Direct photon elliptic flow in Pb-Pb collisions at √sNN = 2.76 TeV

The elliptic flow of inclusive and direct photons was measured at mid-rapidity in two centrality classes 0–20% and 20–40% in Pb–Pb collisions at sNN = 2.76 TeV by ALICE. Photons were detected with the highly segmented electromagnetic calorimeter PHOS and via conversions in the detector material with the e+e− pairs reconstructed in the central tracking system. The results of the two methods were combined and the direct-photon elliptic flow was extracted in the transverse momentum range 0.9 < pT < 6.2 GeV/c. A comparison to RHIC data shows a similar magnitude of the measured direct-photon elliptic flow. Hydrodynamic and transport model calculations are systematically lower than the data, but are found to be compatible. ∗See Appendix A for the list of collaboration members ar X iv :1 80 5. 04 40 3v 2 [ nu cl -e x] 2 F eb 2 01 9 Direct photon elliptic flow in Pb–Pb ALICE Collaboration


Introduction
Heavy-flavour quarks (charm and beauty) are copiously produced by inelastic partonic scatterings in high-energy protonproton (pp) collisions at the CERN Large Hadron Collider (LHC). Their large masses (m Q ) make it possible to calculate their production cross sections with perturbative quantum chromodynamics (pQCD) [1][2][3]. Hence, experimental measurements of heavyquark production provide an excellent test of pQCD in this energy regime. Flavour conservation allows heavy quarks to be only produced in pairs. Charm hadrons and their decay products reflect the initial angular correlation of the heavy-quark pairs, whereas in the case of decays of beauty hadrons the correlation is weakened due to their large masses. The contribution from the simultaneous semileptonic decays of the corresponding heavy-flavour hadron pairs dominates the dilepton yield in the intermediate mass region (IMR) 1 < m < 3 GeV/c 2 . Hence, dielectron measurements can be used to study charm and beauty production. (RHIC) [26][27][28]. These measurements have the advantage that they probe the full p T range of heavy-quark pairs and contain complementary information about the initial correlation of charm quarks, i.e. the underlying production mechanism, which is not accessible in conventional single heavy-flavour measurements. The measurement of direct photons, i.e. those produced in hard scatterings between incoming partons in hadronic collisions, provides another important test of pQCD. Furthermore, at p T < 3 GeV/c, where the applicability of perturbation theory may be questionable, experimental data of direct-photon production in pp collisions serve as a crucial reference to establish the presence of thermal radiation from the hot and dense medium created in heavy-ion collisions [29][30][31][32]. The measurement of real (massless) direct photons at low p T is challenging because of the large background of hadron decay photons. This background can be largely reduced by measuring the contribution of virtual direct photons, i.e. direct e + e − pairs, to the dielectron invariant-mass spectrum above the π 0 mass [29,30].
Proton-proton collisions in which a large number of charged particles are produced have recently attracted the interest of the heavy-ion community [33,34]. These events exhibit features that are similar to those observed in heavy-ion collisions, e.g. collective effects, such as long-range angular correlations [35][36][37][38][39][40] or enhanced strangeness production [41]. Charged-hadron p T spectra in pp collisions at √ s = 13 TeV show a hardening with increasing multiplicity, an effect that arises naturally from jets [42]. Also, heavy-quark production is found to scale faster than linearly with the charged-particle multiplicity in pp collisions at √ s = 7 TeV [43,44]. This motivates the study of dielectron production in high-multiplicity pp collisions. In the low mass region (m ee < 1 GeV/c 2 ), dielectron measurements provide further insight into possible modifications of the light vector and pseudoscalar meson production via their resonance and/or Dalitz decays, whereas in the IMR they allow for complementary studies of the heavy-flavour production. At LHC energies, the contribution from open charm already dominates the dielectron continuum at m ee ≈ 0.5 GeV/c 2 . Moreover, if a thermalised system were created in such high-multiplicity pp collisions, a signal of thermal (virtual) photons should be present. In this letter, first results of charm and beauty production cross sections at midrapidity in inelastic (INEL) and high-multiplicity (HM) pp collisions at √ s = 13 TeV are reported. The paper is organised as follows: the ALICE apparatus and the data samples used in the analysis are described in Section 2, the data analysis is discussed in Section 3, Section 4 introduces the cocktail of known hadronic sources, and the results are presented and discussed in Section 5.

