdistributioninppcollisionsfor40≤^p^chT,jet<60GeV/c, comparedwithpredictionsfromPYTHIAsimulations.Thestatisticaluncertainties areshownasverticalbarsandthesystematicuncertaintiesarerepresentedbya shadedarea.

suppressionofthelarge-anglesymmetricsplittings.Thefractionof jetsnotpassingtheSDselectionissimilarinthemodelsanddata.

However discrepancies are observed inthe angular selection.For instancethe numberofSDsplittingsthat passtheangularcut of R>0.2 isthelowest inthecaseoftheHybrid model,pointing toastrongerincoherentquenchingoftheprongs.

Thesuppressionofsplittingsatlargeopeninganglesisqualita- tivelyexpectedfromvacuumformationtimeandcolourcoherence arguments [26].The widertheopeningangle,theshorterthefor- mation time of the splitting. This makes it more likely that the splitting propagates through, andis modiﬁed by, the medium. If coherence effects are atplay in the medium then it is expected thatsplittingsthatareseparatedbymorethanthecoherenceangle willbemoresuppressedsincetheyradiateenergyindependently.

Fig. 4 shows the comparison ofnSD distributions from Pb–Pb measurements andtheembedded PYTHIAreference.Thedataex-

(5)

Table 3

FractionofjetsthatpasstheSoftDropconditionzcut=⁰.1 inthespeciﬁedrangeofangularseparationandinthe transversemomentumrange40≤p^ch_T_,_jet<60GeV/cforppand80≤p^ch_T_,_jet<120 GeV/cforPb–Pbcollisions.Uncertain- tiesonthedataarewrittenasstatistical(systematic).

Tagged rate (%)

Dataset Pb–Pb pp

Angular Cut R<0.1 R>0.0 R>0.1 R>0.2 R>0.0 Data 38.4±².3(2.5) 92.1±³.5(0.9) 53.6±².7(3.4) 41.8±².4(3.6) 97.3±³.0(1.7)

PYTHIA 34.6 95.5 60.2 46.9 98.6

Hybrid 47.5 93.4 45.8 35.0 N/A

JEWEL 42.0 93.0 51.0 40.0 N/A

Fig. 3.Detector-levelPb–PbdistributionsofzgforR=⁰.4 jetswithvaryingminimum/maximumangularseparationofsubjets(R)forjetsintherange80≤^p^chT,jet<120 GeV/c.Thesystematicuncertaintiesarerepresentedbytheshadedarea.ThecorrespondingvaluesfortheembeddedPYTHIAreference(opensymbols),Hybridmodel(dashed line)andJEWEL(solidline)arealsoshownintheplot.Thelowerplotsshowtheratiosofdata,HybridandJEWELmodeltotheembeddedPYTHIAreference.

hibitashifttowardslowernumberofsplittings.Thediscrepancies between the distributions from PYTHIA and from pp collisions are incorporated as a part of the reference uncertainty via the reweightingproceduredescribed above.Thecorrespondingcurves fortheHybridmodelandJEWELarealsoshownintheplot.

ToexplorethedependenceofthenSD distributiononthefrag- mentation pattern, we also show a calculation in which the pp referencedistributionisbasedsolelyonlight-quarkfragmentation.

Sincethequark fragmentationisharder,we seethat thenumber ofsplittingspeaksatlowervalues,inlinewithwhatweobservein thedata.The smearedJEWELandHybridmodelcalculationagree withthequalitativetrendofthedata.

Thetrendsindicatethatthelargertheopeningangle,themore suppressed the splittings are, and this is qualitatively consistent withlarge-angleprongsbeingmoreresolved by themediumand thusmoresuppressed.Thesameprocesscouldleadtoareduction inthenumberofhardsplittingsasobservedinFig.4.However,it isworth notingthat both theHybridandJEWELmodels,inspite oftheircapturingofthegeneraltrendsofthedata,theydonotin- corporate the physics of colour coherence andall the prongs in the jet lose energy incoherently. This points to a simpler inter- pretationof the results forinstance in terms of formationtimes ofthe splittingsandtheirinterplaywiththemediumlength. The vacuumformationtimet_f≈

ω

/k²_T≈¹/(

ω

R²),with

ω

andkT be- ingtheenergyandrelativetransversemomentum oftheradiated prong,is shorterforlarge-angle splittings,meaning that vacuum, large-anglesplittings,willbeproducedmostlyinthemediumand theirresultingprongswillbefurthermodiﬁedbythemedium.At largeangles,thecomponentofvacuumsplittingsthatpropagatein vacuumislessthanatsmallangles,resultinginanenhancedcon- tributionofmedium-modiﬁcationscomparedtosmall-angle splittings.

