Elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity in Pb-Pb collisions at √sNN=2.76 TeV

JHEP09(2016)028 Published for SISSA by Springer Received:June 7, 2016 Accepted:August 15, 2016 Published:September 6, 2016 Elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity in Pb–Pb collisions at √sNN = 2.76 TeV The ALICE collaboration E-mail: [email protected] Abstract: The elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity (|y|<0.7) is measured in Pb–Pb collisions at √sNN = 2.76 TeV with ALICE at the LHC. The particle azimuthal distribution with respect to the reaction plane can be parametrized with a Fourier expansion, where the second coefficient (v2) represents the elliptic flow. The v2coefficient of inclusive electrons is measured in three centrality classes (0–10%, 10–20% and 20–40%) with the event plane and the scalar product methods in the transverse momentum (pT) intervals 0.5–13 GeV/cand 0.5–8 GeV/c, respectively. After subtracting the background, mainly from photon conversions and Dalitz decays of neutral mesons, a positive v2of electrons from heavy-flavour hadron decays is observed in all centrality classes, with a maximum significance of 5.9σin the interval 2 < pT<2.5 GeV/cin semicentral collisions (20–40%). The value of v2decreases towards more central collisions at low and intermediate pT(0.5 < pT<3 GeV/c). The v2of electrons from heavy-flavour hadron decays at mid-rapidity is found to be similar to the one of muons from heavy-flavour hadron decays at forward rapidity (2.5 < y < 4). The results are described within uncertainties by model calculations including substantial elastic interactions of heavy quarks with an expanding strongly-interacting medium. Keywords: Heavy Ion Experiments ArXiv ePrint: 1606.00321 Open Access, Copyright CERN, for the benefit of the ALICE Collaboration. Article funded by SCOAP3. doi:10.1007/JHEP09(2016)028 JHEP09(2016)028 Contents 1 Introduction 1 2 Experimental apparatus and data sample 3 3 Data analysis 6 3.1 Track selection and electron identification 6 3.2 Flow methods 10 3.3 Inclusive electron elliptic flow and systematic uncertainties 12 3.4 Correction for background electrons 14 3.4.1 Invariant mass method 14 3.4.2 Cocktail method 17 4 Results 21 5 Comparison with model calculations 24 6 Conclusions 25 The ALICE collaboration 34 1 Introduction The main goal of the ALICE [1] experiment is the study of strongly-interacting matter at the high energy density and temperature reached in ultra-relativistic heavy-ion collisions at the Large Hadron Collider (LHC). In these collisions the formation of a deconfined state of quarks and gluons, the Quark-Gluon Plasma (QGP), is predicted by Quantum ChromoDynamic (QCD) calculations on the lattice [2–6]. Because of their large masses, heavy quarks, i.e. charm (c) and beauty (b) quarks, are produced at the initial stage of the collision, almost exclusively in hard partonic scattering processes. Therefore, they interact with the medium in all phases of the system evolution, propagating through the hot and dense medium and losing energy via radiative [7,8] and collisional scattering [9–11] processes. Heavy-flavour hadrons and their decay products are thus effective probes to study the properties of the medium created in heavy-ion collisions. Heavy-quark energy loss in strongly-interacting matter can be studied via the modification of the transverse momentum (pT) spectra of heavy-flavour hadrons and their decay products in heavy-ion collisions with respect to the proton-proton yield scaled by the number of binary nucleon-nucleon collisions, quantified by the nuclear modification factor (RAA). A strong suppression of open charm hadrons and heavy-flavour decay leptons is observed for pT>3 GeV/cin central collisions, both at RHIC (√sNN = 200 GeV) [12–16] – 1 – JHEP09(2016)028 and LHC (√sNN = 2.76 TeV) [17–20] energies. The PHENIX and STAR Collaborations measured a RAA of about 0.25 at pT= 5 GeV/cfor electrons from heavy-flavour hadron decays at mid-rapidity in central Au–Au collisions at √sNN = 200 GeV [13–15]. In addition a similar RAA for D0mesons was measured by STAR [12]. Similar values were measured by the ALICE Collaboration in central Pb–Pb collisions at the LHC for prompt D mesons at mid-rapidity and for muons from heavy-flavour hadron decays at forward rapidity [17–19]. The pTand centrality distributions of the D meson RAA are compatible, within uncertainties, with those of charged pions [18]. In addition, the modification of the pTspectra is studied separately for beauty and charm via the RAA of D mesons and non-prompt J/ψ from beauty hadron decays measured by the ALICE [18] and CMS Collaborations [21,22], respectively. A hint for a smaller suppression for beauty than for charm hadrons is observed at high pTin central Pb–Pb collisions, which is well reproduced by calculations including a mass dependence of the parton energy loss [23–25]. Further insight into the transport properties of the medium is provided by the measurement of the azimuthal anisotropy of heavy-flavour hadrons and heavy-flavour decay leptons with respect to the reaction plane, defined by the beam axis and the impact parameter of the nucleus–nucleus collision. In non-central collisions, the initial geometrical anisotropy in coordinate space of the nucleons participating in the collision is converted, by the interactions among the medium constituents, to a final anisotropy in momentum space of the produced particles. This effect can be characterized by the elliptic flow v2, which is the second order harmonic coefficient of the Fourier expansion of the particle azimuthal distribution [26]. At low pTthe measured large v2of light-flavour hadrons [27–30] is considered as an evidence for the collective hydrodynamical expansion of the medium [31,32]. On general theoretical ground, the formation time of heavy quarks, shorter than 1/(2 mc,b) where mis the mass of the quark (≈0.08 fm/cfor charm), is expected to be smaller than the QGP thermalization time (≈0.6–1 fm/c[33]) with a very small annihilation rate [34]. The heavy-flavour elliptic flow measurements carry information about their degree of thermalization and participation to the collective expansion of the system. It is also relevant for the interpretation of recent results on J/ψ anisotropy [35], because the J/ψ mesons formed from charm quarks in a deconfined partonic phase are expected to inherit the azimuthal anisotropy of their constituent quarks [36,37]. At low and intermediate pT, the v2of heavy-flavour hadrons and their decay products is also expected to be sensitive to the heavy-quark hadronisation mechanism. Hadronisation via the recombination of heavy quarks with light quarks from the thermalized medium could further increase the elliptic flow of heavy-flavour hadrons and their decay products [38–40]. At high pTthe v2measurements can constrain the path-length dependence of the in-medium parton energy loss, which is different for radiative [7,8] and collisional [9–11] energy loss mechanisms. Particles emitted in the direction of the reaction plane have, on average, a shorter in-medium path length than those emitted orthogonally to it, leading to an expected positive elliptic flow [41,42], as observed for charged hadrons [27,29,30,43–45]. At RHIC, a positive elliptic flow of heavy-flavour decay electrons at low and intermediate pTwas reported by the PHENIX and STAR Collaborations [14,46] at mid-rapidity in Au–Au collisions at √sNN = 200 GeV, reaching a maximum value of about 0.15 at – 2 – JHEP09(2016)028 pT= 1.5 GeV/cin semi-central collisions. Elliptic flow values measured at lower colliding energies are found to be consistent with zero [46]. The ALICE Collaboration measured the elliptic flow of D mesons at mid-rapidity [47,48] and heavy-flavour decay muons at forward rapidity [49] in Pb–Pb collisions at √sNN = 2.76 TeV. At intermediate pTa positive v2of prompt D mesons (5.7σeffect in the interval 2 < pT<6 GeV/cfor the 30–50% centrality class), and heavy-flavour decay muons (3σeffect in the interval 