The ALICE detector and data samples
A detailed description of the ALICE apparatus and its performance can be found in [45][46][47][48]. The detectors used in this analysis are briefly described below.
Trajectories of charged particles are reconstructed in the ALICE central barrel with the Inner Tracking System (ITS) and the Time Projection Chamber (TPC) that reside within a solenoid, which provides a homogeneous magnetic field of 0.5 T along the beam direction. The ITS consists of six cylindrical layers of silicon detectors, with radial distances from the beam axis between 3.9 cm and 43 cm. The two innermost layers are equipped with Silicon Pixel Detectors (SPD), the two intermediate layers are composed of Silicon Drift Detectors, and the two outermost layers are made of Silicon Strip Detectors. The TPC, main tracking device in the ALICE central barrel, is a 5 m long cylindrical gaseous detector extending from 85 cm to 247 cm in radial direction. It provides up to 159 spacial points per track for charged-particle reconstruction and particle identification (PID) through the measurement of the specific ionisation energy loss dE/dx in the gas volume.
The PID is complemented by the Time-Of-Flight (TOF) system located at a radial distance of 3.7 m from the nominal interaction point. It measures the arrival time of particles relative to the event collision time provided by the TOF detector itself or by the T0 detectors, two arrays of Cherenkov counters located at forward rapidities [49].
Collision events are triggered by the V0 detector that comprises two plastic scintillator arrays placed on both sides of the interaction point at pseudorapidities 2.8 < η < 5.1 and −3.7 < η < −1.7.
The V0 is also used to reject background events like beam-gas interactions, collisions with de-bunched protons or with mechanical structures of the beam line.
The data samples used in this letter were recorded with ALICE in 2016 during the LHC pp run at √ s = 13 TeV. For the minimumbias event trigger that is used to define the data sample for the analysis of inelastic pp collisions, coincident signals in both V0 scintillators are required to be synchronous with the beam crossing time defined by the LHC clock. Events with high charged-particle multiplicities are triggered on by additionally requiring the total signal amplitude measured in the V0 detector to exceed a certain threshold. At the analysis level, the 0.036 percentile of inelastic events with the highest V0 multiplicity (V0M) is selected to define the high-multiplicity event class. This value is low enough to avoid inefficiencies due to trigger threshold variations during data taking. Track segments reconstructed in the SPD are extrapolated back to the beam line to define the interaction vertex. Events with multiple vertices identified with the SPD are tagged as pile-up and removed from the analysis [48]. The vertex information may be improved based on the information provided by tracks reconstructed in the ITS and TPC. To assure a uniform detector coverage within |η| < 0.8, the vertex position along the beam direction is restricted to ±10 cm around the nominal interaction point. A total of 455 × 10 6 minimum-bias (MB) pp events and 79.2 × 10 6 high-multiplicity pp events are considered for further analysis, which corresponds to an integrated luminosity of L MB int = 7.87 ± 0.40 nb −1 and L HM int = 2.79 ± 0.15 pb −1 , respectively. The luminosity determination is based on the visible cross section for the V0-based minimum-bias trigger, measured in a van der Meer scan carried out in 2015 [50]. A conservative uncertainty of 5% is assigned to this measurement, to account for possible variations of the cross section between the two data-taking periods.

