Measurement of electrons from semileptonic heavy-ﬂavour hadron decays at midrapidity in pp and Pb–Pb collisions at √ s NN = 5 . 02 TeV

The differential invariant yield as a function of transverse momentum ( p T ) of electrons from semileptonic heavy-ﬂavour hadron decays was measured at midrapidity in central (0–10%), semi-central (30–50%) and peripheral (60–80%) lead–lead (Pb–Pb) collisions at √ s NN = 5 . 02 TeV in the p T intervals 0.5–26 GeV/ c (0–10% and 30–50%) and 0.5–10 GeV/ c (60–80%). The production cross section in proton–proton (pp) collisions at √ s = 5 . 02 TeV was measured as well in 0 . 5 < p T < 10 GeV/ c and it lies close to the upper band of perturbative QCD calculation uncertainties up to p T = 5 GeV/ c and close to the mean value for larger p T . The modiﬁcation of the electron yield with respect to what is expected for an incoherent superposition of nucleon–nucleon collisions is evaluated by measuring the nuclear modiﬁcation factor R AA . The measurement of the R AA in different centrality classes allows in-medium energy loss of charm and beauty quarks to be investigated. The R AA shows a suppression with respect to unity at intermediate p T , which increases while moving towards more central collisions. Moreover, the measured R AA is sensitive to the modiﬁcation of the parton distribution functions (PDF) in nuclei, like nuclear shadowing, which causes a suppression of the heavy-quark production at low p T in heavy-ion collisions at LHC.


Introduction
The main goal of ALICE is the study of the Quark-Gluon Plasma (QGP), a state of matter which is expected to be created in ultrarelativistic heavy-ion collisions where high temperatures and high energy densities are reached at the LHC [1]. Due to their large masses (m c ≈ 1.5 GeV/c 2 , m b ≈ 4.8 GeV/c 2 ), charm and beauty quarks (heavy-flavour) are mostly produced via partonic scattering processes with high momentum transfer, which have typical time scales smaller than the QGP thermalisation time (1 fm/c [2]). Furthermore, additional thermal production, as well as annihilation rates, of charm and beauty quarks in the strongly-interacting matter are expected to be small in Pb-Pb collisions even at LHC energies [3,4]. Consequently, charm and beauty quarks experience the full evolution of the hot and dense medium produced in highenergy heavy-ion collisions, therefore they are ideal probes to investigate the properties of the QGP.
Quarks and gluons interact strongly with the medium and they are expected to lose energy through elastic collisions [5,6] and radiative processes [7,8]. Quarks have a smaller colour coupling factor with respect to gluons, hence the energy loss for quarks is expected to be smaller than that for gluons. In addition, the dead-E-mail address: alice -publications @cern .ch. cone effect is expected to reduce small-angle gluon radiation for heavy quarks with moderate energy to mass ratio [9], thus further attenuating the effect of the medium. The combination of all these effects results in the observed hierarchical mass dependent energy loss [8,[10][11][12][13][14][15][16][17][18][19][20][21][22].
In order to quantify medium effects on heavy-flavour observables measured in heavy-ion collisions, they are compared with measurements in proton-proton (pp) collisions, where these effects are expected to be absent.
In pp collisions, heavy-quark production can be described by perturbative Quantum Chromodynamics (pQCD) calculations for all transverse momenta, whereas pQCD is not applicable for the calculation of light quark and gluon production at low transverse momenta [3]. Moreover, measurements of heavy-flavour production cross sections in pp collisions provide the necessary experimental reference for heavy-ion collisions.