3 < pT<5 GeV/cfor the 10–20% and 20–40% centrality classes) is observed. The centrality dependence shows a hint for a decrease of v2towards central collisions. At high pT(pT>8 GeV/cfor D mesons and pT>6 GeV/cfor heavy-flavour decay muons) small values of v2are measured, compatible with zero within large uncertainties. We report on the measurement of the elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity (|y|<0.7) in Pb–Pb collisions at √sNN = 2.76 TeV with ALICE. The measurement is performed in the pTinterval 0.5 < pT<13 GeV/cin three centrality classes 0–10%, 10–20% and 20–40% with the event plane method. The results complement the heavy-flavour decay muon v2measurements at forward rapidity [49] and extend towards lower pTthose of D mesons at mid-rapidity [47]. Moreover, charm hadron decays are expected to mainly contribute to the heavy-flavour decay electron sample at low pT(pT<3 GeV/c), whereas at higher pTthe contribution from beauty hadron decays should become relevant [50,51]. Therefore, the measurement of heavy-flavour decay electron v2provides further inputs on the beauty and charm elliptic flow at mid-rapidity to theoretical calculations that aim at describing the heavy-quark interactions with the medium. The elliptic flow of inclusive electrons obtained with the scalar product method is also compared to the measurements performed with the event plane method to study possible non-flow contributions and biases due to the method itself. This article is organized as follows: the experimental apparatus and data sample used in the analysis are presented in section 2. The analysis strategy, including the electron identification and the procedure for the subtraction of the background due to electrons not originating from heavy-flavour hadron decays, are described in section 3. The elliptic flow of heavy-flavour decay electrons is presented in section 4and compared to theoretical models in section 5. The summary and conclusions of this article are presented in section 6. 2 Experimental apparatus and data sample The ALICE experimental apparatus is described in detail in [1,52]. The global reference system has the z-axis parallel to the beam line, the x-axis pointing towards the centre of the LHC accelerator ring and the y-axis pointing upward. In the following, the subsystems that are relevant for the heavy-flavour decay electron analysis are described. Charged particle tracks are reconstructed at mid-rapidity (|η|<0.9) in the central barrel of ALICE with the Time Projection Chamber (TPC) and the Inner Tracking System (ITS). The electron identification uses information from the ITS, TPC and the Timeof-Flight (TOF) detectors in the pTinterval 0.5 < pT<3 GeV/cand from the TPC and ElectroMagnetic Calorimeter (EMCal) in the pTinterval 3 < pT<13 GeV/c. In the following, the two identification methods will be referred to as ITS-TPC-TOF and – 3 – JHEP09(2016)028 TPC-EMCal analyses, respectively. These detectors are located inside a large solenoidal magnet that provides a uniform magnetic field of 0.5 T along the beam direction. The event characterization is performed with two scintillator detectors, V0, used for triggering, centrality and reaction plane estimation. Together with the Zero Degree Calorimeters (ZDC), they are used to further select events offline. The ITS [53] detector consists of six cylindrical silicon layers surrounding the beam vacuum tube. The first two layers are positioned at 3.9 and 7.6 cm radial distance from the beam line. Dealing with the high particle density in this region requires an excellent position resolution, which is achieved with Silicon Pixel Detectors (SPD). The third and fourth layers are radially positioned at 15 and 23.9 cm and consist of Silicon Drift Detectors (SDD), while the two outermost layers are radially positioned at 38 and 43 cm and are made of Silicon Strip Detectors (SSD). The four SDD and SSD layers enable chargedparticle identification via the measurement of their energy loss dE/dxwith a resolution of about 10–15%. The TPC [54] detector has a cylindrical shape with an inner radius of about 85 cm, an outer radius of about 250 cm, and a length of 500 cm. The TPC is the main tracking detector of the central barrel and is optimized to provide, together with the other central barrel detectors, charged-particle momentum measurement with excellent two-track separation and particle identification. For a particle traversing the TPC, up to 159 space points are recorded and used to estimate its specific energy loss. The resolution of the dE/dx measured in the TPC is approximately 6% for minimum-ionizing particles passing through the full detector. At a radial distance of 3.7 m from the beam axis, the TOF detector [55] improves further the particle identification capability of ALICE. It provides a measurement of the time of flight for the particles from the interaction point up to the detector itself with an overall resolution of about 80 ps for pions and kaons at pT= 1 GeV/cin the Pb–Pb collision centrality intervals used in this analysis. The measured time-of-flight of electrons is well separated from those of kaons and protons up to pT≃2.5 GeV/cand pT≃4 GeV/c, respectively. The EMCal [56] is a Pb-scintillator sampling calorimeter located at a radial distance of about 4.5 m from the beam axis spanning the pseudorapidity range |η|<0.7 and covering 107◦in azimuth. The cell size of the EMCal is approximately 0.014 rad ×0.014 in ∆ϕ×∆η. The energy resolution has been measured to be 1.7⊕11.1/pE(GeV)⊕5.1/E(GeV)%. The EMCal increases the existing ALICE capabilities to measure high-momentum electrons. The V0 detectors [57] 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. The two arrays are arranged in four rings each around the beam pipe. The V0 detectors are used to select beam–beam interactions online. For Pb–Pb collisions, the total signal amplitude is fitted with a model based on the Glauber approach, which is used to classify events according to their centrality classes [58], which correspond to percentiles of the hadronic cross section. For instance, the 0–10% centrality class corresponds to the 10% most central events. In addition, the azimuthal segmentation of the V0 detectors allows for an estimation of the reaction plane direction. – 4 – JHEP09(2016)028 Centrality class Trigger system Nevents Lint (µb−1) 0–10% Central trigger 15×10619.6 10–20% Semi-central trigger 4×1065.2 20–40% Semi-central trigger 8×1065.2 10–20% EMCal trigger 0.7×10629.1 20–40% EMCal trigger 1×10624.4 Table 1. Number of events and integrated luminosity for the different triggers (see text) and centrality classes considered in this analysis. The centrality classes are expressed as percentiles of the hadronic cross section [58]. The ZDCs [59] are located on both sides of the interaction point at z ≈ ±114 m. Parasitic collisions of main bunches with satellite bunches are rejected on the basis of the timing information from the neutron ZDCs. The results presented in this paper are based on a data sample of Pb–Pb collisions recorded with ALICE in November and December 2011 at √sNN = 2.76 TeV. The events were collected with a minimum-bias interaction trigger using information of the coincidence of signals between V0A and V0C detectors. Central and semi-central Pb–Pb collisions were selected online by applying thresholds on the V0 signal amplitudes resulting in two separate trigger classes (central and semi-central triggers). In addition to the central and semi-central data samples, events selected by the EMCal trigger are analysed. The EMCal trigger required an EMCal cluster energy summed over a group of 4×4 cells, implemented as a sliding window, larger than an energy threshold. A centrality-dependent energy threshold was used, varying approximately from 7 GeV in the 0–10% centrality class to 2 GeV in the 80–90% centrality class. The EMCal trigger is in coincidence with the minimum-bias trigger. Detailed trigger information for the ALICE apparatus are reported in [52]. Only events with a reconstructed interaction vertex (primary vertex), determined by extrapolating charged-particle tracks to the beam line, with |z|<10 cm from the nominal interaction point are used in the analysis in order to minimize edge effects at the limit of the central barrel acceptance. In addition, the zposition of the primary vertex reconstructed using tracklets defined by hit pairs in the SPD is required to agree within 0.5 cm with the one of the primary vertex reconstructed with tracks. Since the v2measurements could be biased by multiplicity outliers, the centrality estimated with the V0 information is compared to that estimated using the number of reconstructed tracks in the TPC. Events with an absolute difference between the centrality estimated with the V0 detectors and the one estimated with the TPC detector larger than 5%, corresponding to events with pile-up from different bunch crossings, are rejected from the analysis. The event selection removed about 5% of the total number of events depending on the trigger and the centrality of Pb– Pb collisions. The number of events analysed after applying the event selection are listed in table 1for the different centrality classes and triggers together with the corresponding integrated luminosity. The EMCal trigger is not used in the 0–10% centrality class because of the high statistics achieved with the central trigger. – 5 – JHEP09(2016)028 Analysis ITS-TPC-TOF TPC-EMCal pTrange (GeV/c) 0.5–3 3–13 |y|<0.8 <0.7 Number of TPC points ≥100 ≥100 Number of TPC points in dE/dxcalculation ≥90 – Ratio of found TPC points over findable >0.6 >0.6 χ2/point of the momentum fit in the TPC <3.5 <3.5 DCAxy <2.4 cm <2.4 cm DCAz<3.2 cm <3.2 cm Number of ITS hits ≥5≥3 Number of hits in the SPD layers 2 ≥1 Table 2. Summary of the track selection criteria used in the analyses. 3 Data analysis The elliptic flow of electrons from heavy-flavour hadron decays ve±←−HF 2is obtained from the measurement of the inclusive electron elliptic flow ve± 2by subtracting the elliptic flow of electrons which do not originate from heavy-flavour hadron decays, vBkg 2. Exploiting the additive property of the particle azimuthal angle distribution with respect to the reaction plane, ve±←−HF 2can be expressed as: ve±←−HF 2=(1 + RSB)ve± 2−vBkg 2 RSB ,(3.1) where RSB is the ratio of the heavy-flavour decay electron yield to that of background electrons. In this paper, electrons from heavy-flavour hadron decays include electrons from quarkonium decays, whose contribution is however expected to be small as discussed in section 3.4. In the following sections, the ve± 2and RSB measurements are presented, as well as the two procedures to determine vBkg 2. 3.1 Track selection and electron identification Electron candidate tracks are required to fulfill the track selection criteria summarized in table 2. Tracks are selected by requiring at least 100 associated space points in the TPC with at least 90 used for the dE/dxcalculation and a value of the χ2/point of the momentum fit in the TPC smaller than 3.5. These selection criteria suppress the contribution from short tracks, which are unlikely to originate from the primary vertex. To further reduce the contamination from particles originating either from weak decays of light hadrons or from the interaction of other particles with the detector material, only tracks with a maximum value of the distance of closest approach (DCA) to the primary vertex in both the xy-plane (DCAxy <2.4 cm) and the zdirection (DCAz<3.2 cm) are accepted. In addition, in order to minimize the contribution of electrons coming from γ – 6 – JHEP09(2016)028 ) c (GeV/p 0 1 2 3 4 5 6 TPC σ n 15− 10− 5− 0 5 10 15 20 1 10 2 10 3 10 4 10 5 10 6 10 ALICE = 2.76 TeV NN s 20-40% Pb-Pb, | < 0.7y| kp e d π ) c (GeV/p 0 1 2 3 4 5 6 TPC σ n 15− 10− 5− 0 5 10 15 20 1 10 2 10 3 10 4 10 ALICE = 2.76 TeV NN s 20-40% Pb-Pb, | < 0.7y| kp e π | < 2 TOF σ n| ) c (GeV/p 0 1 2 3 4 5 6 TPC σ n 15− 10− 5− 0 5 10 15 20 1 10 2 10 3 10 4 10 ALICE = 2.76 TeV NN s 20-40% Pb-Pb, | < 0.7y| kp e π | < 2 TOF σ n| ) c < 1.5 (GeV/ T p| < 1, ITS σ n| ) c 1.5 (GeV/≥ T p| < 2, ITS σ n| Figure 1.nTPC σdistributions as a function of momentum in semi-central (20–40%) Pb–Pb collisions at √sNN = 2.76 TeV. Upper left panel: no ITS or TOF electron identification is applied. Upper right panel: the TOF-PID (see text) is applied. Lower panel: the TOF and ITS-PID (see text) are both applied. conversions in the detector material at large radii, hits in both SPD layers are required for all selected tracks in the ITS-TPC-TOF analysis (pT<3 GeV/c). Tracks are required to have at least three out of the four possible hits in the external layers of the ITS (SDD and SSD) in order to have at least three dE/dxmeasurements to be used for the Particle IDentification (PID). This guarantees a good particle identification based on the dE/dxin the ITS. Since the azimuthal coverage of the EMCal had a significant superposition with parts of the SPD detector that were not active during the data taking, this approach has to be modified for the TPC-EMCal analysis (pT>3 GeV/c). In this case, at least one hit in any of the two SPD layers is required and the minimum number of associated ITS hits is reduced to 3. This results in a larger contribution of conversion electrons in the inclusive electron sample. The signal-to-background ratio is, as a consequence, smaller in the TPC-EMCal analysis than in the ITS-TOF-TPC analysis at the same pT. Electron identification is mainly based on the measurement of the specific energy loss in the TPC (dE/dx). The discriminant variable used, nTPC σ, is the deviation of this quantity from the parameterized electron Bethe-Bloch [60] expectation value, expressed in units of the dE/dxresolution [52]. This distribution is shown as a function of the track momentum in semi-central triggered events for the 20–40% centrality class in the upper left panel of figure 1. In the low momentum region the kaon, proton and deuteron dE/dxbands cross – 7 – JHEP09(2016)028 pTrange TPC dE/dxcut ITS dE/dxcut TOF compatibility E/pmatching (GeV/c) with ehypothesis 0.5–1.5 −1< nTPC σ<3|nITS σ|<1|nTOF σ|<2 1.5–3 0 < nTPC σ<3|nITS σ|<2|nTOF σ|<2 3–8 −1< nTPC σ<3 0.8 < E/p < 1.2 8–13 −1< nTPC σ<3−2< nEMCal σ<3 Table 3. Summary of the electron identification criteria used in the analyses (see text for more details). that of electrons. In addition, the particle identification at high momentum is limited by the merging of the dE/dxbands of electrons, pions, muons and other hadrons, therefore the information of other detectors is mandatory to select a pure sample of electrons. Table 3 summarizes the PID cuts. At low pT(0.5 < pT<3 GeV/c), the measured time-of-flight in the TOF detector and the dE/dxin the ITS are used in addition to the TPC dE/dxto further reject hadrons. In the top right panel of figure 1, the nTPC σdistribution is shown after requiring that the measured time-of-flight of the particle is compatible with the electron hypothesis within two sigmas, where sigma is the time-of-flight resolution (|nTOF σ|<2). The kaon and proton contributions in the low momentum region are reduced but not completely removed due to wrongly associated hits in the TOF detector. This source of contamination is further suppressed using the dE/dxin the ITS. This selection is applied using the nITS σ variable, defined in the same way as for the TPC. Electron candidates are selected with |nITS σ|<1 for 0.5 < pT<1.5 GeV/cand with |nITS σ|<2 for 1.5 < pT<3 GeV/c, where the particles species are less separated in nITS σ. In the lower panel of figure 1, the nTPC σ distribution is shown after the additional electron identification criteria in the ITS are applied. A pure electron sample is obtained by selecting tracks with −1< nTPC σ<3 and 0 < nTPC σ<3 in the intervals 0.5 < pT<1.5 GeV/cand 1.5 < pT<3 GeV/c, respectively. In order to keep the contamination below 5%, the stronger requirement in the pTinterval 1.5 < pT<3 GeV/cis applied due to the merging of the pion and electron dE/dxbands in the TPC. In the