Fig. 4.ThenumberofSDbranchesforjetsreconstructedinPb–Pbdataareshown.

Thesystematicuncertaintiesarerepresentedbytheshadedarea.Thedatapointsare comparedtojetsfoundinPYTHIAeventsembeddedintoPb–Pbevents(openmark- ers).TheHybridmodelandJEWELpredictionscorrespondtothered(dashed)and blue(solid)lines.ThelowerpanelshowstheratioofthenSDdistributionindata andtheembeddedPYTHIAreference(grey).TheratiosoftheHybridandJEWEL modelstotheembeddedPYTHIAreferencearealsoshownandtheiruncertainties arepurelystatistical.

7. Summary

ThisLetterpresentsthemeasurementofjetsubstructureusing iterativedeclusteringtechniquesinppandPb–Pbcollisionsatthe LHC.WereportdistributionsofnSD,thenumberofbranchespass- ingthesoftdropselection,andzg,thesharedmomentumfraction of the two-prongsubstructure selected by the mass drop condition,differentiallyinrangesofsplittingopeningangle.

(6)

Generally, good agreement betweendistributions for pp collisions andvacuumcalculationsis foundexcept forthefractionof untagged jets, which is underestimated by the models. In Pb–Pb collisions,asuppressionofthez_g distributionisobservedatlarge anglesrelativetothevacuumreferencewhilstatlowopeningan- glesthereisahintofanenhancement.Theseobservationsare in qualitative agreement withthe expected behaviour of two-prong objects in the case of coherent or decoherent energy loss [26]

intheBMDPS-Z [54,55] framework.However,themodelsthatare comparedtothedatadonotimplementcolour coherenceandyet theycapturethequalitative trendsofthedata.Thissuggeststhat othereffectsmightdrivetheobservedbehaviour, forinstancethe interplay between formation time of the splittings and medium length.

The number of splittings obtained by iteratively declustering the hardest branch in the jet, nSD, is shifted towards lower val- uesinPb–Pb relativetothe vacuumreference.Thissuggeststhat medium-inducedradiationdoesnotcreatenewsplittingsthatpass theSDcut.Onthecontrary,thereisahintoffewersplittingspass- ingtheSDcut,pointingtoaharder,morequark-likefragmentation inPb–Pbcomparedtoppcollisions,inqualitativeagreementwith thetrendsobservedforotherjetshapes[11].

With these measurements, we have explored a region of the Lund planedelimited bythe SoftDrop cut z>0.1.Other regions ofthephase spaceofsplittings willbe scanned systematicallyin thefuturewithlargerdatasamples.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers andtechnicians fortheir invaluablecontributionstotheconstruc- tion of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICECollab- oration gratefully acknowledges the resources and support pro- videdbyall GridcentresandtheWorldwide LHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the followingfundingagencies fortheirsupport inbuildingandrun- ningtheALICEdetector: A.I. AlikhanyanNationalScience Labora- tory(YerevanPhysicsInstitute)Foundation(ANSL),StateCommit- tee of Science and World Federation of Scientists (WFS), Arme- nia; Austrian Academy ofSciences, Austrian Science Fund (FWF):

[M 2467-N36]andÖsterreichischeNationalstiftungfür Forschung, Technologie und Entwicklung, Austria; Ministry of Communica- tions and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Cientíﬁco e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS),FinanciadoradeEstudoseProjetos(Finep)andFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;

MinistryofScience&TechnologyofChina(MSTC),NationalNatural Science Foundationof China (NSFC)andMinistry ofEducation of China(MOEC),China;CroatianScienceFoundationandMinistryof Science andEducation, Croatia; Centro de Aplicaciones Tecnológ- icas yDesarrollo Nuclear (CEADEN),Cubaenergía, Cuba; Ministry ofEducation, Youth andSports of the Czech Republic, Czech Re- public; The Danish Council for Independent Research | Natural Sciences, the CarlsbergFoundation andDanish NationalResearch Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland;Commissariatàl’ÉnergieAtomique (CEA),InstitutNational de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientiﬁque (CNRS) and Région desPays de la Loire, France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionen- forschung GmbH, Germany; General Secretariat for Research and Technology,MinistryofEducation,ResearchandReligions,Greece;

National Research Development and Innovation Oﬃce, Hungary;