Data analysis
Electron 1 candidates are selected from charged-particle tracks reconstructed in the ITS and TPC in the kinematic range |η e | < 0.8 and p T, e > 0.2 GeV/c. Basic track quality criteria are applied, e.g. a sufficient number of space points measured in the TPC and ITS as well as a good track fit. The contribution from secondary tracks is reduced by requiring a maximum distance of closest approach (DCA) to the primary vertex in the transverse plane (DCA xy < 1.0 cm) and in the longitudinal direction (DCA z < 3.0 cm). To further suppress the contribution from photon conversions in the detector material, electron candidates are required to have a hit in the first SPD layer and no ITS clusters shared with other reconstructed tracks. The electron identification is based on the complementary information provided by the TPC and TOF. The detector PID response,   Opposite-and same-sign pairs include correlated background, e.g. originating from π 0 decays with two e + e − pairs in the final state (π 0 → γ ( * ) γ ( * ) → e + e − e + e − ), which includes decay channels with real photons and their subsequent conversion in detector material. Such processes lead to opposite and same-sign pairs at equal rate. The background estimate needs to be corrected for the different detector acceptance of opposite and same-sign pairs. This correction factor is determined by dividing the yields of uncorrelated opposite (M +− ) and same-sign pairs (M ±± ) in mixed events: The dielectron signal is then obtained The signal S is shown together with the opposite-sign spectrum N +− and the combinatorial background B in Fig. 1 for minimum-bias and high-multiplicity events. In the mass interval 0.2 < m ee < 3 GeV/c 2 , the signal-tobackground ratio varies in MB events between 0.3 and 0.04 with a minimum around m ee ≈ 0.5 GeV/c 2 and is roughly constant at 0.2 in the IMR [51]. In HM events, the minimum reaches 0.01 and is about 0.08 in the IMR.
Electron-positron pairs from photon conversion in the detector material, contributing to the low mass spectrum below 0.14 GeV/c 2 , are removed by using their distinct orientation relative to the magnetic field [25].
The data are corrected for the reconstruction efficiencies us- . The signal reconstruction efficiencies were studied as a function of m ee and pair transverse momentum p T, ee separately for the different e + e − sources: resonance and Dalitz decays of relevant mesons as well as correlated semileptonic decays of charm and beauty hadrons. The total signal reconstruction efficiency is obtained by weighting the efficiency of each dielectron source by its expected contribution and is found to be about 20% in 0.7 < m ee < 1.2 GeV/c 2 and approaches 30% at lower and higher masses.
Different aspects of the analysis are considered as possible sources of systematic uncertainties, which are summarised in Table 1. The systematic uncertainties due to the track reconstruction are estimated by comparing the efficiency of the ITS-TPC matching, the requirement of a hit in the first SPD layer, and the requirement of no shared ITS clusters in MC simulations and data. The residual disagreements between data and MC add to a 6.5% uncertainty on the single track level, which leads to a 13% uncertainty for pairs. The MC simulations were also checked to reproduce all details of the PID selection within a systematic uncertainty of 2% for e + e − pairs. The purity of the electron sample is estimated to be >93% over the relevant p T range, with a p T -integrated hadron contamination of about 4%. The resulting hadron contamination on the dielectron signal is found to be negligible. For m ee < 0.14 GeV/c 2 , a 2% uncertainty on the conversion rejection was estimated from the yield change when tightening the selection to reject photon conversions. A 2% uncertainty on the signal yield due to the correction factor R is obtained by repeating the event mixing in different event classes, defined by the position of the reconstructed primary vertex and by the charged-particle multiplicity. The efficiency of the minimum-bias trigger to select inelastic events with an e + e − pair in the ALICE acceptance (|η e | < 0.8 and p T, e > 0.2 GeV/c) is estimated to be (99 ± 1)% from the Monash 2013 tune of Pythia 8.
This and the luminosity uncertainty of 5% [50] are global uncertainties, which are not included in the point-to-point uncertainties. No significant variation of systematic uncertainties on mass or p T, ee is observed in the analysis, and the same total uncertainty of 14% is assigned as point-to-point correlated uncertainties on the differential dielectron cross section in inelastic pp collisions.
The analysis of the high-multiplicity data has additional systematic uncertainties. First, no dedicated high-multiplicity MC simulation was performed. In such events the vertex distribution is biased more than in MB events by the asymmetric pseudorapidity coverage of the two V0 detectors. The change of the detector acceptance with vertex position could lead to a difference in the number of reconstructed electrons of up to 3%, which results in an uncertainty of 6% for e + e − pairs. Second, a possible multiplicity dependence of the reconstruction and PID efficiency is covered by an uncertainty of 6% [57]. Added in quadrature, this amounts to a total uncertainty of 15%.