The medium effects on heavy quarks are quantified through the measurement of the nuclear modification factor, defined as the ratio between the yield of particles produced in ion-ion collisions (d 2 N AA /dp T d y) and the cross section measured in proton-proton collisions at the same energy (d 2 σ pp /dp T d y), normalised by the average nuclear overlap function T AA : R AA (p T , y) = 1 T AA · d 2 N AA /dp T d y The T AA is defined as the average number of nucleon-nucleon collisions N coll , which can be estimated via Glauber model calculations [23,24], divided by the inelastic nucleon-nucleon cross section. In-medium energy loss shifts the transverse momenta towards lower values, therefore at intermediate and high p T (p T 2 GeV/c) a suppression of the production is expected (R AA < 1). Assuming the total cross section evaluated using N coll scaling is not modified, the nuclear modification factor is expected to increase towards lower p T , compensating the depletion at higher momenta. Such a rise was measured by the PHENIX and STAR experiments at RHIC in Au-Au and Cu-Cu collisions at √ s NN = 200 GeV for electrons from heavy-flavour hadron decays [25][26][27]. The nuclear modification factor for electrons from semileptonic heavy-flavour hadron decays was also measured by the ALICE collaboration in Pb-Pb collisions at √ s NN = 2.76 TeV [28,29], where the mentioned trend of R AA was also observed. At low p T , the nuclear modification factor reaches a maximum around 1 GeV/c and tends to decrease at lower p T . This trend can be explained by initial and final state effects, like the collective expansion of the hot and dense system [30][31][32], the interplay between hadronisation via fragmentation and coalescence [22,33,34] and the modification of the parton distribution functions (PDF) inside bound nucleons [35]. Initial-state effects at the LHC are explored with proton-nucleus collisions, where an extended QGP phase is not expected to be formed. The nuclear modification factor of electrons from charm and beauty hadron decays [14,36] and of D mesons [37] in p-Pb collisions at √ s NN = 5.02 TeV was found to be consistent with unity within uncertainties. From this, one can conclude that the strong suppression observed in Pb-Pb collisions is due to substantial final-state interactions of heavy quarks with the QGP formed in these collisions. However, it is important to note that recently the measurement of the elliptic flow of electrons from semileptonic heavy-flavour hadron decays [38] and of D mesons [39] have been published, showing intriguing and not yet fully understood collective effects in high-multiplicity p-Pb collisions in the heavy-flavour sector. This paper reports the measurement of the production cross section in pp collisions, the invariant yields and the nuclear modification factor, R AA , in Pb-Pb collisions as a function of p T of electrons from semileptonic heavy-flavour hadron decays at mid-rapidity at the centre-of-mass energy per nucleon pair √ s NN = 5.02 TeV. In order to study how the yield and R AA change with centrality in Pb-Pb collisions, the measurement was done in three representative classes: the 0-10% class for central Pb-Pb collisions, the 30-50% for semi-central Pb-Pb collisions and 60-80% for peripheral Pb-Pb collisions.

Experimental apparatus and data sample
The ALICE detector is described in detail in Refs. [1,40]. The experiment mainly consists of a central barrel at midrapidity (|η| < 0.9), embedded in a cylindrical solenoid which provides a magnetic field of 0.5 T parallel to the beam direction, and a muon spectrometer at forward rapidity (−4 < η < −2.5).
Charged particles produced in the collisions and originating from particle decays are tracked by the Inner Tracking System (ITS) [41] and the Time Projection Chamber (TPC) [42]. The ITS detector, composed of the Silicon Pixel Detector (SPD), Silicon Drift Detector (SDD), and Silicon Strip Detector (SSD), consists of six cylindrical silicon layers surrounding the beam vacuum pipe. These provide measurements of particle momenta and energy loss (dE/dx) used for charged-particle identification (PID), together with the TPC. The particle identification is complemented by a Time-Of-Flight (TOF) [43] detector, which measures the time-of-flight of charged particles. The TOF detector distinguishes electrons from kaons, protons, Table 1 Number of events and T AA [46,47] used in the analysis, split by collisions system, trigger configuration, and centrality class. and pions up to p T 2.5 GeV/c, p T 4 GeV/c and p T 1 GeV/c, respectively. The ElectroMagnetic Calorimeter (EMCal) [44] covers a pseudorapidity region of |η| < 0.7 and it is used to measure electrons, photons, and jets in an azimuthal region of ∼ 107 o .
