Azimuthal Anisotropy of Heavy-Flavor Decay Electrons in p-Pb Collisions at root s(NN)=5.02 TeV

Angular correlations between heavy-flavor decay electrons and charged particles at midrapidity ( j η j < 0 . 8 ) are measured in p -Pb collisions at ﬃﬃﬃﬃﬃﬃﬃﬃ s NN p ¼ 5 . 02 TeV. The analysis is carried out for the 0% – 20% (high) and 60% – 100% (low) multiplicity ranges. The jet contribution in the correlation distribution from high-multiplicity events is removed by subtracting the distribution from low-multiplicity events. An azimuthal modulation remains after removing the jet contribution, similar to previous observations in two-particle angular correlation measurements for light-flavor hadrons. A Fourier decomposition of the modulation results in a positive second-order coefficient ( v 2 ) for heavy-flavor decay electrons in the transverse momentum interval 1 . 5 < p T < 4 GeV =c in high-multiplicity events, with a significance larger than 5 σ . The results are compared with those of charged particles at midrapidity and those of inclusive muons at forward rapidity. The v 2 measurement of open heavy-flavor particles at midrapidity in small collision systems could provide crucial information to help interpret the anisotropies observed in such systems.

Angular correlations between heavy-flavor decay electrons and charged particles at midrapidity (jηj < 0.8) are measured in p-Pb collisions at ffiffiffiffiffiffiffiffi s NN p ¼ 5.02 TeV. The analysis is carried out for the 0%-20% (high) and 60%-100% (low) multiplicity ranges. The jet contribution in the correlation distribution from high-multiplicity events is removed by subtracting the distribution from low-multiplicity events. An azimuthal modulation remains after removing the jet contribution, similar to previous observations in two-particle angular correlation measurements for light-flavor hadrons. A Fourier decomposition of the modulation results in a positive second-order coefficient (v 2 ) for heavy-flavor decay electrons in the transverse momentum interval 1.5 < p T < 4 GeV=c in high-multiplicity events, with a significance larger than 5σ. The results are compared with those of charged particles at midrapidity and those of inclusive muons at forward rapidity. The v 2 measurement of open heavy-flavor particles at midrapidity in small collision systems could provide crucial information to help interpret the anisotropies observed in such systems. DOI: 10.1103/PhysRevLett.122.072301 Two-particle angular correlations are a powerful tool to study the dynamical evolution of the system created in ultrarelativistic collisions of protons or nuclei. The differences in the azimuthal angle (Δφ) and in pseudorapidity (Δη) between a reference ("trigger") particle and other particles produced in the event are considered. The typical shape of the correlation distribution features a nearside peak at ðΔφ; ΔηÞ ∼ ð0; 0Þ, originating from cases in which the trigger particle is produced in a jet, and an awayside structure centered at Δφ ∼ π and extending over a wide pseudorapidity range, due to the recoil jet [1]. In nucleusnucleus collisions, the correlation distribution also exhibits pronounced structures on the near and away sides extending over a large Δη region, commonly referred to as "ridges" [2]. They can be quantified by the V nΔ coefficient of a Fourier decomposition of the Δφ distribution, which is performed after removing the jet contribution. These coefficients can be factorized into single-particle coefficients v n related to the azimuthal distribution of the particles with respect to the nth-order symmetry planes [3]. In noncentral nucleus-nucleus collisions, the dominant coefficient is that of the second-order harmonic, referred to as elliptic flow (v 2 ), and its value is used to characterize the collective motion of the system. The measurements are well described by models invoking a hydrodynamic expansion of the hot and dense medium produced in the collision. This translates the initial-state spatial anisotropy, due to the asymmetry of the nuclear overlap region, into a momentum anisotropy of the particles emerging from the medium [4]. This collective motion is one of the important features of the quark-gluon plasma (QGP) produced in such collisions.
