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ATLAS CONF NoteATLAS-CONF-2021-020

14th May 2021

Measurement of nuclear modification factor formuons from charm and bottom hadrons in Pb+Pbcollisions at 5.02 TeV with the ATLAS detector

The ATLAS Collaboration

Heavy flavour hadron production provides information about the transport properties andthe microscopic structure of the quark-gluon plasma created in ultra-relativistic heavy-ioncollisions. A measurement of the production of muons from the semi-leptonic decays of charmand bottom hadrons in Pb+Pb and ?? collisions at a nucleon-nucleon center-of-mass energyof 5.02 TeV with the ATLAS detector at the Large Hadron Collider is presented. The Pb+Pbdata were collected in 2015 and 2018 with sampled integrated luminosities of 208 `b−1 and38 `b−1, respectively, and ?? data with a sampled integrated luminosity of 1.17 pb−1 werecollected in 2017. The differential muons yield in Pb+Pb and ?? cross section are measuredin the transverse momentum range from 4 GeV to 30 GeV and pseudorapidity interval upto 2. Muons from heavy flavour semi-leptonic decays are separated from the light flavourhadronic background using the momentum imbalance between the inner detector and the muonspectrometer measurements, and muons coming from charm and bottom decays are furtherseparated via the muon track transverse impact parameter. The nuclear modification factor forthe charm and bottom muons is presented as a function of the muon transverse momentum inintervals of Pb+Pb collision centrality. The measured nuclear modification factors quantifysignificant suppression of the yields for muons coming from the decays of charm and bottomhadron, with stronger effects for muons coming from charm hadron decays.

© 2021 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

1 Introduction

Quark-gluon plasma (QGP) is a state of matter in which the quarks and gluons are deconfined from colorneutral hadronic states. Ultra-relativistic collisions of large nuclei create nuclei-sized droplets of QGP attemperatures in excess of 300–500 MeV [1, 2]. These droplets exist for a mere 10−23 seconds and hencethere is no manner in which an external probe can be fired at the droplet to probe its properties. Instead, the‘probes’ must be generated in the collision itself and then interact with the droplet. Interactions with theQGP, both radiative and collisional, may provide key information regarding the properties and constituentsof the QGP [3]. Specifically, the balance of radiative and collisional energy transfer depends on the massof the constituents [4, 5]. Heavy quarks, charm and bottom, have masses much larger than the droplettemperature. Thus, they are produced in the initial collision via high-momentum-transfer interactionsbetween incident quarks and gluons, where thermal production is highly suppressed. The strong forceinteractions conserve the quantum numbers associated with charm and bottom. Thus, once created, thesequarks can have substantial modifications to their momentum distributions when traversing the QGP, butthey cannot be destroyed. In addition, radiative energy loss is suppressed for heavy quarks due to theso-called ‘dead-cone effect’ [6], i.e., gluon radiation at angle smaller than their mass to energy ratio issuppressed. A key measurement in constraining the relative contribution of radiative energy loss is viathe modification of momentum distributions for charm and bottom quarks separately, since the dead-coneeffect will be more pronounced for bottom relative to charm quarks at the same momentum.

There are numerous publications detailing the modifications of momentum distribution of heavy-flavourhadrons measured in heavy-ion collisions via direct reconstruction and via decay leptons in heavy-ioncollisions at the Relativistic Heavy Ion Collider (RHIC) [7] and the Large Hadron Collider (LHC) [8] – forreviews of current measurements and theory calculations see Refs. [9, 10]. In nucleus-nucleus (A+A)collisions, each event is delineated by its centrality which reflects the overlap of the colliding nuclei. Thegeometry of each event is calculated using a Monte Carlo Glauber model – for details see Ref. [11]. Themodification to particle yields in A+A collisions with respect to ?? collisions is quantified by a nuclearmodification factor 'AA defined as:

'AA =#AA/#evt

〈)AA〉 × f??, (1)

where #AA is the number of observed particles of interest in Pb+Pb collisions, #evt is the number ofminimum bias Pb+Pb events, 〈)AA〉 is the average value of the nuclear thickness function, and f?? is theparticle production cross section in ?? collisions at the same collision energy. If 'AA equals unity, theproduction in A+A collisions is the same as in ?? collisions but scaled up by the larger parton-partonluminosity, while 'AA < 1 indicates a suppression.

The nuclear modification factors for inclusive heavy-flavour muons (i.e. dominated by � and � mesonsemi-leptonic decay muons) have been measured in Pb+Pb collisions at √BNN = 2.76 TeV by the ATLASexperiment [12] and the ALICE experiment [13]. The ALICE experiment measured the nuclear modificationfactor for inclusive heavy-flavour electrons at the same energy [14, 15] and also at √BNN = 5.02 TeV [16].Nuclear modification factors for charm hadrons �0, �B, �

∗,Λ2 have been measured by the CMS [17] andALICE [18, 19] experiments in Pb+Pb collisions at √BNN = 5.02 TeV, and STAR [20–22] experiment inAu+Au collisions at lower energy at√BNN = 200 GeV. These measurements indicate significant suppressionfor heavy-flavour hadrons in Pb+Pb collisions. At transverse momentum (?T) greater than 4 GeV, theprompt �0 'AA is found to be consistent within the uncertainties with the 'AA of inclusive chargedparticles (dominated by c), while �0 hadrons have a smaller suppression (larger 'AA) compared to chargedparticles at lower ?T.