The electron identification in the EMCal is based on the measurement of the E/p ratio, where E is the energy of the EMCal cluster matched to the prolongation of the track with momentum p reconstructed with the TPC and ITS detectors. The V0 detectors [45] consist of two arrays of 32 scintillator tiles covering the pseudorapidity ranges 2.8 < η < 5.1 (V0A) and −3.7 < η < −1.7 (V0C), respectively, and are used for event characterisation.
The results presented in this paper are based on data samples of Pb-Pb collisions recorded in 2015 and of pp collisions at the same energy recorded in 2017. The analysed events were collected with a minimum bias (MB) trigger of a logic AND between the V0A and V0C detectors. Pb-Pb collisions were also recorded using the EMCal trigger, which requires an EMCal cluster energy summed over a group of 4×4 calorimeter cells larger than an energy threshold of 10 GeV. The EMCAL triggered events were used for electron measurements for p T > 12 GeV/c. The centrality classes were defined in terms of percentiles of the hadronic Pb-Pb cross section, defined by selections on the sum of the V0 signal amplitudes [46].
For both collision systems, only events with at least two tracks and a reconstructed primary vertex located between ± 10 cm with respect to the nominal interaction point along the z-axis are considered. Events affected by pile-up from different bunch crossings, which constitute less than 1% of the recorded sample, were rejected [28]. The number of events analysed in the two collision systems with the different trigger configurations is summarised in Table 1, together with the average nuclear overlap function T AA [46,47].

Data analysis
The p T -differential yield of electrons from semileptonic heavyflavour hadron decays is computed by measuring the inclusive electron yield and subtracting the contribution of electrons that do not originate from semileptonic heavy-flavour hadron decays. In the following, the inclusive electron identification strategy and the subtraction of electrons originating from background sources are described.

Track selection and electron identification
The selection criteria are similar to the ones described in Refs. [28,29]. They are summarised together with the kinematic cuts applied in the analyses in Table 2.
It is important to note that only tracks that have hits on both SPD layers are accepted so that electrons from late photon conversions in the detector material are significantly reduced. In the Pb-Pb analysis for p T >3 GeV/c, also tracks with a single hit in the SPD are considered, since the amount of photonic background starts to become negligible. In the analysis in which the EMCal detector is used, specific track-cluster matching criteria are adopted.
As in the procedure followed in Refs. [28,29], electron candidates are identified according to the criteria listed in Table 3. These requirements depend on the data sample and on the transverse momentum interval in which the analyses are performed. Table 2 Track selection criteria used in the analyses. "DCA" is an abbreviation for "distance of closest approach" of a track to the primary vertex.  Table 3 Electron identification criteria. The following momentum-dependent function is used for the electron identification in pp collisions, based on the TPC dE/dx: For the electron selection based on clusters in the EMCAL, a criterion on the "σ 2 s " parameter [29], corresponding to the shorter-axis of the shower shape, is used. For brevity, the "low p T " label is used in place of "p T < 3 GeV/c", as well as "high p T " in place of "p T > 3 GeV/c".
The electron identification in pp collisions is performed by evaluating the signal from the TPC and TOF detectors. The discriminant variable in the former detector is the deviation of dE/dx from the parameterised electron Bethe-Bloch [48] expectation value, expressed in units of the dE/dx resolution, n TPC σ ,e , while in the latter one the analogous variable n TOF σ ,e , referring to the particle timeof-flight, is considered. The criterion |n TOF σ ,e | < 3, used for electron identification up to p T = 3 GeV/c, is required to reduce background from kaons and protons. A momentum dependent criterion on n TPC σ ,e is adopted to guarantee a constant electron identification efficiency of 70% for p T < 3 GeV/c and of 50% for higher transverse momenta by reducing the selection window in n TPC σ ,e , in order to keep the hadron contamination sufficiently low. In the Pb-Pb analysis for p T < 3 GeV/c, the electron identification is performed by applying the same requirement on TOF and due to the large densities of tracks, a selection between −4 < n ITS σ ,e < 2 on the energy deposited in the SDD and SSD detectors is applied in all centrality classes. Finally, the selection on n TPC σ ,e ensures a constant electron identification efficiency of 50% for all centrality classes. The hadron contamination fraction after the PID is estimated by fitting the n TPC σ ,e distribution for each particle species with an analytic function in different momentum intervals [28,29]. The inclusive electron sample is then selected by applying a further criterion on n TPC σ ,e , which is chosen in order to have a constant efficiency as a function of the momentum, as well as to have the hadron contamination under control. This criterion is loosened for p T > 3 GeV/c, due to the lower amount of selected hadrons when the EMCal detector is employed.