pTinterval 3–13 GeV/c, the electron identification is based on the measurement of the TPC dE/dxand the E/pratio, where Eis the energy of the EMCal cluster matched to the prolongation of the track with momentum preconstructed with the TPC and ITS detectors. Unlike for hadrons, the ratio E/pis around 1 for electrons, because they deposit most of their energy in the EMCal. In addition, the EMCal cluster shape is used to improve the purity of the electron sample, because the profile of the shower produced by electrons is more circular than the one produced by hadrons [61]. In the pTinterval 8–13 GeV/c, the EMCal PID selection is applied in terms of nEMCal σ, which is defined as the deviation of the measured E/pfrom the expected hE/pifor electrons obtained from data and normalized by the width of the electron E/pdistribution obtained with a fit Gaussian function. Electron candidates are selected with the identification criteria −1< nTPC σ<3 and −2< nEMCal σ <3 in the pTinterval 8 < pT<13 GeV/c. – 8 – JHEP09(2016)028 Associated electron cuts pTassoc (GeV/c)>0.15 for 0.5 < pT<3 GeV/c >0.3 for 3 < pT<8 GeV/c >0.5 for 8 < pT<13 GeV/c |yassoc|<0.9 Number of TPC points ≥80 Number of ITS hits ≥2 DCAassoc xy <2.4 cm DCAassoc z<3.2 cm TPC dE/dxcut −3< nTPC σ<3 Electron-positron pair cuts me+e−(MeV/c2)<70 for 0.5 < pT<3 GeV/c <140 for 3 < pT<13 GeV/c Table 4. Selection criteria for reconstructing photonic electrons. The transverse momentum of inclusive and associated electrons is written pTand passoc T, respectively. Due to detector acceptance and inefficiencies, not all photonic electrons of the inclusive electron sample are identified with this method. Therefore, the raw yield of reconstructed photonic electrons is corrected for the efficiency to find the associated electron(positron) with the selection criteria described above. This efficiency is estimated with Monte Carlo simulations. A sample of Pb–Pb collisions with enhanced π0and ηyields was generated with HIJING v1.36 [73]. The transport of particles in the detector is simulated with GEANT3 [74]. The simulated π0and η pTdistributions are weighted so as to match the measured π0and π±pTspectra [75,76] and the corresponding η pTspectra assuming mT-scaling [77,78], respectively. The photonic electron reconstruction efficiency increases with the pTof the electron, reaching a value of about 60% at high pT. The inclusiveto-background ratio (1 + RSB) is calculated by dividing the inclusive electron yield by the yield of photonic electrons corrected for the efficiency to find the associated electron. Figure 4shows this ratio for the 0–10% (left), 10–20% (middle) and 20–40% (right) centrality classes. The full markers represent the measurements obtained with the centralitytriggered samples, while in the 10–20% and 20–40% centrality classes the results for the EMCal-triggered sample are reported with open markers. The small decrease observed at pT= 3 GeV/cis due to the different requirements on the minimum number of hits in the SPD layers for the two electron identification strategies. For pTlarger than 2.5–3 GeV/c the contribution from heavy-flavour decay electrons starts to be dominant in the inclusive electron sample. The measurement of vBkg 2(see eq. (3.1)) at low pT(pT<1.5 GeV/c) is performed with a fit to the dN/d∆ϕdistributions of photonic electrons reconstructed with the invariant mass method in each pTinterval (see eq. (3.7)). At higher pT(pT>1.5 GeV/c), the – 15 – JHEP09(2016)028 )c (GeV/ T p 0 2 4 6 8 10 12 ± / Background e ± Inclusive e 0 5 10 15 Centrality trigger EMCal trigger = 2.76 TeV NN s0-10% Pb-Pb, )c (GeV/ T p 0 2 4 6 8 10 12 0 5 10 15 ALICE | < 0.7y| = 2.76 TeV NN s 10-20% Pb-Pb, )c (GeV/ T p 0 2 4 6 8 10 12 0 5 10 15 = 2.76 TeV NN s20-40% Pb-Pb, Figure 4. Ratio of the inclusive electron yield to the one of background electrons obtained with the invariant mass method in Pb–Pb collisions at √sNN= 2.76 TeV in 0–10% (left), 10–20% (middle) and 20–40% (right) centrality classes. The vertical error bars and open boxes represent the statistical and systematic uncertainties, respectively. electron yield becomes too small to perform a pTand ∆ϕ-differential measurement of the photonic electrons. Figure 7shows the v2of photonic electrons measured with the invariant mass method (full markers) as a function of pTin the centrality classes 0–10%, 10–20% and 20–40%. The systematic uncertainties of both the inclusive-to-background ratio and vBkg 2are estimated by varying the selection criteria listed in table 4. For pT>8 GeV/cthe TPC and EMCal PID requirements for the inclusive electron candidates are also varied in order to take into account possible systematic uncertainties from the estimation of the hadron contamination. In addition, for the inclusive-to-background ratio the small dependence of the photonic electron reconstruction efficiency on the pTspectra of the background sources is taken into account by calculating the efficiency for different π0and η pTspectra. The dependence of the centrality on the systematic uncertainty of the inclusive-to-background ratio is found to be negligible. The contributions to the inclusive-to-background ratio systematic uncertainty are summarized in table 5: the final overall systematic uncertainty is obtained summing in quadrature the different contributions. For vBkg 2, the systematic uncertainty of the event plane correction factor R2is estimated using the same procedure as for the inclusive electron v2and is found to be the same. Moreover, the difference between the vBkg 2measured with the invariant mass method and the one obtained with the cocktail method is taken point by point and added as an additional source of asymmetric systematic uncertainty up to pT= 1.5 GeV/c(about −20% in the centrality class 0–10% and −10% in the semi-central centrality classes 10–20%, and 20–40%). The systematic uncertainties coming from the variation of the selection criteria are found to be of the order of ±20% in the 0–10% most-central collisions and ±10 % in the centrality classes 10–20% and 20–40%. Finally, the overall systematic uncertainty on the measured vBkg 2obtained after summing in quadrature the different contributions, are estimated to be +20% −29% in the 0–10% centrality class and +10% −15% in the centrality classes 10–20% and 20–40%. – 16 – JHEP09(2016)028 pTrange (GeV/c): 0.5–1.25 1.25–3 3–8 8–13 Minimum number of TPC points 2% 2% 5% – for the associated electrons Minimum pTof the associated electrons 6% 6% – – Maximum me+e−5% 5% 10% 5% for the electron-positron pair Influence of the pTspectra 5% 10% 5% 3% of photonic sources Hadron contamination in the inclusive electron sample – – – 3% Table 5. Systematic uncertainties of the inclusive-to-background ratio (1 + RSB). The centrality dependence of these systematics is found to be negligible. (See text for more details). 