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The measurement presented here follows the previous ATLAS measurement performed at √BNN =

2.76 TeV [12] of muons coming from heavy-flavour hadron decays in Pb+Pb collisions. This note, basedon higher statistics of combined 2015 and 2018 Pb+Pb datasets and 2017 ?? dataset at 5.02 TeV extendsresults to the transverse momentum range 4 < ?T < 30 GeV. This note also enables the separation ofinclusive heavy-flavour muons into contributions from charm hadron decays (charm muons) and bottomhadron decays (bottom muons) based on the muon track transverse impact parameter, similar to that used inprevious ATLASmeasurements [23, 24]. Results for charm and bottommuon cross sections in ?? collisionsare shown as a function of muon ?T and compared to perturbative QCD (pQCD) calculations. The nuclearmodification factor is presented as a function of muon ?T in various Pb+Pb centrality intervals. Finallythe measured 'AA results, along with the previous measurement of the heavy-flavour muon momentumanisotropies [24], are compared to the expectations from theoretical calculations. 'AA quantifies theaverage energy loss while azimuthal anisotropy such as elliptic flow, E2, quantifies the azimuthal angledependence of energy loss. Simultaneous constraints on the 'AA and E2 of the same final state are importantto distinguish the relative impact of different heavy-quark energy loss mechanisms and to understandthe influence of the initial QGP droplet geometry on the resulting evolution of heavy-flavour quarks inmedium.

2 ATLAS detector

The ATLAS detector [25–27] at the LHC covers nearly the entire solid angle around the collision point.1It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagneticand hadronic calorimeters, and a muon spectrometer incorporating three large superconducting toroidalmagnets with eight coils each. The inner-detector system (ID) is immersed in a 2 T axial magnetic fieldand provides charged-particle tracking in the range |[ | < 2.5.

The high-granularity silicon pixel detector covers the vertex region and typically provides four measurementsper track, with the first hit typically in the insertable B-layer installed before Run 2 [26, 27]. It is followedby the silicon microstrip tracker which usually provides eight measurements per track. These silicondetectors are complemented by the transition radiation tracker (TRT), which enables radially extendedtrack reconstruction up to |[ | = 2.0.

The calorimeter system covers the pseudorapidity range |[ | < 4.9. Within the region |[ | < 3.2,electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr)calorimeters, with an additional thin LAr presampler covering |[ | < 1.8, to correct for energy loss inmaterial upstream of the calorimeters. Hadronic calorimetry is provided by the steel/scintillating-tilecalorimeter, segmented into three barrel structures within |[ | < 1.7, and two copper/LAr hadronic endcapcalorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimetermodules (FCal), covering the forward regions of 3.1 < |[ | < 4.9, optimised for electromagnetic andhadronic measurements respectively. The minimum-bias trigger scintillators detect charged particles over2.07 < |[ | < 3.86 using two hodoscopes of 12 counters positioned at I = ±3.6 m. The zero-degree

1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detectorand the I-axis along the beam pipe. The G-axis points from the IP to the centre of the LHC ring, and the H-axis pointsupwards. Cylindrical coordinates (A, q) are used in the transverse plane, q being the azimuthal angle around the I-axis.The pseudorapidity is defined in terms of the polar angle \ as [ = − ln tan(\/2). Angular distance is measured in units ofΔ' ≡

√(Δ[)2 + (Δq)2.

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calorimeters (ZDC) measure neutral particles at pseudorapidities |[ | ≥ 8.3 and consist of layers ofalternating quartz rods and tungsten plates.

The muon spectrometer (MS) comprises separate trigger and high-precision tracking chambers measuringthe deflection of muons in a magnetic field generated by superconducting air-core toroids. The field integralof the toroids ranges between 2.0 and 6.0 Tm across most of the detector. A set of precision chamberscovers the region |[ | < 2.7 with three layers of monitored drift tubes, complemented by cathode-stripchambers in the forward region, where the background is highest. The muon trigger system covers therange |[ | < 2.4 with resistive-plate chambers in the barrel, and thin-gap chambers in the endcap regions.Events of interest are selected to be recorded by the first-level trigger (L1) system implemented in customhardware, followed by selections made by algorithms implemented in software in the high-level trigger(HLT) [28]. The first-level trigger reduces the 40MHz bunch crossing rate to below 100 kHz (75 kHz) for?? (Pb+Pb) collisions, while the high-level trigger further reduces the average physics output rate to about1.2 kHz for recording.

3 Event Selection

The ?? data used in this analysis were recorded with the ATLAS detector in 2017, while the Pb+Pb datawere recorded in 2015 and 2018. Both ?? and Pb+Pb events were selected online using a trigger thatrequires a muon at the L1 and HLT with a ?T larger than 4 GeV [28, 29]. After selecting run periodswhen the detector subsystems were operational and taking into account the fraction of the total luminositysampled by the triggers, the volume of the datasets used in the analysis correspond to integrated luminositiesof 1.17 pb−1 for ?? data, 208 `b−1 for 2015 Pb+Pb data, and 38 `b−1 for 2018 Pb+Pb data. The 2017?? data, with small average number of interactions per bunch crossing in the range from 0.4 − 4, werecollected to serve as the baseline for Pb+Pb collision measurements at the same center-of-mass energy. Thesmaller sampled luminosity of 2018 Pb+Pb data, which have a larger recorded full luminosity than 2015Pb+Pb data, is due to a smaller fraction of sampled events recorded by specific muon triggers used in theanalysis. The selected Pb+Pb events are further required to satisfy offline minimum-bias Pb+Pb collisioncriteria, identical to those used in Ref. [24]. This additional requirement identifies and rejects 0.2% of theselected events as pileup events based on a combination of the total transverse energy measured in theFCal, denoted by Σ�FCal

T , and the ZDC energy.

The centrality of each Pb+Pb event is characterised by its Σ�FCalT value. For the results shown here,

the minimum-bias Σ�FCalT distribution is divided into percentiles ordered from the most central (large

Σ�FCalT , small impact parameter) to the most peripheral (small Σ�FCal

T , large impact parameter): 0–10%,10–20%, 20–30%, 30–40%, and 40–60%. The interval 0–100% corresponds to the total Pb+Pb inelasticcross section [30]. A Monte Carlo Glauber [11] calculation is used to calculate 〈)AA〉 for each centralityinterval [31].

