Study of J/ψ azimuthal anisotropy at forward rapidity in Pb-Pb collisions at √sNN = 5.02 TeV

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Study of J/ψ azimuthal anisotropy at forward rapidity in Pb-Pb collisions at √sNN = 5.02 TeV © Authors, 2019 Published version ALICE Collaboration ALICE Collaboration. (2019). Study of J/ψ azimuthal anisotropy at forward rapidity in Pb-Pb collisions at √sNN = 5.02 TeV. Journal of High Energy Physics, 2019(12), Article 012. https://doi.org/10.1007/jhep02(2019)012 2019 JHEP02(2019)012 Published for SISSA by Springer Received:December 16, 2018 Revised:January 18, 2019 Accepted:January 20, 2019 Published:February 4, 2019 Study of J/ψazimuthal anisotropy at forward rapidity in Pb-Pb collisions at √sNN = 5.02 TeV The ALICE collaboration E-mail: [email protected] Abstract: The second (v2) and third (v3) flow harmonic coefficients of J/ψmesons are measured at forward rapidity (2.5< y < 4.0) in Pb-Pb collisions at √sNN = 5.02 TeV with the ALICE detector at the LHC. Results are obtained with the scalar product method and reported as a function of transverse momentum, pT, for various collision centralities. A positive value of J/ψ v3is observed with 3.7σsignificance. The measurements, compared to those of prompt D0mesons and charged particles at mid-rapidity, indicate an ordering with vn(J/ψ)< vn(D0)< vn(h±) (n = 2, 3) at low and intermediate pTup to 6 GeV/c and a convergence with v2(J/ψ)≈v2(D0)≈v2(h±) at high pTabove 6–8 GeV/c. In semicentral collisions (5–40% and 10–50% centrality intervals) at intermediate pTbetween 2 and 6 GeV/c, the ratio v3/v2of J/ψmesons is found to be significantly lower (4.6σ) with respect to that of charged particles. In addition, the comparison to the prompt D0-meson ratio in the same pTinterval suggests an ordering similar to that of the v2and v3coefficients. The J/ψ v2coefficient is further studied using the Event Shape Engineering technique. The obtained results are found to be compatible with the expected variations of the eccentricity of the initial-state geometry. Keywords: Hadron-Hadron scattering (experiments) ArXiv ePrint: 1811.12727 Open Access, Copyright CERN, for the benefit of the ALICE Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP02(2019)012 JHEP02(2019)012 Contents 1 Introduction 1 2 Experimental setup and data sample 3 3 Analysis 4 4 Systematic uncertainties 9 5 Results 11 6 Conclusions 14 A Flow coefficients of combinatorial background 16 The ALICE collaboration 23 1 Introduction The study of collisions of ultra-relativistic heavy ions aims to characterize the QuarkGluon Plasma (QGP), a strongly coupled state of matter comprising of deconfined quarks and gluons. One of the main features of heavy-ion collisions is the anisotropic particle flow [1,2]. It arises from initial collision geometry anisotropies being converted by the pressure gradients of the QGP medium to final-state particle momentum anisotropies. The anisotropic flow is described by the coefficients vnof a Fourier series decomposition of the azimuthal distribution of the produced particles [3] dN dϕ∝1+2 ∞ X n=1 vncos[n(ϕ−Ψn)],(1.1) where ϕis the azimuthal angle of the particle and Ψnis the n-th harmonic symmetry plane angle. The dominant second-order flow coefficient (v2) is called elliptic flow and mostly originates from the almond-shaped overlap area between the colliding nuclei in non-central collisions. The third-order flow coefficient (v3) is named triangular flow and is generated by fluctuations in the initial distribution of nucleons in the overlap region [4–8]. Heavy quarks, in particular their bound quark-antiquark states known as quarkonia, are important probes of the QGP. Heavy-quark pairs are created prior to the formation of the QGP through hard parton collisions and thus experience the full evolution of the system. Measurements of the J/ψnuclear modification factor (RAA) as a function of centrality in Pb-Pb collisions at the LHC [9–11] are reproduced by transport [12–14] and statistical hadronization [15,16] models including partial