3.4.2 Cocktail method The vBkg 2was also estimated using the cocktail method. A cocktail of electron spectra from background sources is calculated using a Monte Carlo event generator of hadron decays. This method requires that the momentum and elliptic flow distributions of the relevant background sources are well known. The following electron background sources are included in the cocktail simulation: – Dalitz decays of π0,η,ω,η0,φ – Dielectron decays of η,ρ0,ω,η0,φ – Conversions of decay photons from π0,η,ρ0,ω,η0 – Real and virtual conversion of prompt and thermal photons The contribution from dielectron decays of light vector mesons is small (below 5% of the total background electrons considered above). For the consistency with the invariant mass method, the contributions from Ke3and quarkonia (e.g. J/ψand Υ) decays to the inclusive electron spectrum are not included in the background cocktail. The Ke3and Υ contributions are not expected to be relevant in the pTrange of the analysis. In pp collisions at √s= 7 TeV and √s= 2.76 TeV, the relative contribution from Ke3decays to the electron background was observed to decrease with pT, from a maximum of 0.5% at pT= 0.5 GeV/cfor the same track requirement in the first pixel layer [62]. It is expected to stay below 1% in Pb–Pb collisions in the pTrange considered after taking into account the different RAA of the π0[75] and K±[76]. Neutral pions play an important role in the cocktail. The pTand v2distributions of all light scalar and vector mesons included in the cocktail are deduced from the π0spectra assuming mT[77,78] and KET[28,79–81] scaling, respectively. Indeed, electrons from π0decays are the most important background source, except in the 0–10% and 10–20% centrality classes for high electron pT(pT>8 GeV/cand pT>10 GeV/c, respectively), where contribution from direct photons starts to dominate. The contribution of π0decays – 17 – JHEP09(2016)028 0 2 4 6 8 10 12 14 16 18 -2 )c (GeV/ y d T pd N 2 d ev N 1 T p π2 1 6− 10 5− 10 4− 10 3− 10 2− 10 1− 10 1 10 2 10 3 10 ) / 2 - π + + π( 0 π ) / 2 - π + + πFit to ( = 2.76 TeV NN s10-20% Pb-Pb, ALICE )c (GeV/ T p 0 2 4 6 8 10 12 14 16 18 data/fit 0.6 0.8 1 1.2 1.4 2 4 6 8 10 12 14 16 18 ± π 2 v 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 | < 0.8 y, || > 0.9}η∆{EP-V0, | 2 v | < 0.5 y, || > 0.9}η∆{SP-V0, | 2 v Fit input 2 v ± πSystematic uncertainty from = 2.76 TeV NN s10-20% Pb-Pb, ALICE )c (GeV/ T p 2 4 6 8 10 12 14 16 18 data/fit 0.4 0.6 0.8 1 1.2 1.4 Figure 5. Measured pTspectra [76] (left) and v2[28,45,82] (right) of π±in the centrality class 10–20% in Pb–Pb collisions at √sNN = 2.76 TeV, together with the fit and extrapolation used in the cocktail method. The π0pTspectrum [75] is also shown. The vertical error bars and open boxes represent the statistical and systematic uncertainties, respectively. In the bottom left panel the ratios of the pTspectra over the fit are shown with the corresponding systematic uncertainty. to the electron background is twofold: via the Dalitz decay π0→e+e−γand via conversions in the detector material of photons from the decay π0→γγ. In principle, the π0pTand v2distributions used in the Monte Carlo event generator should be based on measured π0spectra [75] and v2. However, because of the higher statistical precision of the combined charged pion pTspectra [76] and the fact that neutral-pion and charged-pion pTspectra are found to be consistent, the average of the measured chargedpion pTspectra, (π++π−)/2, is used as input for the cocktail calculations. The upper-left panel of figure 5shows the comparison of the neutral and charge-averaged yields of pions in the centrality class 10–20% together with a fit to the π±data with a modified Hagedorn function [83]. The pTspectra are extrapolated up to 25 GeV/cusing the fit function. In the last pTinterval of the measured inclusive electron spectra (10 < pT<13 GeV/c), about 10% of electrons from Dalitz π0decays are expected to come from a π0with a pTlarger than 25 GeV/c. At such high pT, due to the similar v2of all particle species at high pT, this contribution is found to be negligible. The systematic uncertainty on the heavy-flavour decay electron v2arising from the background sources is estimated to be smaller than 6% in the last two pTintervals 8–10 and 10–13 GeV/c. The bottom-left panel of figure 5shows the ratio of the π±data, as well as π0data, to the fit function. The former is consistent with unity within 5% over the full pTrange, whereas the latter is considered in the vBkg 2 systematic uncertainties. The pT-dependent π±elliptic flow [28,45,82] is used as input for the cocktail calculations. The upper-right panel of figure 5shows the v2of charged pions measured in the 10–20% centrality class together with the fit function that is used in the cocktail simula- – 18 – JHEP09(2016)028 )c (GeV/ T p 0 2 4 6 8 10 12 14 2 v 0 0.05 0.1 0.15 0.2 0.25 ALICE Simulation = 2.76 TeV NN s 10-20% Pb-Pb, 0 π Dalitz decays 0 π from ± e Figure 6.v2of electrons from π0Dalitz decays (red markers) and v2of π0(blue markers) as a function of pTin the centrality class 10–20% in Pb–Pb collisions at √sNN = 2.76 TeV as obtained from the simulation used in the cocktail method. Only statistical errors are shown. tions. The ratio of the data to the fit function is presented in the bottom-right panel. The function used to fit the v2of charged pions is an empirical function made by the convolution of trigonometric and error functions. Measurements performed with the scalar product [28] and event plane [45,82] methods have been used at low-intermediate pT(pT<6 GeV/c) and higher pT(3 < pT<16 GeV/c), respectively. The scalar product and event plane methods give compatible results within the uncertainties in the common pTrange 3 < pT <6 GeV/c. The v2values are extrapolated from pT= 16 GeV/cup to pT= 25 GeV/c. The elliptic flow of electrons from π0Dalitz decays is estimated from that of π0mesons using the PYTHIA 6 [84] event generator to simulate the Dalitz decay. The parameterized v2of π0and the one of their decay electrons are shown in figure 6as a function of pT. The treatment of electrons from photon conversions in the detector material uses the GEANT4 functionality of pair production [85]. It has been implemented in the cocktail by forcing all decay photons to produce an e+e−pair immediately after their creation without propagating them through the ALICE apparatus. The contribution of electrons from photon conversions is scaled according to the radiation length of the crossed material. At low pT(pT<3 GeV/c), electron tracks are required to be associated with two hits in the SPD. The effective converter thickness is estimated to be x/X0= (0.77 ±0.07)%, including the beam pipe, air and part of the innermost pixel layer at y=0[62]. The indicated radiation thickness is averaged over the pseudorapidity range of the analysis. At higher pT (pT>3 GeV/c), tracks with one hit in the SPD are also used. Therefore, the material of the second pixel layer is also taken into account, leading to an effective converter thickness of x/X0= (2.15 ±0.11)% [62]. The results of the cocktail for photon conversion were found to be consistent within uncertainties with a full simulation test where the generated particles were propagated through the ALICE apparatus using GEANT3 [86]. The elliptic flow of electrons from the conversion of π0decay photons is found to be comparable to the one of electrons from π0Dalitz decays. – 19 – JHEP09(2016)028 The contributions of direct photons, thermal photons from the hot partonic and hadronic phase and photons that could be produced in the interactions of hard scattered partons with the medium, are included in the cocktail of background electrons. These sources can give both electrons from photon conversion in the detector material and electrons from virtual photons. The production of real prompt photons was measured at midrapidity in Pb–Pb collisions in the pTinterval 0.9–14 GeV/c[87]. The spectra are fitted and extrapolated towards lower and higher pT(0.5 < pT<25 GeV/c). At intermediatehigh pT(pT>5 GeV/c), the pTspectrum of real prompt photons has been calculated with next-to-leading-order perturbative QCD calculations for pp collisions at 2.76 TeV [88,89] and scaled to fit the ALICE measurements in Pb–Pb collisions [87]. This assumes that the other contributions are negligible in this pTrange and that the shape of the pTspectra of real prompt photons is not modified in heavy-ion collisions, which is justified by the experimental results. At low pT, the dominant contribution of thermal photons in the measured real direct photon pTspectra was taken into account by adding an exponential term to the fit function. The pTspectra of virtual photons are obtained using the Kroll-Wada function [72]. The elliptic flow of real direct photons was measured in the centrality class 0–40% [90]. To estimate the elliptic flow in the smaller centrality classes 0–10%, 10–20% and 20–40%, the measurement is scaled by the ratio of the measured charged pion v2in the 0–40% centrality class. Finally, the elliptic flow of virtual photons is assumed to be identical to the one of real photons. The elliptic flow of background electrons is estimated by summing