Muons with 4 < ?T < 30 GeV and |[ | < 2 reconstructed in both the ID and the MS are selected andrequired to pass ‘medium’ selection requirements, detailed in Ref. [32]. Selected muons are required to bematched with an online muon candidate that fires the event trigger. Each muon is assigned a weight whichis the inverse of the product of the reconstruction and trigger efficiencies, evaluated for muons as a functionof their kinematic variables, and in the case of Pb+Pb data as a function of centrality as well.

The muon reconstruction and identification efficiency is factorized as the product of the individualreconstruction efficiencies in the ID and MS. The ID and MS efficiencies are determined in the large ??

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dataset collected in 2017 at√B = 13 TeV using the tag-and-probe method using �/k → `+`− events, as

detailed in Ref. [32]. They are applied to the ?? data at√B = 5.02 TeV used in this note, in fine intervals

of muon ?T and [. The expected difference between muon reconstruction efficiency at√B = 5.02 TeV and√

B = 13 TeV is approximately 0.3% [32], and is not considered in this note. The MS efficiencies for 2015and 2018 Pb+Pb data are obtained from the high-statistics ?? data at

√B = 13 TeV in the corresponding

years in fine intervals of muon ?T and [. The resulting MS efficiency is found to be 10% lower at muon?T < 5 GeV in 2018 data than that in 2015, and plateaus at the same value of 97% above 7 GeV. TheID efficiency in Pb+Pb events is obtained from Pb+Pb data using the same �/k → `+`− tag-and-probemethod in intervals of muon ?T and [. The measured Pb+Pb ID efficiency is about 98% with the efficiencyin 2018 being 3% lower than that in 2015 at 1 < |[ | < 2 independent of ?T, while no difference between2015 and 2018 is observed at |[ | < 1. No centrality dependence is observed for MS and ID efficiencies formuuons in Pb+Pb collisions.

The central values of muon trigger efficiency are obtained from �/k → `+`− Pythia8 [33] simulations infine intervals of muon ?T and [ using the tag-and-probe method [29]. All generated events were passedthrough a Geant4 simulation [34, 35] of the ATLAS detector under the same conditions present duringdata-taking and were digitized and reconstructed in the same way as the data. The same central values areused in ?? and Pb+Pb data. A small mis-modelling of the trigger performance in simulation, quantified bythe ratio of measured efficiencies in ?? data and the simulations, is corrected as an additional multiplicativecorrection, and is typically in the range 0.9–1. To account for different online muon momentum responsein ?? and Pb+Pb data, as well as slightly different trigger detector performance in 2015 and 2018, anadditional correction factor, determined as Pb+Pb to ?? data-driven efficiency ratios, is applied to Pb+Pbdata as a function of muon ?T, [, centrality, and year of Pb+Pb data-taking.

4 Signal extraction

As detailed in previous ATLAS publications [12, 23, 24, 36], the background contributions in the selectedmuon samples (labelled ‘bkg’ in Figures) have three components. The first one is called ‘prompt muonbackground’ including contributions from decays of non-open-heavy-flavour particles such as directquarkonia, low-mass resonances, g-leptons, and massive electroweak bosons,// . The second componentis the ‘hadronic background’ resulting from c and decaying into muons in the volume of the ID orpunching through the calorimeter. The last component is from random combination of uncorrelatedtrack segments from the ID and MS called as ‘fake muon background’. The prompt muon backgroundis estimated in simulations; while hadronic and fake backgrounds are subtracted from the signal muonsby fitting the muon momentum imbalance, d = (?ID − ?MS)/?ID, where ?ID is the muon momentummeasured in the ID, and ?MS is that measured in the MS corrected for the energy loss inside the calorimeter.The d distribution shapes of hadronic and fake backgrounds are extracted from simulation while theiryields are determined from the fit procedure.

The prompt muon background contribution in ?? events is estimated based on Pythia8 simulationsof prompt �/k, k(2S), and P(nS) production with implementation of non-relativistic QCD color octetmodel [37], and, and / productions with the PowhegBox v2 MC program [38] interfaced to the Pythia8parton shower model. The CT10 PDF set [39] is used in the matrix element, while the CTEQ6L1 PDFset [40] is used for the modelling of non-perturbative effects in the initial-state parton shower. The simulatedprompt muon background processes are all further scaled by process-dependent single scaling factors tomatch previous ATLAS measurements in ?? collisions at

√B = 5.02 TeV [41, 42]. Other contributions

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from low-mass resonances and g-leptons in the measured muon ?T range are found to be less than 1% [23,36] and are neglected in this analysis. In Pb+Pb collisions, the estimated prompt muon background ratestake into account nuclear modifications measured in Refs. [43–46].

A muon from hard scattering has a symmetric d distribution peaked at zero, while the hadronic backgroundhas a broader d distribution and the peak shifted toward higher values. This change in shape is dueto differences in the energy loss and kinematics of this background and the muons, where only energyloss of muons is properly corrected and added to the MS momentum measurement. Different shapesof the d distributions for the hadronic background and for other muons enable the isolation of hadronicbackground using a template-fitting procedure [23, 24]. The templates for the charm and bottom muon ddistributions are determined from multijet hard-scattering Pythia8 ?? collision events at

√B = 5.02 TeV

filtered on the presence of a generator-level muon with parameter values as in the A14 tune [47] andusing the NNPDF23LO parton distribution functions [48]. The templates for the charm and bottommuon d distributions (and track transverse impact parameter 30 distributions, described below) in multijethard-scattering QCD Pythia8 samples are found to be identical to those from non-diffractive QCD Pythia8samples; while hard-scattering QCD Pythia8 samples have much higher muon filter efficiency. The dtemplates for the prompt muon background are obtained from simulations of prompt �/k productionin ?? collisions at