to full J/ψ(re)generation by – 1 – JHEP02(2019)012 recombination of thermalized charm quarks. Such (re)generation component is dominant at low transverse momentum (pT) as shown by the comparison [11,17] of the RAA as function of pTwith transport model calculations. In the case of the statistical hadronization model, the produced J/ψreflects the dynamics of the charm quarks at the QGP phase boundary. The measured pTspectra seem to support this idea [18]. Measurements of the azimuthal anisotropies of J/ψproduction in high-energy heavy-ion collisions can bring new important insights on the charm quark dynamics. A recent measurement of the elliptic flow of J/ψat forward rapidity in central and semicentral Pb-Pb collisions at the center of mass energy per nucleon pair of √sNN = 5.02 TeV indicates a significant positive v2coefficient [19]. This result is compatible with the hypothesis of J/ψproduction via recombination of thermalized c and ¯c quarks from the QGP medium predominantly at low pT, but the magnitude and the transverse momentum dependence of the v2coefficient differ significantly from theoretical calculations [12–14]. Moreover, the v2coefficient is found to be quite significant at high pT, in contrast with the expectations of small azimuthal asymmetry originating mainly from path-length dependent J/ψdissociation in the medium. Furthermore, a positive J/ψ v2coefficient at intermediate and high pThas been observed in p-Pb collisions [20,21], in which neither a significant contribution from charm-quark recombination nor sizable path-length effects are expected [22]. Recent measurements of D-meson azimuthal asymmetry in Pb-Pb collisions are interpreted as collective behavior of the charm quarks at low pTand path-length dependent charm-quark energy loss at high pT[23,24]. Hydrodynamic calculations [25] show that vn≈κnnfor n = 2 and 3, where nis the eccentricity coefficient of the initial-state collision geometry. The parameters κnencode the response of the QGP medium and depend on the particle type and mass as well as its transverse momentum. At low pT, the flow coefficients of light-flavoured particles increase with increasing pT[26,27]. This increase of vncoefficients as a function of pTdepends of the particle mass and can be attributed to the radial expansion of the QGP medium. At 3–4 GeV/c, the flow coefficients reach a maximum. The position of the maximum, divided by the number of constituent quarks nq, does not dependent strongly on the particle mass as predicted by coalescence models [28]. Furthermore, the vnvalues at the maximum, divided by nq, are similar for all measured light-flavoured particles, with deviations of up to ±20% between mesons and baryons [27]. At high pTabove 6–8 GeV/c, the observed azimuthal anisotropy of the final-state particles is believed to come from path-length dependent parton energy loss inside the QGP. Calculations [29] show that the corresponding v2and v3coefficients exhibit approximately linear dependence on 2and 3, respectively. Nevertheless, the correlation between the flow coefficients and the initial-state eccentricities is weaker with respect to the hydrodynamic case, especially between v3and 3. Interestingly, the particle-mass dependence of v2and v3appears to be strongly reduced in the ratio v3/v2in semi-central collisions for light-flavored particles [27]. Whether the above considerations also hold for heavy quarks and quarkonia is an open question whose answer could help to understand the origin of charm quark azimuthal anisotropies and characterize their interactions with the flowing medium. – 2 – JHEP02(2019)012 In the present analysis, the J/ψ v2and v3coefficients as well as the ratio v3/v2as a function of the transverse momentum and the collision centrality are measured. Wherever possible, the data are compared to existing mid-rapidity charged-particle (predominantly π±) and prompt D0-meson results. In addition, the dependence of the J/ψ v2coefficient on the initial-state conditions is studied with the Event Shape Engineering (ESE) technique [30]. Fluctuations in the initial-state energy density distribution lead to event-byevent variations of the flow observed at a given centrality [31]. The ESE technique consists of selecting events with the same centrality but different flow and therefore initial-state geometry eccentricity [32,33]. Recently, the ESE technique has been applied to the measurement of mid-rapidity D-meson production in Pb-Pb collisions at √sNN = 5.02 TeV [34]. The obtained results indicate a correlation between the D-meson azimuthal anisotropy and the flow of light-flavoured particles. The J/ψmesons are reconstructed at forward rapidity (2.5< y < 4.0) via their µ+µ− decay channel. The measured J/ψmesons originate from both prompt J/ψ(direct and from decays of higher-mass charmonium states) and non-prompt J/ψ(feed down from b-hadron decays) production. This letter is organized as follows. A brief description of the ALICE apparatus and the data sample used is given in section 2. Section 3outlines the employed analysis technique. The evaluation of the systematic uncertainties is discussed in section 4, while the results are reported in section 5. Finally, conclusions are presented in section 6. 2 Experimental setup and data sample The ALICE detectors essential for the present analysis are briefly described below. A full overview of the ALICE apparatus and its performance can be found in refs. [35,36]. The muon spectrometer, which covers the pseudorapidity range -4 < η < -2.5, is used to reconstruct muon tracks. The spectrometer consists of a front absorber followed by five tracking stations. The third station is placed inside a dipole magnet. The tracking stations are complemented by two trigger stations located downstream behind an iron wall. The Silicon Pixel Detector (SPD) [37] is employed to reconstruct the position of the primary vertex and to determine the flow direction. The SPD consists of two cylindrical layers covering |η|<2.0 and |η|<1.4, respectively. It is placed in the central barrel of ALICE. The central barrel is operated inside a solenoidal magnetic field parallel to the beam line. The SPD is also used to reconstruct the so-called tracklets, track segments formed by the clusters in the two SPD layers and the primary vertex [38]. The V0 detector [39] consists of two arrays of 32 scintillator counters each, covering 2.8 < η < 5.1 (V0A) and -3.7 < η < -1.7 (V0C), respectively. It provides the minimum-bias (MB) trigger and is used for event selection and determination of collision centrality [40]. In addition, two tungsten-quartz neutron Zero Degree Calorimeters (ZDCs), installed 112.5 meters from the interaction point along the beam line on each side, are used for event selection. The present analysis is based on the data sample of Pb-Pb collisions collected by ALICE in 2015 at √sNN = 5.02 TeV. The trigger required coincidence of MB and dimuon triggers. The MB trigger was provided by the V0 detector requesting signals in both V0A and – 3 – JHEP02(2019)012 V0C arrays. The dimuon unlike-sign trigger required at least a pair of opposite-sign track segments in the muon trigger stations. The transverse momentum threshold of the trigger algorithm was set such that the efficiency for muon tracks with pT= 1 GeV/cis 50%. The sample of single muons or like-sign dimuons were collected using the same trigger algorithm, but requiring at least one track segment or at least a pair of like-sign track segments, respectively. The integrated luminosity of the analyzed data sample is about 225 µb−1. The beam-induced background is filtered out offline by applying a selection based on the V0 and the ZDC timing information [41]. The interaction pile-up is removed by exploiting the correlations between the number of clusters in the SPD, the number of reconstructed SPD tracklets and the total signal in the V0A and V0C detectors. The primary vertex position is required to be within ±10 cm from the nominal interaction point along the beam direction. The data are split in intervals of collision centrality, which is obtained