the various background electron sources according to their relative contribution to the total background. The main background contributions are due to π0and prompt photons. In addition, the contributions of thermal photons (at low pTin the 0–10% and 10–20% most central Pb–Pb collisions) and ηare also relevant. The total systematic uncertainty of vBkg 2estimated with the cocktail method is obtained by adding in quadrature the contributions from several sources, namely: – the statistical and systematic uncertainties of the v2and pTmeasurements of π±and direct photons, – the quality of the fits and extrapolations of the π±and direct photon spectra, – the systematic uncertainties on the KETand mTscaling used to estimate the v2and pTdistributions of higher mass mesons, respectively, – the approximation of the π0pTand v2distributions by the corresponding π±spectra. The first one leads to the largest systematic uncertainty. It is evaluated by parameterizing the data along the upper and lower ends of their statistical and systematic uncertainties added in quadrature and generating again the complete cocktail of electron spectra based on these new parameterizations. The right panel of figure 5shows examples of such fits for the pTdependence of the π±v2in the centrality class 10–20%. The uncertainties of the measured pTspectra have a smaller influence on the resulting vBkg 2than those of the measured v2spectra. The uncertainty on the KETscaling assumption is estimated by – 20 – JHEP09(2016)028 comparing the kaon v2obtained by KETscaling to the measured one [28]. The resulting systematic uncertainty is 8% for 0–10%, 6% for 10–20% and 4% for 20–40%. These numbers are consistent with those reported in [28]. Because of their similar mass, it is expected that the elliptic flow of ηand the one of K are similar and thus these numbers are taken directly for the η KETscaling uncertainty. For the other heavier mesons the KET scaling does not hold precisely [28,81]; however, these other particles have an extremely low weight in the cocktail, and thus these uncertainties are neglected. The mT-scaling approach ensures that, at high pT, the transverse-momentum distributions are the same for all meson species. The normalization of the heavier meson spectra relative to the pion spectrum was determined by the ratios of heavier meson yields to neutral pion yields at high pT(pT>5 GeV/c). The values together with their uncertainties used in the analysis are taken from [78]. At low pT(pT<3–4 GeV/c) some deviations from the mT-scaling approach are expected due to in-medium effects like radial flow. The mT-scaling based cocktail is found to be in agreement within statistical uncertainties with a cocktail based on the η/π0-ratio measured in pp collisions at √s= 7 TeV [91]. Also, due to the similarity of the elliptic flow of decay electrons and conversion electrons originating from the dominating mother mesons (π0and η), the material budget uncertainty was found to have no significant effect. Two additional sources of systematic uncertainty related to the electron track reconstruction were studied. First, reconstructed electron candidates have a limited pTresolution. In particular, Bremsstrahlung in the detector material shifts their reconstructed pT towards lower values. Secondly, hits in the SPD can be wrongly associated to a track with a probability increasing with decreasing pT. This leads to an increase of the amount of electrons from photon conversions occurring beyond the SPD layers in the inclusive electron sample and a degradation of the pTand ϕresolutions of tracks used in the analysis. The resulting effects on vBkg 2were evaluated with the cocktail method using SPD hit mismatch probabilities and resolution maps obtained with a full simulation of the ALICE apparatus. No significant change of vBkg 2was observed. The vBkg 2estimated with the cocktail method is shown as a function of pT (0.5 < pT<13 GeV/c) in the centrality classes 0–10%, 10–20% and 20–40% in figure 7, together with the one obtained with the invariant mass method (0.5 < pT<1.5 GeV/c). The results are consistent within the systematic uncertainties in the three centrality classes. 4 Results The elliptic flow of heavy-flavour decay electrons ve±←−HF 2is computed using eq. (3.1). The systematic uncertainties on ve± 2,RSB and vBkg 2are propagated to ve±←−HF 2. The error propagation for the background subtraction is based on an approximation of a second order error propagation [92,93], where differently from the Gaussian approximation, not only linear effects of the error propagation are considered but also quadratic effects. This is necessary especially in case the non-linearity of the subtraction can not be neglected anymore. The basic concept is that the upper and lower systematic errors are both found by independently varying the uncertainties of the input variables by one sigma up and – 21 – JHEP09(2016)028 )c (GeV/ T p 0 2 4 6 8 10 12 | > 0.9}η∆{EP, | 2 v 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 ± Background e Invariant mass method Cocktail method = 2.76 TeV NN s0-10% Pb-Pb, )c (GeV/ T p 0 2 4 6 8 10 12 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 ALICE | < 0.7y| = 2.76 TeV NN s10-20% Pb-Pb, )c (GeV/ T p 0 2 4 6 8 10 12 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 = 2.76 TeV NN s20-40% Pb-Pb, Figure 7. Background electron v2as a function of pTmeasured with the invariant mass method (full markers) and with the cocktail simulation (empty markers) in the 0–10% (left panel), 10–20% (middle panel) and 20–40% (right panel) centrality classes in Pb–Pb collisions at √sNN = 2.76 TeV. down. The value of ve±←−HF 2is obtained only with the event plane method, because the charged-pion v2measurements with the scalar product method are not available at high pTfor the estimation of vBkg 2using the cocktail method. At low-intermediate pT (pT<6 GeV/c), the ve±←−HF 2extracted with the EP and the SP methods are expected to be compatible within uncertainties, as seen from the measured inclusive electron and charged pion v2. Figure 8shows the elliptic flow of electrons from heavy-flavour hadron decays at midrapidity (|y|<0.7) as a function of pTin Pb–Pb collisions at √sNN = 2.76 TeV for the 0–10%, 10–20% and 20–40% centrality classes. At low pT, the systematic uncertainties are large because of the small signal-to-background ratio. The central value of ve±←−HF 2is slightly increasing with pTup to ∼1.5 GeV/cwhere it reaches a maximum in all centrality classes. A positive v2is observed in all centrality classes, with a maximum significance of 5.9σin the pTinterval 2–2.5 GeV/cin semi-central collisions (20–40%). At higher pT, the measured v2of heavy-flavour decay electrons exhibits a slight decrease as pTincreases, becoming consistent with zero within large uncertainties for pT>4 GeV/c. A positive v2 is also observed in the pTinterval 10–13 GeV/cin the 20–40% centrality class, however the large uncertainties do not allow for a conclusion. Figure 9shows the centrality dependence of the elliptic flow of heavy-flavour decay electrons in two pTintervals (1.25–1.5 GeV/cand 2.5–3 GeV/c). In the interval 1.25 < pT <1.5 GeV/cthe contribution from charm hadron decays is expected to be dominant in the heavy-flavour decay electron sample, whereas in the higher pTinterval the beauty-hadron decays should start to be relevant. In pp collisions at √s= 2.76 TeV, beauty hadron decays are indeed the dominant source of heavy-flavour decay electrons for pT>4.5 GeV/c[94]. A decreasing trend of ve±←−HF 2towards central collisions is observed. This is consistent with a final-state anisotropy in momentum space driven by the initial geometrical anisotropy of the nucleons participating in the collision, which increases towards peripheral collisions. This result indicates that the interactions with the medium constituents transfer to heavy quarks, mainly charm, information on the azimuthal anisotropy of the system, possibly suggesting that charm quarks participate in the collective expansion of the