√B = 5.02 TeV. The hadronic background and fake muon d templates are obtained

from non-diffractive QCD simulations of ?? collisions at√B = 5.02 TeV in Pythia8, with the A14

tune and NNPDF23LO parton distribution functions. The fake muon contribution is fixed relative to thehadronic background with the ratio obtained from simulation. The momentum of the reconstructed muonsselected in Pythia8 simulation is calibrated to match the muon momentum response in ?? and Pb+Pb data.The calibration is performed via shift and smearing parameters [24] determined from the invariant massresponse of �/k → `+`− events. The same calibration is applied to all muon candidates including thosefrom background contributions. Alternative calibrations for background contributions are used for thesystematic uncertainty evaluation. The signal muon d distribution shape shows no obvious dependence onmuon ?T, but is found to be broader in the more forward pseudorapidity and more central Pb+Pb collisions,both due to deteriorating muon momentum resolution in the ID. The hadronic background d distributionbecomes broader at higher ?T and more central collisions. Examples of the d template fit are shown inFigure 1 for muons with 6 < ?T < 7 GeV in ?? collisions and 20–30% Pb+Pb collisions. The yields ofinclusive heavy-flavour muons and hadronic background muons are extracted from the d template fits.

Charm and bottom muons are further separated using the muon track transverse impact parameter, 30,which is calculated relative to the beam spot [49]. Background contributions are subtracted from datadistributions of 30 as shown in the upper panels in Figure 2. For each of the three background sources, the30 shape is determined in simulations. In ?? data analysis, the 30 shape templates of various backgroundsources are obtained from the same Pythia8 simulations as those used to build d templates. In Pb+Pb dataanalysis, the same Pythia8 events overlaid with minimum bias Pb+Pb events collected in 2015 are used tobuild the background 30 templates to approximate background distributions in Pb+Pb collisions. The 30distributions in simulations and 2018 Pb+Pb data are smeared to match those in 2015 Pb+Pb data usinghigh quality prompt tracks. The prompt muon background 30 distribution normalization is constrainedby Monte Carlo simulation based yield estimate. The hadronic and fake background 30 distributionnormalization factors are extracted from the d template fit. The signal muon 30 distribution in Pb+Pb datais narrower than in ?? data due to a smaller transverse beam size. The background 30 distribution getsmoderately narrower with increasing ?T and shows no evident centrality dependence. After subtraction, theremaining 30 distribution in data contains only contributions from heavy-flavour muons. Due to differentlifetimes of charm and bottom hadrons, corresponding muons have different 30 distributions, and theirfractional contributions can be extracted using a template-fitting procedure.

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Figure 1: Fits to d for muons with 6 < ?T < 7 GeV in ?? collisions (left) and 20–30% centrality interval of Pb+Pbcollisions (right). The ratios of the data to fit results are shown in the lower panels. The prompt muon backgroundcontributions are very small in the fitted muon kinematic region. The grey bands indicate the statistical and systematicuncertainties combined in quadrature.

For ?? data, the charm and bottom muon 30 templates are obtained from the muon-filtered multijetPythia8 simulations at

√B = 5.02 TeV, as done for d templates. Bottom muons contain the 1 → 2 → `

cascade contribution. The 30 distributions of signal muons show no obvious dependence on the muon ?T,but they become broader with increasing parent � and � hadron ?T. The simulated samples in Pythia8are reweighted to match the inclusive � and � meson ?T spectra from Fixed Order Next-to-Leading-Logresummation (FONLL) calculations [50, 51]. The charm and bottom baryon-to-meson ratios in thesimulations are corrected to match the measured values in Ref. [52, 53]. The relative yield of �+ withrespect to �0 is corrected to match the measured value in Ref. [54, 55]. In the Pb+Pb analysis, the charmand bottom muon 30 templates are obtained from the ?? Pythia8 simulations overlaid with minimum-bias2015 Pb+Pb events, similar to what is done for the background 30 templates. Besides the FONLL andbaryon-to-meson correction as applied in ?? collisions, an additional correction is applied to match themodified charm and bottom hadron ?T spectra measured in Pb+Pb collisions by ALICE [18] and CMS [17].Examples of 30 template fits for muons with 6 < ?T < 7 GeV are shown in Figure 2 for ?? collisionsand 20–30% Pb+Pb collisions. From the 30 template fit the relative fraction between charm and bottommuons is extracted. The 30 fit is performed in the range of |30 | < 0.5 mm as events with |30 | > 0.5 mm arestatistically limited in both data and simulations and have little sensitivity to charm muon contribution.

5 Systematic uncertainties

Systematic uncertainties associated with the various steps of the analysis are assessed. The measuredcross section in ?? collisions, per-event yields in Pb+Pb collisions and 'AA are recalculated for systematicvariation of each source and then compared to the nominal results. The resulting difference is considered assystematic uncertainty. The systematic uncertainties of different variations are considered as uncorrelated,and are therefore summed in quadrature.

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Figure 2: (Top) 30 templates for different background contributions and data 30 distributions before (solid points)and after (open points) background subtraction for muons with 6 < ?T < 7 GeV in ?? collisions (left) and 20–30%centrality interval of Pb+Pb collisions (right). (Bottom) Fits to background subtracted 30 distribution for muons with6 < ?T < 7 GeV in ?? collisions (left) and 20–30% centrality interval of Pb+Pb collisions (right). Data to fittedresult ratios are shown in the lower panels. The vertical dashed lines indicate the 30 range, |30 | < 0.5 mm, used inthe fit procedure. The grey bands indicate the statistical and systematic uncertainties combined in quadrature.