DepartmentofAtomicEnergy,GovernmentofIndia (DAE),Depart- mentofScience andTechnology,GovernmentofIndia(DST),Uni- versity GrantsCommission,GovernmentofIndia(UGC)andCoun- cil of Scientiﬁc and Industrial Research (CSIR), India; Indonesian Institute ofScience,Indonesia;CentroFermi- MuseoStoricodella FisicaeCentroStudieRicercheEnricoFermiandIstitutoNazionale diFisicaNucleare(INFN),Italy;InstituteforInnovativeScienceand Technology,NagasakiInstitute ofAppliedScience(IIST),Japan So- ciety forthe Promotion ofScience (JSPS) KAKENHI andJapanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia yTecnología (CONA- CYT), through Fondo de Cooperación Internacional en Ciencia y Tecnología(FONCICYT)andDirecciónGeneraldeAsuntos delPer- sonal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council ofNorway,Norway;CommissiononScience andTechnol- ogy for Sustainable Development in the South (COMSATS), Pak- istan; Pontiﬁcia Universidad Católica del Perú, Peru; Ministry of ScienceandHigherEducationandNationalScienceCentre,Poland;

KoreaInstituteofScienceandTechnologyInformationandNational Research Foundation of Korea (NRF), Republic ofKorea; Ministry of Education and Scientiﬁc Research, Institute of Atomic Physics and Ministryof Research andInnovation and Institute of Atomic Physics,Romania;JointInstitute forNuclear Research(JINR),Min- istryofEducationandScienceoftheRussianFederation,National Research Centre Kurchatov Institute, Russian Science Foundation andRussianFoundationforBasicResearch,Russia;MinistryofEd- ucation, Science, Research andSport of the Slovak Republic, Slo- vakia;NationalResearchFoundationofSouthAfrica,SouthAfrica;

SwedishResearchCouncil(VR)andKnut&AliceWallenbergFoun- dation (KAW), Sweden; European Organization for Nuclear Re- search,Switzerland;NationalScienceandTechnologyDevelopment Agency(NSDTA),SuranareeUniversityofTechnology(SUT)andOf- ﬁce of the Higher Education Commission under NRU project of Thailand,Thailand;TurkishAtomicEnergyAgency(TAEK),Turkey;

National Academy of Sciences of Ukraine, Ukraine; Science and TechnologyFacilitiesCouncil(STFC),UnitedKingdom;NationalSci- enceFoundationoftheUnitedStatesofAmerica(NSF)andUnited StatesDepartment ofEnergy, Oﬃceof Nuclear Physics(DOE NP), UnitedStatesofAmerica.

References

[1]M.Dasgupta,F.A.Dreyer,G.P.Salam,G.Soyez,Inclusivejetspectrumforsmall- radiusjets,J.HighEnergyPhys.06(2016).

[2] L.Asquith,etal.,JetSubstructureattheLargeHadronCollider:Experimental Review.

[3]CMSCollaboration,A.M.Sirunyan,etal.,Measurementofjetsubstructureob- servablesintt eventsfromproton-protoncollisionsat√

s=^{13 TeV,}^Phys.^Rev.

D98 (9)(2018),arXiv:1808.07340 [hep-ex].

[4]A.J.Larkoski,I.Moult,B.Nachman,Jetsubstructureatthelargehadroncollider:

areviewofrecentadvancesintheoryandmachinelearning,arXiv:1709.04464 [hep-ph].

[5]K.J.Eskola,H.Paukkunen,C.A.Salgado,NuclearPDFsatNLO- statusreportand reviewoftheEPS09results,Nucl.Phys.A855(2011).

[6]A.Majumder,M.VanLeeuwen,Thetheoryandphenomenologyofperturbative QCDbasedjetquenching,Prog.Part.Nucl.Phys.A66(2011).

[7]ALICECollaboration,J.Adam,etal.,Measurementofjetquenchingwithsemi- inclusivehadron-jetdistributionsincentralPb–Pb collisionsat √_s

NN=².76 TeV,J.HighEnergyPhys.09(2015).

[8]STARCollaboration,L.Adamczyk,etal.,Measurementsofjetquenchingwith semi-inclusivehadron+jetdistributionsinAu+Aucollisionsat√_s

NN=^{200 GeV,} Phys.Rev.C96 (2)(2017).

[9]CMSCollaboration,A.M.Sirunyan,etal.,Studyofjetquenchingwith Z+jet correlationsinPb–Pband ppcollisionsat √_s

NN=⁵.02 TeV,Phys.Rev.Lett.

119 (8)(2017).

[10]ATLASCollaboration,M.Aaboud,etal.,Measurementofphoton–jettransverse momentumcorrelationsin5.02TeVPb+Pband ppcollisionswithATLAS, Phys.Lett.B789(2019).