In the Pb-Pb analysis for p T > 3 GeV/c, the electron candidates are first selected by the measurement of the TPC dE/dx with the criterion −1 < n TPC σ ,e <3. Then, the selection 0.8 < E/p < 1.3 on the energy over momentum ratio is applied. Unlike for hadrons, the ratio E/p is close to 1 for electrons because they deposit most of their energy in the EMCal. Furthermore, the electromagnetic showers of electrons are more circular than the ones produced by hadrons. Generally, the shower shape produced in the calorimeter has an elliptical shape which can be characterised by its two axes: In pp events, the hadron contamination is below 1% at low p T , while it reaches about 40% at p T = 10 GeV/c. In Pb-Pb, the largest hadron contamination is measured in the most central collisions, where a contamination of about 7% and 10% mainly due to kaon and proton crossing the electron band at p T = 0.5 GeV/c and p T = 1 GeV/c respectively is present. The total hadron contamination contribution amounts to 5% at p T = 3 GeV/c in central events and tends to decrease towards more peripheral collisions. In the EMCal analysis a maximum residual contamination of about 10% is subtracted at the highest transverse momenta in the 0-10% centrality class. In both collision systems, the hadron contamination is subtracted statistically from the inclusive electron candidate yield. In Pb-Pb collisions, the rapidity ranges used in the ITS-TPC-TOF (p T < 3 GeV/c) and TPC-EMCal (p T > 3 GeV/c) analyses are restricted to |y| < 0.8 and |y| < 0.6, respectively, to avoid the edges of the detectors, where the systematic uncertainties related to particle identification increase.

Subtraction of electrons from non heavy-flavour sources
The selected inclusive electron sample does not only contain electrons from open heavy-flavour hadron decays, but also different sources of background: 1. electrons from Dalitz decays of light neutral mesons, mainly π 0 and η, and from photon conversions in the detector ma- Number of clusters in TPC terial as well as from thermal and hard scattering processes, called photonic in the following; 2. electrons from weak decays of kaons: Photonic electrons are reconstructed statistically by pairing electron (positron) tracks with opposite charge tracks identified as positrons (electrons), called associated electrons in the following, forming the so-called unlike-sign pairs. The combinatorial background is subtracted using the like-sign invariant mass distribution in the same interval. Associated electrons are selected with the criteria listed in Table 4, which are intentionally looser than the ones applied for the inclusive electron selection, shown in Table 2, in order to maximise the probability to find the photonic partners.
Due to the limited acceptance of the detector and the rejection of some associated electrons by applying the mentioned criteria, a certain fraction of photonic pairs is not reconstructed. Therefore, the raw yield of tagged photonic electrons is corrected for efficiency to find the associated electron (positron), the so called tagging efficiency (ε tag ). This is evaluated using Monte Carlo (MC) simulations; pp and Pb-Pb collisions are simulated by the PYTHIA 6 [51] and HIJING [52] event generators, respectively. Primary particle generation is followed by particle transport with GEANT3 [53] and a detailed detector response simulation and reconstruction. The tagging efficiency is defined as the ratio of the number of true reconstructed unlike-sign pair electrons and the number of those generated in the simulations. The simulated p T distributions of π 0 or η mesons are weighted in MC to match the measured spectra. In both pp and Pb-Pb collisions, the weighting factor for It was observed in the previous analysis [28] that the contribution from J/ψ decays reaches a maximum of around 5% in the region 2 < p T < 3 GeV/c in central Pb-Pb collisions, decreasing to a few percent in more peripheral events. At lower and higher momenta, this contribution quickly decreases and becomes negligible, hence it is not subtracted in the present analyses. The associated systematic uncertainty is taken from similar works [28,29]. Due to the requirement of hits in both pixel layers, it was also observed from similar studies in previous measurements [28] that the relative contribution from K e3 decays to the electron background is negligible, hence this contribution is not subtracted in the present analyses. Additional sources of background, such as electrons from W and Z /γ * decays, are subtracted from the fully corrected and normalised electron yield in Pb-Pb collisions at high p T . These contributions are obtained from calculations using the POWHEG event generator [57] for pp collisions and scaling it by N coll , assuming R AA = 1. The contribution from W decays increases from 1% at p T = 10 GeV/c to about 20% at p T = 25 GeV/c in the 0-10% centrality class, while the Z contribution reaches about 10% at the same transverse momentum.