5.1 Muon efficiency

The systematic uncertainties from themuon reconstruction efficiency andmuon trigger efficiency correctionsfor ?? collisions are dominated by the uncertainty in determining these efficiencies in data with thetag-and-probe method [29, 32]. These are evaluated following the procedures in previous ATLASmeasurements [29, 32], including variations in the tag-and-probe efficiency extraction method, online-offline matching requirement, and muon purity in the selected sample. The Pb+Pb efficiency is affected bythe systematic uncertainty sources mentioned above due to the use of the ?? efficiency in the factorizedtreatment. An additional uncertainty in Pb+Pb is associated with the determination of the ID reconstructionefficiency in data using the tag-and-probe method. Additional uncertainties in the trigger efficiencycorrection are determined from the efficiency ratio of Pb+Pb to pp and residual discrepancies in fullycorrected Pb+Pb muon spectra measured in 2015 and 2018 data taking periods. Apart from specific Pb+Pbuncertainties, other uncertainties are correlated between collision systems and thus cancel in 'AA.

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5.2 Background removal

The systematic uncertainty in the momentum imbalance templates includes uncertainty in muon momentumcalibration parameter, systematic variation with dedicated hadronic background calibration and systematicvariation due to d − 30 correlation in the hadronic background. Charm muon yields are more sensitive tothe background removal procedure as charm muons have narrower 30 distributions when the backgroundcontamination is large. The systematic uncertainties in the calibration parameters, which originate fromthe uncertainty in the determination of �/k → `+`− invariant mass response [56], contribute 3% relativeuncertainty to the final charm muon yields and 1% to the bottom muon yields. Since the hadronicbackground could have a different momentum response than that for real muons, the results are alsoexamined using a data-driven hadronic background momentum calibration in the background-dominatedregion d > 0.2. The difference is included as a systematic uncertainty which is about 10% (4%) for charm(bottom) muon yields at low ?T and decreases with increasing ?T. To account for small d − 30 correlationof hadronic background, the corresponding d template in different 30 selections are used and the resultingdifference is assigned as an additional systematic uncertainty. The relative uncertainty due to backgroundd − 30 correlation is about 3% for charm muon yields and less than 1% for bottom muon yields. The dtemplate related systematic uncertainties are considered as correlated between ?? and Pb+Pb data, and arepartially canceled in 'AA.

In the analysis, the magnitudes of the prompt muon background contribution is held at a fixed valueobtained from Pythia8 simulations scaled to match existing measurements. To assess the associateduncertainty, the ?? and Pb+Pb analyses are repeated by varying the estimated magnitudes of the differentprompt muon sources by the corresponding experimental uncertainties in their production rates [41, 42]and 'AA values [43–46]. The sensitivity to fake muon rate estimation is evaluated by varying the fakecandidate selection criteria in simulations. The resulting relative variation on the fake rate is about 20–40%,and yields 5% variations on average in the measured charm and bottom yields. The fake muon systematicuncertainty is considered as uncorrelated in ?? and Pb+Pb results.

5.3 Charm-bottom separation

The impact parameter template systematic uncertainties includes several components: uncertainties onFONLL calculations [50, 51], baryon-to-meson ratio measurements [50, 51] and �+/�0 measurements [57,58] are propagated to ?? and Pb+Pb results, and they are considered as correlated in ?? and Pb+Pb results.The muon ?T spectra predicted by FONLL are weighted to match the measured charm and bottom muonspectra reported in this note. The resulting weighting factors are used to adjust signal 30 templates toquantify the bias due to observed mis-modelling in the FONLL calculations. The resulting difference of1 − 5% in muon yields is assigned as an additional uncertainty and is considered as being correlated in ??and Pb+Pb results. Uncertainties on the nuclear modification of parent hadrons in Pb+Pb are propagatedfollowing the experimental uncertainties on � and � hadron 'AA from Ref. [17, 18]. Minimum biasPb+Pb events collected in 2018, in place of 2015 events, are used to overlay with Pythia8 simulationsto test the sensitivity to slightly different overlay condition. Resulting changes in the muon yields due todifferent overlay conditions are assigned as systematic uncertainty in the Pb+Pb results. Uncertainties inthe determination of 30 shift and smearing parameters are found to have a negligible impact, less than0.5% on the extracted charm and bottom yields.

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5.4 Global normalization

In the 2017 ?? data, the LUCID-2 detector [59] is used for the primary luminosity measurement. Theuncertainty in the integrated luminosity is derived using the methods described in Ref. [60], and is 1.6%.For Pb+Pb collisions, the systematic uncertainty in 〈)AA〉 is estimated by varying the Monte Carlo Glaubermodel parameters as detailed in Ref. [31].

5.5 Summary

Table 1: Contributions to systematic uncertainties given in percent for cross-section in ??, yields in Pb+Pb, andnuclear modification factor of charm and bottom muons. Ranges indicate the minimum and maximum systematicuncertainties found in all muon ?T and centralities in a given source.

Sourcef?? (%) #AA(%) 'AA (%)

2 → ` 1 → ` 2 → ` 1 → ` 2 → ` 1 → `

muon efficiency 0.9 − 1.9 0.6 − 1.8 1.0 − 16 0.4 − 16 0.3 − 16 0.2 − 16

background removal 4.3 − 12 0.8 − 3.8 2.5 − 30 1.0 − 5.1 1.9 − 27 0.5 − 4.7

charm-bottom separation 4.5 − 9.8 3.2 − 8.0 9.2 − 37 6.2 − 16 5.1 − 23 4.1 − 13

global normalization 1.6 1.6 0.9 − 4.6 0.9 − 4.6 1.8 − 4.9 1.8 − 4.9

total systematic uncertainty 6.6 − 13 3.8 − 8.9 10 − 48 6.7 − 18 6.7 − 35 5.5 − 17

Table 1 summarizes relative uncertainties on the measurement of charm and bottom muon production in ??and Pb+Pb collisions, and on the nuclear modification factor 'AA. The leading source of the uncertainty inall muon ?T bins and centralities is coming from the background removal and charm-bottom separationuncertainties and at low muon ?T in central Pb+Pb collisions from the evaluation of the muon efficiency.