based on the total signal in the V0A and V0C detectors [40]. The muon selection is identical to that used in ref. [20]. The dimuons are reconstructed in the acceptance of the muon spectrometer (2.5< y < 4.0) and are required to have a transverse momentum between 0 and 12 GeV/c. 3 Analysis The flow coefficients vnof the selected dimuons are measured using the scalar product (SP) method [2,42], in which they are calculated from the expression vn{SP}=hhunQSPD∗ nii Rn , Rn=shQSPD nQV0A∗ nihQSPD nQV0C∗ ni hQV0A nQV0C∗ ni, (3.1) where un= exp(inϕ) is the unit flow vector of the dimuon, QSPD n,QV0A nand QV0C nare the event flow vectors measured in the SPD, V0A and V0C detectors, respectively, and nis the harmonic number. The brackets h···idenote an average over all events, the double brackets hh···ii an average over all particles in all events, and ∗the complex conjugate. The SPD event flow vector QSPD nis calculated from the azimuthal distribution of the reconstructed SPD tracklets. The V0A and V0C event flow vectors QV0A nand QV0C nare calculated from the azimuthal distribution of the signal in the V0 detector. The components of all three event flow vectors are corrected for non-uniform detector acceptance and efficiency using a recentering procedure (i.e. by subtracting of the Qn-vector averaged over many events from the Qn-vector of each event) [43]. The denominator Rnin the above equation is called resolution and is obtained as a function of collision centrality. The gap in pseudorapidity between unand QSPD n(|∆η|>1.0) suppresses short-range correlations (“non-flow”), which are unrelated to the azimuthal asymmetry in the initial geometry and come from jets and resonance decays [19]. In the following, the vn{SP}coefficients are denoted as vn. The J/ψflow coefficients are extracted by a fit of the superposition of the J/ψsignal and the background to the dimuon flow coefficients as a function of the dimuon invariant – 4 – JHEP02(2019)012 mass [44] vn(Mµµ) = NJ/ψ NJ/ψ +NB +− vJ/ψ n+NB +− NJ/ψ +NB +− vB n(Mµµ),(3.2) where vJ/ψ nis the flow coefficient of the signal and vB nis the Mµµ-dependent flow coefficient of the background. The NJ/ψ and NB +−are the signal and the background dimuon yields, respectively, as a function of Mµµ. They are obtained by fitting the Mµµ distribution with a mixture of an extended Crystal Ball (CB2) function for the J/ψsignal and a VariableWidth Gaussian (VWG) function for the background [45]. The J/ψpeak position and width are left free, while the CB2 tail parameters are fixed to the values reported in ref. [46]. The statistical uncertainties of NJ/ψ and NB +−are not considered in the fit of vn(Mµµ), given their negligible contribution to the statistical uncertainty of the vJ/ψ ncoefficient. The ψ(2S) signal is not included in the fit of vn(Mµµ) because of its extremely low significance in central and semi-central collisions. In previous measurements [19,20], the Mµµ dependence of the background flow coefficients was parameterized by an arbitrary function. This approach leads to an increase of the statistical uncertainty of the J/ψflow coefficients, because the parameters of the function are not fixed. Moreover, an additional systematic uncertainty arises from the fact that the functional form of the background distribution is unknown. In the present analysis, we adopt a different approach. It is known that, in collisions of heavy ions, the dimuon background in the vicinity of the J/ψis mostly combinatorial and can be described satisfactorily with the event-mixing technique [9,17]. This technique consists in forming dimuons by combining muons from two different events having similar collision centrality. The flow coefficients of the combinatorial background are fully determined by the flow coefficients of the single muons from which the background dimuons are formed. One can show that for any given kinematical configuration of the background dimuon, its flow coefficients can be expressed as vB n(Mµµ) = hv(1) n(p(1) T, η1) cos[n(ϕ1−ϕ)] + v(2) n(p(2) T, η2) cos[n(ϕ2−ϕ)]iMµµ h1+2 ∞ P m=1 v(1) m(p(1) T, η1)v(2) m(p(2) T, η2) cos[m(ϕ1−ϕ2)]iMµµ ,(3.3) where v(1) n(p(1) T, η1) and v(2) n(p(2) T, η2) are the flow coefficients of the two muons as a function of their transverse momenta and pseudorapidities, ϕ1and ϕ2are the azimuthal angles of the two muons and ϕis the azimuthal angle of the dimuon. The brackets h···iMµµ denote an average over all dimuons (p(1) T,p(2) T,η1,η2,ϕ1,ϕ2) that belong to any given Mµµ interval. The details on the derivation of eq. (3.3) are given in appendix A. In case of the event mixing, the numerator in eq. (3.3) is calculated as Du(1) nQ(1),SPD n R(1) n cos(n(ϕ1−ϕ)) + u(2) nQ(2),SPD n R(2) n cos(n(ϕ2−ϕ))EMµµ ,(3.4) where u(1) nand u(2) nare the unit vector of the two muons, Q(1) nand Q(2) nare the SPD flow vectors for the events containing the two muons, and R(1) nand R(2) nare their resolutions. – 5 – JHEP02(2019)012 The brackets h···iMµµ denote an average over all mixed-event dimuons belonging to any given Mµµ interval. The denominator in eq. (3.3) reflects the modification of the dimuon yield due to the flow of single muons. Since the event flow vectors of the two mixed events are not correlated, the mixed-event dimuon yield is not modified by the single muon flow. Thus, the denominator is obtained directly as the ratio NB +−/Nmix +−, where Nmix +−is the number of mixed-event unlike-sign dimuons as a function of Mµµ. The ratio is calculated after a proper normalization of Nmix +−using the like-sign dimuons from the same and mixed events. The normalization factor is obtained as [17] R Mµµ Nmix +−rNsame ++ Nsame −− Nmix ++ Nmix −− dMµµ R Mµµ Nmix +−dMµµ ,(3.5) where Nsame ++ (Nsame −− ) and Nmix ++ (Nmix −− ) are the numbers of like-sign (positive and negative charges) same-event and mixed-event dimuons, respectively. The integral is calculated in the invariant mass interval between 2.2 and 4.5 GeV/c2. Assuming a purely combinatorial background, the vB n(Mµµ) coefficient, obtained with the event-mixing procedure described above, is used directly in order to fix the background term of the fit from eq. (3.2). All the analysis steps discussed in this section are performed separately in each considered dimuon transverse momentum and centrality interval. The event mixing and the normalization of Nmix +−are done in 5%-wide collision centrality intervals. Examples of the Mµµ fit and the mixed-event distribution Nmix +−as a function of Mµµ in several centrality and pTintervals are shown in figure 1. At low and intermediate pT, the mixed-event distribution describes the dimuon background on a percent level with a residual difference presumably originating from the single muon flow. However, at high pT, this difference becomes much larger (up to ≈35% in the vicinity of the J/ψmass in 8 < pT<12 GeV/cand 30–50% centrality interval) and goes beyond a possible single muon flow contribution. This points to the presence of a correlated dimuon background. Such a background is believed to originate from production of heavy-flavor quark pairs and to become significant in semi-central and peripheral collisions at high pT[47,48]. Examples of the v2(Mµµ) fit based on the analysis approach described above are presented in figure 2. As can be seen, the fit performs quite satisfactorily, with the mixed-event v2coefficient being able to describe the shape and amplitude of the background v2in the entire considered invariant mass interval from 1.5 to 4.5 GeV/c2. This is not surprising at low and intermediate pT, where the mixed-event dimuon distribution describes rather precisely the background dimuon distribution (top and middle panels in figures 1and 2). Remarkably, however, the mixed-event approach performs satisfactorily also at high pT in semi-central collisions, where the contribution of the correlated background is significant (bottom right panels in figures 1and 2). Given that the denominator in eq. (3.3) is obtained as the ratio NB +−/Nmix +−, this means that the flow coefficient of the correlated background is significantly lower than that of the