Efficiency correction and normalisation
After the statistical subtraction of the hadron contamination and the background from photonic electrons, the raw yield of electrons and positrons in bins of p T is divided by the number of analysed events (N MB ev ), by the transverse momentum value at the bin centre p centre T and the bin width p T , by the width y of the covered rapidity interval, by the geometrical acceptance (ε geo ) times the reconstruction (ε reco ) and PID efficiencies (ε eID ), and by a factor of two to obtain the charge averaged invariant differential yield, since in the analyses the distinction between positive and negative charges is not done: . (2) The production cross section in pp collisions is calculated by multiplying the invariant yield of Eq. (2) by the minimum bias trigger cross section at √ s = 5.02 TeV, that is 50.9 ± 0.9 mb [58]. The per-event yield of electrons from the EMCal triggered sample was scaled to the minimum bias yield by normalisation factors determined with a data-driven method based on the ratio of the energy distributions of EMCal clusters for the two triggers, as described in Ref.
[29]. The normalisation is 64.5 ± 0.5 in 0-10% and 246 ± 2.6 in 30-50% centrality intervals, respectively. The efficiencies are determined using specific MC simulations, where every collision event is produced with at least either a cc or bb pair and heavy-flavour hadrons are forced to decay semileptonically to electrons [28,29]. The underlying Pb-Pb events were simulated using the HIJING generator [52] and heavy-flavour signals were added using the PYTHIA 6 generator [51]. The efficiency of reconstructing electrons from semileptonic heavy-flavour hadron decays is about 20% at p T = 0.5 GeV/c, then it increases with p T up to 58% in pp collisions. In Pb-Pb collisions, it follows the same trend, increasing from 5% to 10% in the same p T range.

Systematic uncertainties
The overall systematic uncertainties on the p T spectra are calculated summing in quadrature the different contributions, which are assumed to be uncorrelated. They are summarised in Table 5 and discussed in the following.
The systematic uncertainties on the total reconstruction efficiency arising from the comparison between MC and data are estimated by varying the track selection and PID requirements around the default values chosen in the analyses. The analysis is repeated Table 5 Contributions to the systematic uncertainties on the cross section (yield) of electrons from heavy-flavour hadron decays in pp (Pb-Pb) collisions, quoted for the transverse momentum intervals 0.5 < p T < 0.7 GeV/c and 8 < p T < 10 GeV/c. These p T intervals are listed because the detectors used for particle identification in the two cases are different. In addition, they also represent the first and the last p T intervals in common for the centrality classes in Pb-Pb collisions, as well as for the pp cross section. At higher p T the uncertainties are generally lower, apart from the one related to the electroweak background, which stays below 4%. The uncertainties quoted with * are not summed in quadrature together with the others, because they are the R AA normalization uncertainties.
with tighter and looser conditions with respect to the default selection criteria and the systematic uncertainty is calculated as the root mean square (RMS) of the distribution of the resulting corrected yields (or cross sections in pp) in each centrality and p T interval. The systematic uncertainty estimated in pp collisions is less than 2%, while in Pb-Pb collisions it reaches a maximum value of 4% in 0-10% centrality class for p T < 0.9 GeV/c.