6 Results

Figure 3 shows the differential cross section for muons from charm and bottom hadron decays within|[ | < 2 as a function of muon ?T in ?? collisions at

√B = 5.02 TeV. The measurements are compared with

theoretical calculations of muons from � and � hadron decays in the FONLL resummation framework [61].Uncertainties on the FONLL calculations include parton distribution function uncertainties, variations of theheavy-flavour quark masses, and changes in the renormalisation and factorisation scales. For muons fromcharm quarks, the FONLL calculation reaches the experimental data with its upper edge of the uncertaintyband at ?T < 10 GeV, while it underestimates the data at higher ?T. Similar difference between FONLLcalculations and prompt charm measurements is observed in previous measurements at LHC energies, forexample, with ALICE measurements of prompt � mesons [62] and inclusive heavy-flavour leptons [16,63], and LHCb measurement of prompt � meson [64]. The measured cross section for muons from bottomquarks is a factor of 1.3–1.4 higher than FONLL calculated central value (including 1 → 2 → `) but stillinside FONLL uncertainty band at low ?T, while the calculated central value agrees with the data within

10

experimental uncertainties for ?T > 10 GeV, similar to that observed in previous ATLAS measurement ofnon-prompt charmonium [56] and ALICE measurement of non-prompt � meson [57].

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Figure 3: Differential cross section of charm (left) and bottom (right) muons as a function of muon ?T, plotted at thecenters of the ?T intervals, in ?? collisions at

√B = 5.02 TeV in comparison to FONLL calculations. Data results

and FONLL calculations for bottom muons both include 1 → 2 → ` contribution. Statistical uncertainties on thedata are shown as vertical lines and systematic uncertainties on the data and calculation are shown as boxes.

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2)×30-40% (40-60%

Figure 4: Differential per-event invariant yields of muons from charm hadron decays (left) and bottom hadrondecays (right) as a function of ?T, plotted at the centers of the ?T intervals, for different centrality intervals in Pb+Pbcollisions at √BNN = 5.02 TeV. For each centrality interval from peripheral to central, an additional scaling factor of2 is applied to the plotted points for visual clarity. Statistical uncertainties are shown as vertical lines and systematicuncertainties as boxes.

Figure 4 shows the differential per-event invariant yields for muons from charm and bottom hadron decays,as a function of muon ?T in Pb+Pb collisions at √BNN = 5.02 TeV. To quantify the modification of themomentum distribution between ?? and Pb+Pb collisions the nuclear modification factor is calculatedfollowing Eq. 1 in several centrality intervals. The resulting charm and bottom muon 'AA as a function of?T is shown in Figure 5 for the ?T range of 4 < ?T < 30 GeV. There is a substantial suppression of bothmuons from charm and bottom hadron decays for all analyzed Pb+Pb centrality intervals. The suppressionincreases monotonically from the 40–60% interval to the most central 0–10% interval. The monotonic

11

centrality dependence follows expectations as the heavy quarks spend a longer time in the hotter and largerQGP droplet in collisions with larger nuclear overlap, i.e. more central intervals. Charm muon 'AA showsweak ?T dependence in all ?T bins in all centrality intervals, while bottom muon 'AA first decreases withincreasing muon ?T up to 10 GeV and then remains mostly unchanged in all centralities.

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30-40%10-20%

Figure 5: Nuclear modification factor, 'AA, for muons from charm hadron decay (top panels) and bottom hadrondecay (bottom panels) hadron decays as a function of ?T for five different centrality intervals. The centrality intervalsare separated for clarity into the left (0–10%, 20–30%, 40–60%) and right (10–20%, 30–40%) panels. Statisticaluncertainties are shown as vertical lines and uncorrelated systematic uncertainties as boxes around the points.Correlated fractional systematic uncertainties, including )AA and ?? luminosity uncertainties, are isolated as coloredboxes around unity for different centrality intervals.

Muons from charm decays have a stronger suppression compared with muons from bottom decays at low?T in all centrality intervals. This different suppression is highlighted in Figure 6, which overlays the dataalready presented in Figure 5 for both charm and bottom muon 'AA versus ?T in the 0–10% and 40–60%centrality intervals. The mass ordering of the measured 'AA follows expectations as the lighter charmquarks are expected to lose more energy in the QGP as compared with bottom quarks. Thus charm quarksare pushed to lower ?T, and emerge with a stronger suppression when compared with cross section in ??collisions.

Figure 6 also compares the experimental data with theoretical calculations referred to as dreena-b [65]and dab-mod [66, 67]. The dreena-b calculation includes radiative and collisional energy loss of the

12

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Figure 6: Nuclear modification factor, 'AA, (top) and elliptic flow, E2 [24] (bottom) of muon from bottom hadrondecays and charm hadron decays for 0–10% (left) and 40–60% (right) centrality intervals as a function of ?T.Statistical uncertainties are shown as vertical lines and systematic uncertainties as boxes. Also shown are theoreticalcalculations dreena-b and dab-mod models.

heavy quarks traversing the QGP, the latter modelled via a 1 + 1D Bjorken expansion [68] with path-lengthdistributions calculated following the procedure described in Ref. [69]. The width of the band correspondingto the dreena-b theoretical uncertainties reflects the range of magnetic to electric screening masses asconstrained by non-perturbative calculations [68]. As discussed in Ref. [65], the predicted 'AA is higherfor � mesons than for � mesons, converging to the same value at ?T ≈ 25 GeV as is expected whenthe particle ?T becomes much larger than the mass of the heavier 1 quark. The corresponding 'AA formuons shown for direct comparison with the experimental data is calculated using Pythia8 that simulatesmeson decay kinematics. The dreena-b prediction is in reasonable agreement with the experimentaldata. The dab-mod framework used here includes calculations with only Langevin drag and diffusioncontributions of the heavy quarks in the QGP. The curves shown here are obtained with Trento geometricinitial conditions [70], heavy-quark Langevin dynamics with the Moore and Teaney parameterization [71],and coupling values for charm (bottom) of �/2c) = 2.23 (2.79), where � is the spatial diffusion coefficientand ) is the temperature. The decoupling temperature of heavy quarks from the medium is ) = 160 MeVand both coalescence and fragmentation are implemented for hadronisation. The dab-mod predictionswith only Langevin dynamics shown in Figure 6 as colored solid lines are in qualitative agreement with theexperimental data, but have a stronger ?T dependence than the experimental data, particularly in the mostcentral collisions.