system. – 22 – JHEP09(2016)028 )c (GeV/ T p 0 2 4 6 8 10 12 | > 0.9}η∆{EP, | 2 v 0.1− 0 0.1 0.2 0.3 0.4 0.5 = 2.76 TeV NN s0-10% Pb-Pb, )c (GeV/ T p 0 2 4 6 8 10 12 0.1 0 0.1 0.2 0.3 0.4 0.5 ALICE Heavy-flavour decay electrons | < 0.7y| = 2.76 TeV NN s 10-20% Pb-Pb, )c (GeV/ T p 0 2 4 6 8 10 12 0.1 0 0.1 0.2 0.3 0.4 0.5 = 2.76 TeV NN s20-40% Pb-Pb, Figure 8. Elliptic flow of electrons from heavy-flavour hadron decays in the 0–10% (left panel), 10–20% (middle panel) and 20–40% (right panel) centrality classes in Pb–Pb collisions at √sNN = 2.76 TeV at mid-rapidity as function of pT. The symbols are placed at the centre of the pTinterval whose width is shown by the horizontal error bar. The vertical error bars and open boxes represent the statistical and systematic uncertainties, respectively. The results are obtained with the event plane method and an eta gap |∆η|>0.9. Centrality (%) 0 5 10 15 20 25 30 35 40 | > 0.9}η∆{EP, | 2 v 0 0.05 0.1 0.15 0.2 0.25 c < 1.5 GeV/ T p1.25 < c < 3 GeV/ T p2.5 < ALICE | < 0.7yHeavy-flavour decay electrons, | = 2.76 TeV NN s Pb-Pb, Figure 9. Elliptic flow of electrons from heavy-flavour hadron decays at mid-rapidity as a function of the centrality class in Pb–Pb collisions at √sNN = 2.76 TeV. The symbols are placed at the centre of the centrality interval whose width is shown by the horizontal error bar. The vertical error bars and open boxes represent the statistical and systematic uncertainties, respectively. The elliptic flow of prompt D mesons was measured at mid-rapidity in the centrality classes 0–10%, 10–30% and 30–50% for pT>2 GeV/c[47,48]. The results are similar to those of heavy-flavour decay electrons after taking into account the decay kinematics, which shifts their maximum value of v2to lower pTwith respect to their parent D mesons. At forward rapidity (2.5 < y < 4), the elliptic flow of heavy-flavour decay muons vµ±←−HF 2was measured with various methods in the centrality classes 0–10%, 10–20% and 20–40% [49]. Figure 10 shows the comparison of ve±←−HF 2at mid-rapidity and vµ±←−HF 2at foward rapidity obtained with the two-particle Q-cumulant method with |∆η|>1.7. The observed v2of heavy-flavour decay leptons is similar at midand forward rapidity. – 23 – JHEP09(2016)028 )c (GeV/ T p 0 2 4 6 8 10 12 2 v 0.2− 0.1− 0 0.1 0.2 0.3 0.4 0.5 ALICE = 2.76 TeV NN s 0-10% Pb-Pb, )c (GeV/ T p 0 2 4 6 8 10 12 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 = 2.76 TeV NN s10-20% Pb-Pb, | < 0.7y, || > 0.9}η∆{EP, | 2 v HF, ← ± e < 4 y, 2.5 < | > 1.7}η∆{2, | 2 v HF, ← ± µ )c (GeV/ T p 0 2 4 6 8 10 12 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 = 2.76 TeV NN s20-40% Pb-Pb, Figure 10. Elliptic flow of heavy-flavour decay electrons at mid-rapidity (|y|<0.7) (closed symbols) as a function of pTcompared to the elliptic flow of heavy-flavour decay muons at forward rapidity [49] (2.5 < y < 4) (open symbols) in the 0–10% (left panel), 10–20% (middle panel) and 20–40% (right panel) centrality classes in Pb–Pb collisions at √sNN = 2.76 TeV. The symbols are placed at the centre of the pTinterval whose width is shown by the horizontal error bar. The vertical error bars and open boxes represent the statistical and systematic uncertainties, respectively. 5 Comparison with model calculations Figure 11 shows the comparison of the measured heavy-flavour decay electron elliptic flow in the 20–40% centrality class with theoretical model calculations. BAMPS [95,96] is a partonic transport model based on the Boltzmann approach to multi-parton scatterings. Two versions are presented. In the first one, BAMPS el. [95], heavy quarks interact with the medium via collisional (elastic) processes computed with running strong coupling constant. The binary cross section is scaled with a correction factor in order to mimic the contribution of radiative processes, which are not included. The heavy-flavour decay electron elliptic flow and nuclear modification factor measured at RHIC are used to tune this factor. In the second version, BAMPS el. + rad. [96], radiative processes are included as well. In both approaches, the hadronisation uses a vacuum fragmentation function. TAMU [97] is a heavy-flavour transport model that incorporates energy loss via collisional processes with resonance formation and dissociation in an evolving hydrodynamic medium. The hydrodynamical expansion of the medium is constrained by the measured pTand v2spectra of light-flavour hadrons. The hadronisation contains a component of recombination of heavy quarks with light-flavour quarks from the QGP. Diffusion processes in the hadronic phase are also included. POWLANG [98] is a transport model based on the Langevin transport equation with collisional energy loss in an expanding, deconfined medium. Hadronisation uses a vacuum fragmentation function. A more recent version of POWLANG [99] uses an in-medium hadronisation resulting in a larger v2for the D meson. 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Van Hoorne35 ,113 , M. van Leeuwen58 , T. Vanat85 , P. Vande Vyvre35 , D. Varga137 , A. Vargas2, M. Vargyas124 , R. Varma48 , M. Vasileiou90 , A. Vasiliev81 , A. Vauthier72 , O. V´azquez Doce94 ,36 , V. Vechernin133 , A.M. Veen58 , M. Veldhoen58 , A. Velure18 , E. Vercellin26 , S. Vergara Lim´on2, R. Vernet8, L. Vickovic117 , J. Viinikainen124 , Z. Vilakazi127 , O. Villalobos Baillie102 , A. Villatoro Tello2, A. Vinogradov81 , L. Vinogradov133 , T. Virgili30 , V. Vislavicius33 , Y.P. Viyogi134 , A. Vodopyanov67 , M.A. V¨olkl95 , K. Voloshin59 , S.A. Voloshin136 , G. Volpe32 ,137 , B. von Haller35 , I. Vorobyev94 ,36 , D. Vranic98 ,35 , J. Vrl´akov´a40 , B. Vulpescu71 , B. Wagner18 , J. Wagner98 , H. Wang58 , M. Wang7, D. Watanabe129 , Y. Watanabe128 , M. Weber35 ,113 , S.G. Weber98 , D.F. Weiser95 , J.P. Wessels55 , U. Westerhoff55 , A.M. Whitehead91 , J. Wiechula34 , J. Wikne22 , G. Wilk78 , J. Wilkinson95 , G.A. Willems55 , M.C.S. Williams105 , B. Windelband95 , M. Winn95 , S. Yalcin70 , P. Yang7, S. Yano47 , Z. Yin7, H. Yokoyama129 , I.-K. Yoo97 , J.H. Yoon51 , V. Yurchenko3, A. Zaborowska135 , V. Zaccolo82 , A. Zaman16 , C. Zampolli105 ,35 , H.J.C. Zanoli121 , S. Zaporozhets67 , N. Zardoshti102 , A. Zarochentsev133 , P. Z´avada61 , N. Zaviyalov100 , H. Zbroszczyk135 , I.S. Zgura63 , M. Zhalov87 , H. Zhang18 ,7, X. Zhang75 ,7, Y. Zhang7, C. Zhang58 , Z. Zhang7, C. Zhao22 , N. Zhigareva59 , D. Zhou7, Y. Zhou82 , Z. Zhou18 , H. Zhu18 ,7, J. Zhu7,114 , A. Zichichi27 ,12 , A. Zimmermann95 , M.B. Zimmermann55 ,35 , G. Zinovjev3, M. Zyzak42 iDeceased ii Also at: Georgia State University, Atlanta, Georgia, United States iii Also at: Also at Department of Applied Physics, Aligarh Muslim University, Aligarh, India iv Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia 1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2Benem´erita Universidad Aut´onoma de Puebla, Puebla, Mexico 3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine 4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India 5Budker Institute for Nuclear Physics, Novosibirsk, Russia – 37 – JHEP09(2016)028 6California Polytechnic State University, San Luis Obispo, California, United States 7Central China Normal University, Wuhan, China 8Centre de Calcul de l’IN2P3, Villeurbanne, France 9Centro de Aplicaciones Tecnol´ogicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 10 Centro de Investigaciones Energ´eticas Medioambientales y Tecnol´ogicas (CIEMAT), Madrid, Spain 11 Centro de Investigaci´on y de Estudios Avanzados (CINVESTAV), Mexico City and M´erida, Mexico 12 Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Rome, Italy 13 Chicago State University, Chicago, Illinois, U.S.A. 14 China Institute of Atomic Energy, Beijing, China 15 Commissariat `a l’Energie Atomique, IRFU, Saclay, France 16 COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan 17 Departamento de F´ısica de Part´ıculas and IGFAE, Universidad de Santiago de Compostela, Santiago de Compostela, Spain 18 Department of Physics and Technology, University of Bergen, Bergen, Norway 19 Department of