Similarly, the systematic uncertainty arising from the photonicelectron subtraction technique is estimated as the RMS of the distribution of yields obtained by varying the selection criteria listed in Table 4. In pp collisions this contribution has a maximum of 4% for 0.5 < p T < 0.7 GeV/c and then it gradually decreases with increasing p T , while in the 0-10% Pb-Pb centrality class it is the dominant source of systematic uncertainty, being 13% in the first p T interval. This systematic uncertainty mainly arises when the invariant mass criterion on the photonic pairs is varied and it reflects the large contribution of photonic electrons in the low-p T region.
In order to further test the robustness of the photonic electron tagging, the requirement on the number of clusters for electron candidates in the SPD is relaxed in order to increase the fraction of electrons coming from photon conversions in the detector material. A variation of 3% is observed for the measured pp cross section in the full p T range, while in central Pb-Pb collisions the observed deviation amounts to 10% for 0.5 < p T < 0.7 GeV/c, decreasing with increasing p T . This systematic uncertainty is less relevant in semi-central collisions, and it is compatible with the variation determined in pp measurements for 1.5 < p T < 3 GeV/c.
In addition, the systematic uncertainty related to the subtraction of the background electrons from W and Z /γ * is estimated by propagating 15% of uncertainty, which covers the possible difference between the measurements and the theoretical calculations [59-61]. The uncertainty from the subtraction on the final result, which is relevant only at high p T , is less than 4% for electrons from semileptonic heavy-flavour hadron decays in central (0-10%) Pb-Pb collisions for 24 < p T < 26 GeV/c, and less than 1% in other centrality classes for the same p T interval. In the pp analysis, a 5% systematic uncertainty is found while varying the selection criterion in the TPC for p T > 8 GeV/c due to the increasing relative amount of hadrons. An additional systematic uncertainty of 5%, related to the precision of the estimated hadron contamination, is assigned for p T > 8 GeV/c. In Pb-Pb collisions, a 10% systematic uncertainty is assigned for p T > 12 GeV/c due to the variation of electron identification in the TPC, while this contribution is within 5% at lower p T . Moreover, a 6% uncertainty is assigned due to the E/p selection criterion. Finally, for p T < 3 GeV/c, different functional forms are used for the parametrisation of the pion contribution in the fitting procedure adopted to evaluate the hadron contamination. A systematic uncertainty of about 6% is assigned for p T < 3 GeV/c in the 0-10% centrality class, while this contribution decreases for more peripheral collisions.
In the pp (Pb-Pb) analysis, a systematic uncertainty of about 2% (3%) is assigned due to the incomplete knowledge of the efficiency in matching tracks reconstructed in the ITS and TPC and another 2% (5%) for the track matching between TPC and TOF.
The effects due to the presence of non-uniformity in the correction for the space-charge distortion in the TPC drift volume or irregularities in the detector coverage are then evaluated by repeating the analysis in different geometrical regions. In pp collisions, a maximum systematic uncertainty of 5% is estimated from varying the pseudorapidity range used for the cross section measurement. The same value is assigned in the 30-50% and 60-80% Pb-Pb centrality intervals, while a 10% systematic uncertainty is assigned for 0.5 < p T < 0.7 GeV/c in the 0-10% centrality interval, due to the larger sensitivity to the electrons from photon conversions. An additional uncertainty of 10% for p T < 1 GeV/c and of 5% up to p T = 3 GeV/c is estimated from varying the azimuthal region in central Pb-Pb collisions. Furthermore, the analysis of Pb-Pb collisions is repeated using different interaction rate regimes. A 5% deviation is observed at low p T in central Pb-Pb collisions when selecting only high (> 5 kHz) or low (< 5 kHz) interaction rate events.