It is notable that both of these calculations also predict the azimuthal anisotropies of the heavy-flavour

13

muons. ATLAS has previously published azimuthal anisotropies quantified by the elliptic flow coefficient,E2, for muons from charm and bottom hadron decays [24]. The lower panels of Figure 6 show thoseATLAS measurements for E2 as a function of ?T in comparison with both the dreena-b and dab-modcalculations. The dreena-b calculations give qualitative agreement with both E2 and 'AA for both charmand bottom muons, while the above described implementation of dab-mod underpredicts the charm muonE2 even though it qualitatively matches the 'AA. In all theoretical implementations, a larger coupling ofcharm and bottom quarks to the QGP results in a reduced 'AA (i.e. more suppression) and an increased E2(i.e. larger anisotropy). Thus, increasing the coupling of charm to the QGP in dab-mod, for example, couldbring the predicted E2 to closer agreement with data but would simultaneously decrease 'AA pushing thecalculation further below the data. That said, another key component of these calculations is the modellingof the QGP space-time evolution, and thus it could be instructive in the future to compare the differenttheory calculations with a common QGP model to test whether the 'AA and E2 differences arise from theQGP modelling or the energy-loss implementation.

5 10 15 20 25 30 [GeV]

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)µ→0B→b( / )µ→0D→c (DREENA-B

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) µ→b( / )µ→c(

)µ→0B→b( / )µ→0D→c (DREENA-B

)µ→0B→b( / )µ→0D→c (DAB-MOD

Figure 7: The ratio of charm muon 'AA to bottom muon 'AA, 'charmAA /'bottom

AA , for 0–10% (left) and 40–60%(right) Pb+Pb centrality intervals as a function of muon ?T. Statistical uncertainties are shown as vertical lines andsystematic uncertainties as boxes. Also shown are theoretical calculations from dreena-b and dab-mod in the samecentrality intervals for the decay muons.

Figure 7 shows the results for charm muon to bottom muon 'AA ratios as a function of ?T in comparisonwith dreena-b and dab-mod calculations. The large uncertainty in measured result is due to the strongnegative correlation between charm and bottom muon 'AA uncertainties. As indicated by the measured'AA ratios, charm muons are significantly more suppressed than bottom muons in ?T < 8 GeV. However,no strong conclusion about the relative strength of their suppression can be drawn at higher ?T due tothe large uncertainties. Compared with measured results, calculations underpredict the 'AA ratios in0–10% centrality, while they mostly capture the magnitude and ?T dependence in the data in 40–60%centrality. As shown in Figure 6, the discrepancy between data and model in 0–10% is primarily from theunder-prediction of charm muon 'AA.

14

7 Conclusion

The ATLAS experiment at the LHC measures production and nuclear modification for muons coming fromsemileptonic decays of heavy-flavour hadrons in ?? and Pb+Pb collisions at 5.02 TeV. The measurementuses 2017 ?? data and combined 2015, 2018 Pb+Pb data corresponding to integrated luminosities of1.17 pb−1 and 246 `b−1 respectively. Compared to previous ATLAS measurement of heavy-flavourmuons [12], charm and bottom muon separated results with smaller systematic uncertainties coveringa wider ?T range are achieved in this note. The differential cross section measured in ?? collisions formuons coming from bottom-quark containing hadrons is reproduced with FONLL calculations. For muonscoming from charm-quark containing hadrons, the FONLL calculation is lower than the data at all measured?T and agrees with it within the systematics of the calculations below 10 GeV. The 'AA measurementsindicate a significant suppression of the yield of muons from both charm and bottom hadron decays, with asuppression that increases monotonically from peripheral to central collisions. The suppression is strongerfor charm quarks compared to bottom quarks, as expected theoretically [6]. The simultaneous constraintimposed by the measurements of 'AA presented here and the previously published flow measurements [24]could provide important information for understanding heavy-quark transport and QGP properties.

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Figure 8: Nuclear modification factor, 'AA, for muons from charm and bottom hadron decays as a function of#part (average number of participants in Pb+Pb collisions in a given centrality interval extracted from MC Glaubercalculations) for four different muon ?T intervals. Statistical uncertainties are shown as vertical lines and systematicuncertainties as boxes around the points. The horizontal size of the boxes indicates #part uncertainties. Also shownare theoretical calculations dreena-b and dab-mod in the same centrality selections for the decay muons.

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Figure 10: Nuclear modification factor, 'AA, (top panels) and elliptic flow E2 from Ref. [24] (bottom panels) ofmuon from bottom hadron decays and charm hadron decays for three Pb+Pb centrality intervals as a function of ?T.Statistical uncertainties are shown as vertical lines and systematic uncertainties as horizontal lines. Also shown aretheoretical calculations dreena-b and dab-mod models.

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Figure 11: The ratio of charm muon 'AA to bottom muon 'AA for three Pb+Pb centrality intervals as a functionof ?T. Statistical uncertainties are shown as vertical lines and systematic uncertainties as boxes. Also shown aretheoretical calculations from dreena-b and dab-mod in the same centrality intervals.

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Figure 12: The ratio of charm muon 'AA to bottom muon 'AA for five Pb+Pb centrality intervals as a function of ?T.Statistical uncertainties are shown as vertical lines and systematic uncertainties as boxes. Also shown are theoreticalcalculations for muons and hadrons from dreena-b in the same centrality intervals.