Physics, Aligarh Muslim University, Aligarh, India 20 Department of Physics, Ohio State University, Columbus, Ohio, United States 21 Department of Physics, Sejong University, Seoul, South Korea 22 Department of Physics, University of Oslo, Oslo, Norway 23 Dipartimento di Fisica dell’Universit`a ‘La Sapienza’ and Sezione INFN Rome, Italy 24 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Cagliari, Italy 25 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Trieste, Italy 26 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Turin, Italy 27 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Bologna, Italy 28 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Catania, Italy 29 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Padova, Italy 30 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Universit`a and Gruppo Collegato INFN, Salerno, Italy 31 Dipartimento di Scienze e Innovazione Tecnologica dell’Universit`a del Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy 32 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy 33 Division of Experimental High Energy Physics, University of Lund, Lund, Sweden 34 Eberhard Karls Universit¨at T¨ubingen, T¨ubingen, Germany 35 European Organization for Nuclear Research (CERN), Geneva, Switzerland 36 Excellence Cluster Universe, Technische Universit¨at M¨unchen, Munich, Germany 37 Faculty of Engineering, Bergen University College, Bergen, Norway 38 Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia 39 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 40 Faculty of Science, P.J. ˇ Saf´arik University, Koˇsice, Slovakia 41 Faculty of Technology, Buskerud and Vestfold University College, Vestfold, Norway 42 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany 43 Gangneung-Wonju National University, Gangneung, South Korea 44 Gauhati University, Department of Physics, Guwahati, India 45 Helmholtz-Institut f¨ur Strahlenund Kernphysik, Rheinische Friedrich-Wilhelms-Universit¨at Bonn, Bonn, Germany 46 Helsinki Institute of Physics (HIP), Helsinki, Finland 47 Hiroshima University, Hiroshima, Japan 48 Indian Institute of Technology Bombay (IIT), Mumbai, India 49 Indian Institute of Technology Indore, Indore (IITI), India 50 Indonesian Institute of Sciences, Jakarta, Indonesia 51 Inha University, Incheon, South Korea 52 Institut de Physique Nucl´eaire d’Orsay (IPNO), Universit´e Paris-Sud, CNRS-IN2P3, Orsay, France – 38 – JHEP09(2016)028 53 Institut f¨ur Informatik, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany 54 Institut f¨ur Kernphysik, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany 55 Institut f¨ur Kernphysik, Westf¨alische Wilhelms-Universit¨at M¨unster, M¨unster, Germany 56 Institut Pluridisciplinaire Hubert Curien (IPHC), Universit´e de Strasbourg, CNRS-IN2P3, Strasbourg, France 57 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia 58 Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands 59 Institute for Theoretical and Experimental Physics, Moscow, Russia 60 Institute of Experimental Physics, Slovak Academy of Sciences, Koˇsice, Slovakia 61 Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 62 Institute of Physics, Bhubaneswar, India 63 Institute of Space Science (ISS), Bucharest, Romania 64 Instituto de Ciencias Nucleares, Universidad Nacional Aut´onoma de M´exico, Mexico City, Mexico 65 Instituto de F´ısica, Universidad Nacional Aut´onoma de M´exico, Mexico City, Mexico 66 iThemba LABS, National Research Foundation, Somerset West, South Africa 67 Joint Institute for Nuclear Research (JINR), Dubna, Russia 68 Konkuk University, Seoul, South Korea 69 Korea Institute of Science and Technology Information, Daejeon, South Korea 70 KTO Karatay University, Konya, Turkey 71 Laboratoire de Physique Corpusculaire (LPC), Clermont Universit´e, Universit´e Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France 72 Laboratoire de Physique Subatomique et de Cosmologie, Universit´e Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 73 Laboratori Nazionali di Frascati, INFN, Frascati, Italy 74 Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy 75 Lawrence Berkeley National Laboratory, Berkeley, California, United States 76 Moscow Engineering Physics Institute, Moscow, Russia 77 Nagasaki Institute of Applied Science, Nagasaki, Japan 78 National Centre for Nuclear Studies, Warsaw, Poland 79 National Institute for Physics and Nuclear Engineering, Bucharest, Romania 80 National Institute of Science Education and Research, Bhubaneswar, India 81 National Research Centre Kurchatov Institute, Moscow, Russia 82 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 83 Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands 84 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom 85 Nuclear Physics Institute, Academy of Sciences of the Czech Republic, ˇ Reˇz u Prahy, Czech Republic 86 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States 87 Petersburg Nuclear Physics Institute, Gatchina, Russia 88 Physics Department, Creighton University, Omaha, Nebraska, United States 89 Physics Department, Panjab University, Chandigarh, India 90 Physics Department, University of Athens, Athens, Greece 91 Physics Department, University of Cape Town, Cape Town, South Africa 92 Physics Department, University of Jammu, Jammu, India 93 Physics Department, University of Rajasthan, Jaipur, India 94 Physik Department, Technische Universit¨at M¨unchen, Munich, Germany 95 Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany 96 Purdue University, West Lafayette, Indiana, United States 97 Pusan National University, Pusan, South Korea 98 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum f¨ur Schwerionenforschung, Darmstadt, Germany 99 Rudjer Boˇskovi´c Institute, Zagreb, Croatia 100 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia – 39 – JHEP09(2016)028 101 Saha Institute of Nuclear Physics, Kolkata, India 102 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 103 Secci´on F´ısica, Departamento de Ciencias, Pontificia Universidad Cat´olica del Per´u, Lima, Peru 104 Sezione INFN, Bari, Italy 105 Sezione INFN, Bologna, Italy 106 Sezione INFN, Cagliari, Italy 107 Sezione INFN, Catania, Italy 108 Sezione INFN, Padova, Italy 109 Sezione INFN, Rome, Italy 110 Sezione INFN, Trieste, Italy 111 Sezione INFN, Turin, Italy 112 SSC IHEP of NRC Kurchatov institute, Protvino, Russia 113 Stefan Meyer Institut f¨ur Subatomare Physik (SMI), Vienna, Austria 114 SUBATECH, Ecole des Mines de Nantes, Universit´e de Nantes, CNRS-IN2P3, Nantes, France 115 Suranaree University of Technology, Nakhon Ratchasima, Thailand 116 Technical University of Koˇsice, Koˇsice, Slovakia 117 Technical University of Split FESB, Split, Croatia 118 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 119 The University of Texas at Austin, Physics Department, Austin, Texas, U.S.A. 120 Universidad Aut´onoma de Sinaloa, Culiac´an, Mexico 121 Universidade de S˜ao Paulo (USP), S˜ao Paulo, Brazil 122 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 123 University of Houston, Houston, Texas, United States 124 University of Jyv¨askyl¨a, Jyv¨askyl¨a, Finland 125 University of Liverpool, Liverpool, United Kingdom 126 University of Tennessee, Knoxville, Tennessee, United States 127 University of the Witwatersrand, Johannesburg, South Africa 128 University of Tokyo, Tokyo, Japan 129 University of Tsukuba, Tsukuba, Japan 130 University of Zagreb, Zagreb, Croatia 131 Universit´e de Lyon, Universit´e Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, France 132 Universit`a di Brescia 133 V. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, Russia 134 Variable Energy Cyclotron Centre, Kolkata, India 135 Warsaw University of Technology, Warsaw, Poland 136 Wayne State University, Detroit, Michigan, United States 137 Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, Hungary 138 Yale University, New Haven, Connecticut, United States 139 Yonsei University, Seoul, South Korea 140 Zentrum f¨ur Technologietransfer und Telekommunikation (ZTT), Fachhochschule Worms, Worms, Germany – 40 –