Surprisingly, the presence of similar long-range ridge structures and a positive v 2 coefficient were also observed for light-flavor hadrons in high-multiplicity proton-lead (p-Pb) collisions by the ALICE [5], ATLAS [6],and CMS [7] Collaborations at the LHC. The pattern of the v 2 coefficient as a function of the particle mass and transverse momentum is similar in p-Pb and Pb-Pb collisions [8,9]. The PHENIX and STAR Collaborations at RHIC also measured a positive v 2 coefficient for charged hadrons in high-multiplicity d-Au and 3 He-Au collisions [10][11][12]. A near-side structure extended over a large Δη range was also reported for highmultiplicity proton-proton (pp) collisions by the CMS [13] and ATLAS [6] Collaborations. The interpretation of a positive v 2 in these small collision systems is currently highly debated [14]. One possible interpretation is based on collective effects induced by a hydrodynamical evolution of the particles produced in the collision [15,16]. Other approaches include mechanisms involving initial-state effects, such as gluon saturation within the color-glass condensate effective field theory [17,18], or final-state color-charge exchanges [19,20].
Because of their large masses, heavy quarks are produced in hard scattering processes during the early stages of hadronic collisions [21]. In heavy-ion collisions, the elliptic flow of charm mesons [22][23][24][25] and heavy-flavor decay leptons [26][27][28][29][30] was found to have similar magnitude to that of charged particles [31], dominated by light-flavor hadrons. A search for a nonzero v 2 in the correlation pattern of heavy-flavor particles in high-multiplicity p-Pb collisions could provide further insight on the initial-and final-state origin of the anisotropies in this collision system, helping in constraining the models that describe the ridge structures. The production mechanisms of heavy quarks, involving a large squared four-momentum transfer, are also different from those of light-flavor quarks. This creates the possibility to investigate whether the onset of the anisotropy of the particle azimuthal distribution is affected by the details of hard scattering and fragmentation processes.
In this Letter, we present the measurement of v 2 for open heavy-flavor particles at midrapidity in high-multiplicity p-Pb collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV via azimuthal correlations of electrons from charm and beauty hadron decays, and charged particles. This result complements our previous studies of hidden charm particles based on the measurement of the correlations between J=ψ mesons at forward rapidity and charged particles at midrapidity in high-multiplicity p-Pb collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV and 8.16 TeV, which found evidences for a positive v 2 of J=ψ mesons [32]. A positive v 2 of muons at forward and backward rapidity, which are predominantly produced by heavy-flavor decays for transverse momentum ðp T Þ greater than 2 GeV=c, was also measured in high-multiplicity p-Pb collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 5. The data sample used for the analysis was collected by the ALICE experiment [37,38] in 2016 during the LHC p-Pb run at ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV. The center-of-mass reference frame of the nucleon-nucleon collision was shifted in rapidity by 0.465 units in the proton-going direction with respect to the laboratory frame. The events were recorded using a minimum-bias trigger, which required coincident signals in the two scintillator arrays of the V0 detector, covering the full azimuthal angle in the pseudorapidity (η) ranges 2.8 < η < 5.1 (V0-A) and −3.7 < η < −1.7 (V0-C). Together with the V0 information, signals from the two Zero-Degree Calorimeters were used to reject the beam-induced background. Only events with a primary vertex reconstructed within AE10 cm from the center of the detector along the beam axis were accepted. About 6 × 10 8 events, corresponding to an integrated luminosity of L int ¼ 295 AE 11 μb −1 , were obtained after these selections. Only events in high-(0%-20%) and low-multiplicity (60%-100%) classes, evaluated using the signal amplitude in the V0-A detector [39], were considered.