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Figure 13: Top: nuclear modification factors, 'AA (upper panels) elliptic flow, E2 (middle panels), and triangle flow,E3 (lower panels) both from Ref. [24], of muons from charm (blue) and bottom (red) hadron decays as a function of ?Tin three different Pb+Pb centrality intervals (0–10%, 10–20% and 20–30%). Bottom: The ratio of charm muon 'AAto bottom muon 'AA (upper panels), charm muon to bottom muon E2 difference E22 − E

12 (middle panels) and charm

muon to bottom muon E3 difference E23 − E13 (lower panels) for three Pb+Pb centrality intervals (0–10%, 10–20% and

20–30%) as a function of ?T. Statistical uncertainties are shown as vertical lines and systematic uncertainties ashorizontal lines.

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Figure 14: Top: nuclear modification factors, 'AA (upper panels) elliptic flow, E2 (middle panels), and triangle flow,E3 (lower panels) both from Ref. [24], of muons from charm (blue) and bottom (red) hadron decays as a function of?T in two different Pb+Pb centrality intervals (30–40% and 40–60%). Bottom: The ratio of charm muon 'AA tobottom muon 'AA (upper panels), charm muon to bottom muon E2 difference E22 − E

12 (middle panels) and charm

muon to bottom muon E3 difference E23 − E13 (lower panels) for two Pb+Pb centrality intervals (30–40% and 40–60%)

as a function of ?T. Statistical uncertainties are shown as vertical lines and systematic uncertainties as horizontallines.

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Figure 15: Nuclear modification factors, 'AA, of muons from charm hadron decays (left) and bottom hadrondecays (right) as a function of HF muon ?T in the 0 − 10% Pb+Pb centrality interval. The charm muon results arecompared to prompt �0 meson 'AA as a function of �0 meson ?T from the ALICE Collaboration [18] and the CMSCollaboration [17]. Bottom muon results are compared to non-prompt �0 mesons from the ALICE Collaborationand non-prompt �/k from the CMS Collaboration [72] as a function of non-prompt �0 or non-prompt �/k ?T.Statistical uncertainties are shown as vertical lines and systematic uncertainties as boxes. Also shown are theoreticalcalculations from dreena-b in the same Pb+Pb centrality intervals for �/� meson 'AA, as well as the corresponding'AA results for the decay muons. It is notable that for the charm case, the higher 'AA for decay muons relative to �0

may be explained by decay kinematics.

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Figure 16: Nuclear modification factor, 'AA, of muon from charm hadron decays and bottom hadron decays as afunction of ?T in 10–20% (left) and 30–40% (right) centrality intervals in comparison to light hadrons from previousATLAS publication [73]. Statistical uncertainties are shown as vertical lines and systematic uncertainties as boxes.

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Figure 17: Correlation between nuclear modification factor ('AA) and elliptic flow (E2) of muon from charm hadrondecays (top) and bottom hadron decays (right) measured in different centrality intervals for three different ?Tselections. Total uncertainties are shown as vertical/horizontal error bars. Also shown are theoretical calculationsfrom dreena-b and dab-mod without including any uncertainties.

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-1, 5.02 TeV, 1.17 pbpp0-10%

µ→c

µ→b

5 10 15 20 25 30 [GeV]

Tp

0

0.1

0.2

2v

µ→0D→c Langevin DAB-MOD

µ→0B→b Langevin DAB-MOD

µ→0D→c loss const EDAB-MOD

µ→0B→b loss const EDAB-MOD

5 10 15 20 25 30 [GeV]

Tp

0.5

1

AA

R PreliminaryATLAS-1bµPb+Pb, 5.02 TeV, 246

-1, 5.02 TeV, 1.17 pbpp10-20%

µ→c

µ→b

5 10 15 20 25 30 [GeV]

Tp

0

0.1

0.2

2v

µ→0D→c Langevin DAB-MOD

µ→0B→b Langevin DAB-MOD

µ→0D→c loss const EDAB-MOD

µ→0B→b loss const EDAB-MOD

5 10 15 20 25 30 [GeV]

Tp

0.5

1

AA

R PreliminaryATLAS-1bµPb+Pb, 5.02 TeV, 246

-1, 5.02 TeV, 1.17 pbpp20-30%

µ→c

µ→b

5 10 15 20 25 30 [GeV]

Tp

0

0.1

0.2

2v

µ→0D→c Langevin DAB-MOD

µ→0B→b Langevin DAB-MOD

µ→0D→c loss const EDAB-MOD

µ→0B→b loss const EDAB-MOD

5 10 15 20 25 30 [GeV]

Tp

0.5

1

AA

R PreliminaryATLAS-1bµPb+Pb, 5.02 TeV, 246

-1, 5.02 TeV, 1.17 pbpp30-40%

µ→c

µ→b

5 10 15 20 25 30 [GeV]

Tp

0

0.1

0.2

2v

µ→0D→c Langevin DAB-MOD

µ→0B→b Langevin DAB-MOD

µ→0D→c loss const EDAB-MOD

µ→0B→b loss const EDAB-MOD

5 10 15 20 25 30 [GeV]

Tp

0.5

1

AA

R PreliminaryATLAS-1bµPb+Pb, 5.02 TeV, 246

-1, 5.02 TeV, 1.17 pbpp40-60%

µ→c

µ→b

5 10 15 20 25 30 [GeV]

Tp

0

0.1

0.2

2v

µ→0D→c Langevin DAB-MOD

µ→0B→b Langevin DAB-MOD

µ→0D→c loss const EDAB-MOD

µ→0B→b loss const EDAB-MOD

Figure 18: The ratio of charm muon 'AA to bottom muon 'AA for five Pb+Pb centrality intervals as a function of ?T.Statistical uncertainties are shown as vertical lines and systematic uncertainties as boxes. Also shown are dab-modcalculations with Langevin and constant energy loss in the same centrality intervals.

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