Cocktail of known hadronic sources
The dielectron spectrum measured in pp collisions at A fit of the obtained charged-pion p T -spectrum with a modified Hagedorn function is then taken as proxy for the neutral-pion p T -distribution. The simulated cross section per unit rapidity of the π 0 is dσ /dy| y=0 = 155.2 mb. For the η meson a fit of the measured η/π 0 ratio in pp collisions at The Monash 2013 tune of Pythia 8 describes the ρ/π 0 and ω/π 0 ratios measured in pp collisions at √ s = 2.76 and 7 TeV, respectively [55,56]. Therefore, MC simulations obtained with this tune at √ s = 13 TeV are used to obtain the ρ/π 0 and ω/π 0 ratios. Based on the η/π 0 , ρ/π 0 and ω/π 0 data, the ratios at high p T are 0.5 ± 0.1, 1.0 ± 0.2 and 0.85 ± 0.17, respectively. The η and φ mesons are generated assuming m T scaling, replacing p T with . For the m T scaling, particle yields are normalised at high p T relative to the π 0 yield: 0.40 ± 0.08 for η (from Pythia 6 calculations) and 0.13 ± 0.04 for φ [64]. The detector response, including momentum and angular resolutions, as well as Bremsstrahlung effects obtained from full MC simulations, is applied to the decay electrons as a function of p T, e , η e and the azimuth ϕ e . This results in a mass resolution of approximately 1%.
The following sources of systematic uncertainties were evaluated: the input parameterisations of the measured spectra as a function of p T (π ± , η/π 0 and ω/π 0 ), the branching fractions of all included decay modes, the m T scaling parameters and the resolution smearing. For the high-multiplicity cocktail, the input hadron p T -distributions are adjusted according to the measured modifications of the charged-hadron p T spectra [42]. The uncertainties of the cocktail from light-hadron decays are about ±15%, reaching up to +50% in the region dominated by the η meson due to uncertainties in the extrapolation to low p T . The multiplicity dependence has an uncertainty that varies between about 12% at low p T and 40% at high p T . The Perugia 2011 tune of Pythia 6.4, which includes NLO parton showering processes, is used to estimate the contributions of correlated semileptonic decays of open charm and beauty hadrons [53,65]. As an alternative, the NLO event generator Powheg is also considered [66][67][68][69]. The resulting same-sign spectrum is subtracted from the opposite-sign distribution as in the data analysis. Detector effects are implemented as for the light-hadron cocktail. The spectra are normalised to cross sections at midrapidity that are based on FONLL [1][2][3] extrapolations of the ALICE measurements at 7 TeV [8][9][10]. Following the description in [70], this leads to cross sections per unit rapidity of dσ cc /dy| y=0 = 1296 +172 −162 μb and dσ bb /dy| y=0 = 68 +15

Results
The dielectron cross sections are reported within the ALICE central barrel acceptance |η e | < 0.8 and p T, e > 0.2 GeV/c, i.e. without correction to full phase space. The result, integrated over p T, ee < 6 GeV/c, is shown as a function of m ee in the left panel of Fig. 2. The data are compared with the expectation from the hadronic decay cocktail, using Pythia for the heavy-flavour components, and found to be in agreement within uncertainties. Good agreement between data and cocktail calculations is also found as a function of p T, ee , which is shown for three m ee intervals in the right panel of Fig. 2. Figs. 3 and 4 show the ratios of the dielectron spectra in high-multiplicity over inelastic events as a function of m ee for different p T, ee intervals. To account for the trivial scaling with charged-particle multiplicity, the ratio is scaled by the factor dN ch /dη(HM)/ dN ch /dη(INEL) = 6.27 ± 0.22, where dN ch / dη(HM) = 33.29 ± 0.39 and dN ch /dη(INEL) = 5.31 ± 0.18 are the charged-particle multiplicities in |η ch | < 0.5 measured in highmultiplicity and inelastic pp collisions, respectively [42]. In this ratio, the multiplicity-independent uncertainties cancel and the total  systematic uncertainty reduces to 9%. The ratio is in good agreement with the hadronic decay cocktail calculations over the whole measured m ee and p T, ee range. This is the first measurement sensitive to the production of π 0 , η, ω and φ in high-multiplicity pp collisions. The result confirms the hypothesis that these light mesons have the same multiplicity dependence as a function of m T , which was used in the construction of the high-multiplicity hadron cocktail. From the agreement between data and cocktail in the high-p T range (3 < p T, ee < 6 GeV/c), which is dominated by open beauty, it can be also concluded for the first time that the open beauty production has a multiplicity dependence similar to that of open charm. This puts additional constraints on mechanisms used to describe heavy-flavour production in highmultiplicity pp collisions, such as multiple parton interactions, percolation or hydrodynamic models.