The uncertainty from the EMCal trigger normalisation in Pb-Pb collisions at p T > 12 GeV/c is estimated as the RMS of the rejection factor values computed at different transverse momenta [29]. The RMS is 4% and assigned as the systematic uncertainty. The uncertainties on the R AA normalisation are the quadratic sum of the uncertainties on the average nuclear overlap functions in Table 1, the normalisation uncertainty due to the luminosity and the uncertainty related to the determination of the centrality intervals, which reflects the uncertainty on the fraction of the hadronic cross section used in the Glauber fit to determine the centrality [16,62].

p T -differential cross section in pp collisions and invariant yield in Pb-Pb collisions
The p T -differential production cross section of electrons from semileptonic heavy-flavour hadron decays in pp collisions at √ s = 5.02 TeV is shown in Fig. 1. The data in the region 0.5 < p T < 10 GeV/c is compared with the Fixed-Order-Next-to-

Nuclear modification factor
The nuclear modification factor of electrons from semileptonic heavy-flavour hadron decays measured in central (0-10%), semi-central (30-50%), and peripheral (60-80%) Pb-Pb collisions at √ s NN = 5.02 TeV is shown in Fig. 3. The measured cross sec- Statistical and systematic uncertainties of the p T -differential yields and cross sections in Pb-Pb and pp collisions, respectively, are propagated as uncorrelated uncertainties. The uncertainties on the R AA normalisation are reported in Fig. 3 as boxes at unity. The measured R AA shows a clear dependence on the collision centrality, since in most central events it reaches a minimum of about 0.3 around p T = 7 GeV/c, while moving to more peripheral Pb-Pb collisions the R AA gets closer to unity at p T > 3 GeV/c. Such a suppression is not observed in proton-lead collisions at the same energy where the QGP is not expected to be formed and the nuclear modification factor is consistent with unity [14,36,37]. Thus the suppression of electron production is due to final-state effects, such as partonic energy loss in the medium. Since electrons from semileptonic beauty decays are expected to dominate the spectrum at high p T while charm production dominates at low p T [14], the measurements show that charm and beauty quarks lose energy in the medium. The centrality dependence of the R AA is compatible with the hypothesis of a partonic energy loss dependence on medium density, being larger in a hotter and denser QGP, like the one created in the most central collisions. In addition, it reflects a path-length dependence of energy loss. Moreover, it has been shown in Refs. [67,68] that a centrality selection bias is present in peripheral Pb-Pb collisions which reduces the R AA below unity even in the absence of any nuclear modification effects. This effect may be responsible for a significant part of the apparent suppression seen in the R AA of electrons from semileptonic heavy-flavour hadron decays in the 60-80% centrality class.
For p T < 7 GeV/c, the R AA of electrons from semileptonic heavy-flavour hadron decays increases with decreasing p T as a consequence of the scaling of the total heavy-flavour yield with . This initial-state effect is studied in p-Pb collisions, however, the present uncertainties on the R pPb measurement do not allow quantitative conclusions on the modification of the PDF in nuclei in the low p T region to be made [36]. Furthermore, the amount of electrons from semileptonic heavy-flavour hadron decays is reduced due to the presence of hadrochemistry effects. For example, + c baryons decay into electrons with a branching ratio of 5%, while for the D mesons the branching ratio is less than 10%. Since in Pb-Pb collisions more charm quarks might hadronize into baryons [69], this effect reduces the total amount of electrons from semileptonic heavy-flavour hadron decays. Additional effects, such as collective motion induced by the medium, also have an influence on the measured R AA . Also, it has been observed that the radial flow can provoke an additional yield enhancement at intermediate p T [70][71][72][73]. In this case, the radial flow pushes up slow particles to higher momenta, causing a small increase in the nuclear modification factor around p T = 1 GeV/c.
It should be noted that the R AA measurements in the most central collisions at √ s NN = 2.76 TeV [28] and 5.02 TeV are compatible within uncertainties, as shown in Fig. 3. This effect was predicted by the Djordjevic model [74], and it results from the combination of a higher medium temperature at 5.02 TeV, which would decrease the R AA by about 10%, with a harder p T distribution of heavy quarks at 5.02 TeV, which would increase the R AA by about 5% if the medium temperature were the same as at 2.76 TeV. An analogous behaviour between the measured R AA at the two energies is also observed for the D mesons [16].