Electrons with transverse momentum (p e T ) in the interval 1.5 < p e T < 6 GeV=c and jηj < 0.8 (corresponding to −1.26 < y e cms < 0.34, where y e cms is the electron rapidity in the center-of-mass reference frame) were selected using similar criteria as discussed in Ref. [40]. Charged tracks were reconstructed using the Inner Tracking System (ITS), comprising six layers of silicon detectors with the innermost two composed of pixel detectors, and the Time Projection Chamber (TPC), a gaseous detector and the main tracking device. Tracks were required to have hits on both pixel layers of the ITS and a distance of closest approach to the primary vertex of less than 1 cm along the beam axis and 0.25 cm in the transverse plane, to reduce the contamination of electrons from photon conversions and particle weak decays [41]. The particle identification employed a selection on the specific ionization energy loss inside the TPC of −1 < n TPC σ < 3, where n σ is the difference between the measured and expected detector response signals for electrons normalized to the response resolution. A selection (−3 < n TOF σ < 3) was also applied using the Time of Flight (TOF) detector to further separate hadrons and electrons. The electron reconstruction efficiency was calculated using Monte Carlo simulations of events containing cc and bb pairs generated with PYTHIA 6.4.21 [42] and the Perugia-2011 tune [43], and an underlying p-Pb collision generated using HIJING 1.36 [44]. The generated particles were propagated through the detector using the GEANT3 transport package [45]. With the selections described above, the resulting electron reconstruction efficiency is about 28% (32%) at p e T ¼ 1.5 GeV=c (6 GeV=c). The contamination from charged hadrons, estimated as described in Ref. [46], amounts to about 1% (10%) for 1.5 < p e T < 4 GeV=c (4 < p e T < 6 GeV=c). The selected electrons are composed of signal heavyflavor decay electrons (HFe), originating from semileptonic decays of open heavy-flavor hadrons, and background electrons. The main background sources are photon conversions (γ → e þ e − ) in the beam vacuum tube, and in the material of the innermost ITS layers, and Dalitz decays of neutral mesons (π 0 → γe þ e − and η → γe þ e − ), defined as non-heavy-flavor decay electrons (NonHFe) hereafter. Background contributions from other Dalitz decays, or decays of kaons and J=ψ mesons, are negligible in the p T range studied in the analysis [40] and were not considered. To estimate the background contribution, dielectron pairs were defined by pairing the selected electrons with opposite-charge electron partners to form unlike-signed pairs (ULS) and calculating their invariant mass (M e þ e − ). Partner electrons were selected, applying similar but looser track quality and particle identification criteria than those used for selecting signal electrons. The dielectron pairs from NonHFe sources have a small invariant mass, while heavy-flavor decay electrons can form ULS pairs mainly through random combinations with other electrons, resulting in a continuous invariant-mass distribution. The combinatorial contribution was estimated from the invariant-mass distribution of like-signed (LS) electron pairs. The NonHFe background contribution was then evaluated by subtracting the LS distribution from the ULS distribution in the invariant-mass region M e þ e − < 140 MeV=c 2 . More details on the procedure can be found in Refs. [40,47]. The efficiency (ε NonHFe ) of finding the partner electron to identify non-heavy-flavor decay electrons was calculated with the aforementioned Monte Carlo simulations, and is about 60% for 1.5 < p e T < 2 GeV=c, rising to 76% for 4 < p e T < 6 GeV=c. The number of heavy-flavor decay electrons (N HFe ) can be expressed as where N ULSe and N LSe are the number of electrons which form unlike-sign and like-sign pairs, respectively, with M e þ e − < 140 MeV=c 2 , and N e is the number of selected electrons.
The two-particle correlation distributions between electrons (trigger) and charged (associated) particles were obtained for three different p e T intervals (1.5 < p e T < 2 GeV=c, 2 < p e T < 4 GeV=c, and 4 < p e T < 6 GeV=c). Associated charged particles with 0.3 < p ch T < 2 GeV=c and jηj < 0.8 were selected with similar criteria as used for electrons, apart from requiring a hit in at least one, instead of both, of the two pixel layers and not applying any particle identification. The single-track reconstruction efficiency and the contamination from secondary particles [41] were estimated using Monte Carlo simulations of p-Pb collisions produced with the DPMJET 3.0 event generator [48] and GEANT3 [45] for the particle transport. Both were found to be independent of the event multiplicity. With the selections described above, the tracking efficiency varies from 75% to 85% depending on track momentum and primary vertex position, and the contamination of secondary particles varies from 3% to 5.5% with decreasing p ch T . The ðΔφ; ΔηÞ correlation distribution between heavyflavor decay electrons and charged particles is obtained with the equation where S corresponds to d 2 N e-ch ðΔη; ΔφÞ=dΔηdΔφ. The correlation distributions for all trigger electrons and for non-heavy-flavor decay trigger electrons are denoted as S e and S NonHFe , respectively. The hadron contamination in S e is statistically removed by subtracting a scaled dihadron correlation distribution. The S NonHFe distribution is evaluated from its two contributions S ID NonHFe and S nonID NonHFe . The former corresponds to correlations from background electron triggers with an identified electron partner, and the latter to the expected contribution from background trigger electrons without an identified partner. The identified background distribution, S ID NonHFe , is evaluated using correlations of trigger electrons paired with unlike-sign and like-sign electrons, with a similar procedure as that used to evaluate N NonHFe [see Eq. (1)]. The nonidentified distribution, S nonID NonHFe , is estimated assuming that both identified and nonidentified NonHFe triggers have the same correlation distribution, apart from reconstructed partner electrons used to calculate M e þ e − , which are removed from S ID NonHFe to obtain S IDÃ NonHFe . The correlation distribution for heavy-flavor decay electrons was corrected for the electron and charged particle reconstruction efficiencies and for the secondary particle contamination. It was also corrected for the limited two-particle acceptance and detector inhomogeneities using the event mixing technique [8]. The mixed-event correlation distribution was obtained by combining electrons in an event with charged particles from other events with similar multiplicity and primary vertex position. The correlation distribution for heavy-flavor decay electrons was divided by the number of heavy-flavor decay trigger electrons [N HFe , from Eq. (1)] corrected by their reconstruction efficiency.