In which leads to a 6% uncertainty on the dielectron-based cross section measurement. Like the statistical and systematic uncertainties, these branching fraction uncertainties are fully correlated between the Pythia and Powheg based results.
The results are consistent with extrapolations from lower energies based on pQCD calculations discussed in the previous section. There is a strong anti-correlation between the fitted charm and beauty cross sections. The sizeable difference in the cross sections between the two MC event generators are comparable to what is observed at √ s = 7 TeV [25]. The different cross sections obtained from fits with Pythia and Powheg simulations are caused by acceptance differences of e + e − pairs from heavy-flavour hadron decays in these two event generators because of different kinematic correlations of the heavy quark pairs, in particular in rapidity. The fraction of e + e − pairs that fall into the ALICE acceptance and the intermediate mass region originating from cc pairs at midrapidity is 14% in Pythia and 10% in Powheg. This points to important differences in the heavy quark production mechanisms between the two generators. It should be stressed that single heavy-flavour measurements appear insensitive to these differences as the cross sections obtained from such measurements agree between Pythia and Powheg based extrapolations [7,11,22]. Therefore, dielectrons provide complementary information on heavy-flavour production that, if properly modelled, should lead to consistent cross sections with Pythia and Powheg. Table 2 also summarises the corresponding cross sections for the high-multiplicity data. In case of Pythia, the measured charm cross section translates into an enhancement of 1.86 ±0.40 (stat.) ± 0.40 (syst.) relative to the charged-particle multiplicity increase. This is consistent with the modelled multiplicity dependence used  This is consistent with the multiplicity dependence observed for open charm, but a scaling with charged-particle multiplicity cannot be excluded. The fraction of real direct photons to inclusive photons can be extracted from the dielectron spectrum at small invariant masses assuming the equivalence between this fraction and the ratio of virtual direct photons to inclusive photons. The data are fitted minimising the χ 2 , in bins of p T, ee , with the sum of the light-flavour cocktail ( f LF (m ee )), open heavy-flavour contribution ( f HF (m ee )) and a virtual direct photon component ( f direct (m ee )), whose shape is described by the Kroll-Wada equation [77,78] in the quasi-real virtual photon regime (p T, ee m ee ).  tion r is then extracted by fitting the data in the mass interval 0.14 < m ee < 0.32 GeV/c 2 , i.e. above the π 0 mass to suppress the most dominant hadron background, with the following expression: No significant direct photon contribution is observed in neither the inelastic nor the high-multiplicity events [51]. Upper limits at 90% confidence level (C.L.) are extracted with the Feldman-Cousins method [79] and summarised in Table 3 together with predictions from perturbative QCD calculations for inelastic events [80]. The current uncertainties prevent any conclusions on the scaling of direct-photon production with charged-particle multiplicity.

Summary and conclusion
We have presented the first measurement of dielectron production at midrapidity (| y e | < 0.

Acknowledgements
The ALICE Collaboration would like to thank Werner Vogelsang for providing the NLO pQCD calculations for direct photon production.
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 out-