Comparison with model predictions
In Fig. 4 the measured R AA in the 0-10% (left panel) and 30-50% (right panel) centrality intervals are compared with model calculations [74][75][76][77][78][79][80][81]. The model calculations take into account different hypotheses about mass dependence of energy loss processes, transport dynamics, charm and beauty quark interactions with the QGP constituents, hadronisation mechanisms of heavy quarks in the plasma, and heavy-quark production cross section in nucleusnucleus collisions.
Most of the models provide a fair description of the data in the region p T < 5 GeV/c in both centrality classes, except for BAMPS [76]. The predictions from the MC@sHQ+EPOS2 [81], PHSD [77], TAMU [78], and POWLANG [80] models also include nuclear modification of the parton distribution functions, which is necessary to predict the observed suppression of the R AA at low p T . The following observations about the comparison with model calculations are fully in agreement with what is observed in the R AA measurements of D mesons [16]. The nuclear modification factor for central Pb-Pb collisions is well described by the TAMU [78] prediction at p T < 3 GeV/c within the uncertainties related to the shadowing effect on charm quarks. However, this model tends to overestimate the R AA for p T > 3 GeV/c, probably due to the missing implementation of the radiative energy loss in the model, which may become the dominant energy loss mechanism at high p T .
The agreement with TAMU [78] at low p T , on the other hand, confirms the dominance of elastic collisions at low momenta, together with the importance of the inclusion of shadowing effects in the model calculations [35], which reduce the total heavy-flavour production in Pb-Pb collisions with respect to an expectation from the binary scaling.
In semi-central Pb-Pb collisions the TAMU [78] and POWLANG [80] predictions are close to the lower edge of the uncertainties of the measured R AA for p T < 3 GeV/c. The latter calculation describes the data better up to p T 8 GeV/c, while the former provides a good description even at higher transverse momenta. The CUJET3.0 [75] and Djordjevic [74,79] models provide a good description of the R AA within the uncertainties in both centrality intervals for p T > 5 GeV/c, suggesting that the dependence of radiative energy loss on the path length in the hot and dense medium is well understood.

Conclusions
The invariant yield of electrons from semileptonic heavyflavour hadron decays was measured in central (0-10%), semicentral (30-50%), and peripheral (60-80%) Pb-Pb collisions at √ s NN = 5.02 TeV. The measurement of the nuclear modification factor in all the centrality classes for p T < 10 GeV/c is provided using as reference the cross section measured in pp collisions at the same centre-of-mass energy. The systematic uncertainties of this measurement are reduced by a factor of about 2 compared to the published reference in pp collisions at  is removed via the photonic tagging method. In addition, compared with the measurements performed in pp and Pb-Pb collisions at 2.76 TeV, the p T range is extended, and an additional centrality class is added. The measured R AA confirms the evidence of a strong suppression with respect to what is expected from a simple binary scaling for large p T . This is a clear signature of the medium induced energy loss on heavy quarks traversing the QGP produced in heavyion collisions.
The measurement of electrons from semileptonic heavy-flavour hadron decays in different centrality classes exhibits the dependence of energy loss on the path length and energy density in the hot and dense medium. The R AA at high p T (above 5 GeV/c) is fairly described in the 0-10% and 30-50% centrality intervals by model calculations that include both radiative and collisional energy loss. This indicates that the centrality dependence of radiative energy loss is theoretically understood. Further investigations and measurement of electrons from semileptonic decays of beauty hadrons will give more information about the mass dependence of the energy loss in the heavy-flavour sector.
With the good precision of the results presented here, the Pb-Pb data exhibit their sensitivity to the modification of the PDF in nuclei, like nuclear shadowing, which causes a suppression of the heavy-quark production in heavy-ion collisions. The implementation of the nuclear modification of the PDF in theoretical calculations is a necessary ingredient in order for the model predictions to correctly describe the measured R AA [28].

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support pro-