The two-dimensional correlation distribution was projected onto Δφ for jΔηj < 1.2 and divided by the width of the selected Δη interval. A baseline term, constant in Δφ, was subtracted from the correlation distributions. Its values, reported in Table I, were calculated as the weighted average of the three lowest points of the distribution, following the "zero yield at minimum" approach [49]. The resulting correlation distributions in the two considered multiplicity classes (0%-20% and 60%-100%) are shown in Fig. 1 for 2 < p e T < 4 GeV=c. An enhancement of the near-and away-side peaks is present in high-multiplicity collisions. To study this feature, the baseline-subtracted correlation distribution obtained in low-multiplicity events was subtracted from the correlation distribution measured in highmultiplicity events, as described in Ref. [5]. This removes the jet-induced correlation peaks, assuming that they are the same in low-and high-multiplicity events. The correlation distribution was restricted to the ð0; πÞ range by reflecting the symmetrical points. The resulting distribution, shown in Fig. 2, was fitted with the Fourier decomposition of Eq. (3). An azimuthal anisotropy, dominated by the second-order term V HFe-ch 2Δ , was found.
1 Δη PHYSICAL REVIEW LETTERS 122, 072301 (2019) 072301-3 The measured V HFe-ch 2Δ in high-multiplicity events does not exclude the possibility of having a V HFe-ch 2Δ contribution in the low-multiplicity events, as described in Ref. [6].
The systematic uncertainties on the azimuthal correlation distribution can originate from (i) potential biases in the procedure employed to select electron candidates and estimate the hadron contamination, (ii) removal of the background electrons not produced in heavy-flavor hadron decays, and (iii) choice of the associated particle selection. A systematic uncertainty related to the electron reconstruction efficiency arises from imprecisions in the description of the detector response. It was studied by varying the electron selection in the ITS and TPC. The uncertainty affecting the removal of the hadron contamination was estimated by varying the particle identification criteria in the TPC (n TPC σ ). A total uncertainty of less than 0.5% was estimated from these sources. The uncertainty related to the efficiency of finding the partner electron and to the stability of the S NonHFe distribution was studied by varying the selection for partner tracks and pair invariant mass, resulting in an uncertainty of less than 0.5%. The uncertainty on the associated track reconstruction efficiency, obtained by varying the associated track selection criteria and by comparing the probabilities of track prolongation from TPC to ITS in data and simulations, was estimated to be 3% [50]. A systematic effect due to the contamination of the associated particles by secondaries comes from residual discrepancy between Monte Carlo simulations and data in the relative abundances of particle species and was studied by varying the selection on the distance of closest approach to the primary vertex. It was quantified to be 1% (correlated in Δφ), with an additional 1% (correlated) for jΔφj < 1. Combining the uncertainties from all the above sources results in a 3% total systematic uncertainty (correlated in Δφ) and an additional 1% (also correlated) for jΔφj < 1.
The systematic uncertainties from the above mentioned sources are also present in the V HFe-ch

2Δ
. The uncertainty related to the electron selection and the identification of non-heavy-flavor decay electrons on V HFe-ch

2Δ
were quantified to be about 2%-3% and 5%, respectively. The contamination of the associated particles by secondaries leads to a 3% systematic uncertainty. In order to test whether the observed Δφ modulation and the nonzero V HFe-ch 2Δ could originate from a residual jet contribution, due to possible differences between the jet structures in low-and high-multiplicity collisions, the Δη integration region was modified by excluding central intervals of jΔηj < Δη gap , varying Δη gap from 0.2 to 0.6. The observed variation on V HFe-ch 2Δ was 11%-15%, depending on the electron p T interval, and was taken as the systematic uncertainty from the jet subtraction. The stability of the (3)] to the azimuthal correlation distribution between heavy-flavor decay electrons and charged particles, for high-multiplicity p-Pb collisions after subtracting the jet contribution based on low-multiplicity collisions. The distribution is shown for 2 < p e T < 4 GeV=c and 0.3 < p ch T < 2 GeV=c. The figure shows only statistical uncertainty. and baselines in high-(b HM ) and low-multiplicity (b LM ) collisions.   Table I. The measured V HFe-ch 2Δ is larger than zero with a significance of 4.6σ for the 2 < p e T < 4 GeV=c range. The significance for V HFe-ch 2Δ > 0 in the interval 1.5 < p e T < 4 GeV=c, considering statistical and systematic uncertainties, is about 6σ.
Assuming its factorization in single-particle v 2 coefficients [8], V HFe-ch 2Δ can be expressed as the product of the second-order Fourier coefficients of the heavy-flavor decay electron (v HFe 2 ) and charged particle (v ch 2 ) azimuthal distributions, hence v HFe The v ch 2 value in the range 0.3 < p ch T < 2 GeV=c was obtained from the weighted average of the values measured in smaller p ch T ranges in Ref.
[8], providing v ch 2 ¼ 0.0594AE0.0010ðstatÞAE 0.0059ðsystÞ. The obtained v HFe 2 values are reported in Fig. 3 and compared to v 2 of charged particles, dominated by light-flavor hadrons, and to inclusive muons at large rapidity, mostly originating from heavy-flavor hadron decays for p μ T > 2 GeV=c. The heavy-flavor decay electron v 2 is lower than v ch 2 , though the uncertainties are large, and the p T interval of electron parents (heavy-flavor hadrons) is considerably broader than the range addressed in the light-flavor hadron measurement. The v 2 values for heavy-flavor electrons and inclusive muons are similar, although a direct comparison is not straightforward, given the different rapidities and the contamination in the muon sample for p μ T < 2 GeV=c. The v HFe 2 in p-Pb collisions has similar magnitude to that measured in noncentral Pb-Pb collisions at ffiffiffiffiffiffiffi ffi s NN p ¼ 2.76 TeV [29]. The significance for v HFe 2 > 0 is 5.1σ for 1.5 < p e T < 4 GeV=c, providing very strong indications for the presence of long-range anisotropies for heavy-flavor particles in high-multiplicity p-Pb collisions.
In summary, we report the measurement of v 2 for open heavy-flavor particles at midrapidity in high-multiplicity p-Pb collisions. The analysis was carried out via a Fourier decomposition of the azimuthal correlation distribution between heavy-flavor decay electrons and charged particles. After removing the jet contribution and fitting the high-multiplicity correlation distributions, a V 2Δ -like modulation was obtained, qualitatively similar to the one observed for charged particles [5]. The measured heavyflavor decay electron v 2 is positive with a significance of more than 5σ in the 1.5 < p e T < 4 GeV=c range. Its values are possibly lower than charged particle v 2 [5], and similar to inclusive muon v 2 at large rapidity [33]. Complementing previous results for light-flavor hadrons [5], this measurement provides new information on the behavior of heavyflavor hadrons to understand the azimuthal anisotropies observed in small collision systems.
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 provided by all Grid Centres and the Worldwide LHC Computing Grid  [1] X.-N. Wang, Studying mini-jets via the p T dependence of the two particle correlation in azimuthal angle φ, Phys. Rev. D 47, 2754(1993. [15] K. Werner, I. Karpenko, and T. Pierog, The "Ridge" in Proton-Proton Scattering at 7 TeV, Phys. Rev. Lett. 106, 122004 (2011