combinatorial one. The systematic effect arising from the presence of the correlated background and the corresponding uncertainties are discussed in section 4. The approach described above performs equally well also in case – 6 – JHEP02(2019)012 1.5 2 2.5 3 3.5 4 4.5 2 cCounts / 50 MeV/ 50 100 150 200 250 300 350 400 450 3 10× Data Total fit Signal fit Background fit Event mixing = 5.02 TeV NN sALICE Pb-Pb 0-10% <4.0y2.5< c<2 GeV/ T p0< ) 2 c (GeV/ µµ M 1.5 2 2.5 3 3.5 4 4.5 Ratio 0.96 0.98 1 1.02 Data / Total fit Data / Event mixing Background fit / Event mixing 1.5 2 2.5 3 3.5 4 4.5 2 cCounts / 50 MeV/ 50 100 150 200 250 3 10× 10-50% c<2 GeV/ T p0< ) 2 c (GeV/ µµ M 1.5 2 2.5 3 3.5 4 4.5 Ratio 0.9 0.95 1 1.05 1.5 2 2.5 3 3.5 4 4.5 2 cCounts / 50 MeV/ 20 40 60 80 100 120 140 160 3 10× 0-10% c<6 GeV/ T p2< ) 2 c (GeV/ µµ M 1.5 2 2.5 3 3.5 4 4.5 Ratio 0.96 0.98 1 1.02 1.04 1.5 2 2.5 3 3.5 4 4.5 2 cCounts / 50 MeV/ 20 40 60 80 100 3 10× 10-50% c<6 GeV/ T p2< ) 2 c (GeV/ µµ M 1.5 2 2.5 3 3.5 4 4.5 Ratio 0.95 1 1.05 1.5 2 2.5 3 3.5 4 4.5 2 cCounts / 50 MeV/ 200 400 600 800 1000 1200 1400 1600 0-10% c<12 GeV/ T p6< ) 2 c (GeV/ µµ M 1.5 2 2.5 3 3.5 4 4.5 Ratio 0.9 1 1.1 1.2 1.5 2 2.5 3 3.5 4 4.5 2 cCounts / 50 MeV/ 500 1000 1500 2000 2500 10-50% c<12 GeV/ T p6< ) 2 c (GeV/ µµ M 1.5 2 2.5 3 3.5 4 4.5 Ratio 1 1.2 1.4 Figure 1. (Color online) The Mµµ distribution in low (top panels), intermediate (middle panels) and high (bottom panels) pTintervals for central (left panels) and semi-central (right panels) collisions. The data are fitted to a combination of an extended Crystal Ball (CB2) function for the signal and a Variable-Width Gaussian (VWG) function for the background. The distributions are compared to the ones obtained with the event-mixing technique (see text for details). Only statistical uncertainties are shown. – 7 – JHEP02(2019)012 )c (GeV/ T p 2 4 6 8 10 2 v 0 0.05 0.1 0.15 0.2 Unbiased V0A 2 q20% lowV0A 2 q20% high- = 5.02 TeV NN sALICE Pb-Pb <4.0y, 2.5<ψInclusive J/ 5-40% )c (GeV/ T p 2 4 6 8 10 (unbiased) 2 v)/ V0A 2 q(low/high2 v 1− 0 1 2 V0A 2 low-qψJ/ V0A 2 high-qψJ/ σ1±: Fit V0A 2 low-qψJ/ σ1±: Fit V0A 2 high-qψJ/ V0A 2 low-q ± µ V0A 2 high-q ± µ = 5.02 TeV NN sALICE Pb-Pb <4.0y2.5< 5-40% Figure 7. (Color online) Left: the J/ψ v2as a function of pTfor shape selected and unbiased samples in the 5–40% centrality interval in Pb-Pb collisions at √sNN = 5.02 TeV. Points are slightly shifted along the horizontal axis for better visibility. Statistical and systematic uncertainties are shown as bars and boxes, respectively. Right: ratio of the J/ψ v2in lowest and highest qV0A 2eventshape classes and the unbiased sample. The shaded bands represent the result with a constant function ±1σ. The J/ψresults are compared to the ratios for the single muons v2obtained with the same event-shape classes. 6 Conclusions In summary, the elliptic and triangular flow coefficients of inclusive J/ψmesons at forward rapidity have been measured in Pb-Pb collisions at √sNN = 5.02 TeV over a broad range of transverse momentum and in various centrality intervals. This is the first measurement of the v3coefficient for inclusive J/ψproduction, indicating a positive value with 3.7σ significance for 0 < pT<12 GeV/c. The obtained inclusive J/ψ v2and v3coefficients as well as the ratio v3/v2are compared to the results for charged particles and prompt D0mesons at mid-rapidity. At low and intermediate pT, the v2and v3results exhibit an ordering with the charged particles having largest values, followed by the prompt D0mesons and finally the J/ψhaving the smallest values. In semi-central collisions at intermediate pT, the J/ψ v3/v2ratio is found to be significantly lower compared to that of charged particles. Despite the large uncertainties, the values of the prompt D0ratio are somewhat lower than the charged particles and higher than the J/ψmesons, hinting at a possible ordering similar to that observed for the v2and v3coefficients. At high pT, the v2of the charged particles, the prompt D0mesons and the J/ψseem to converge to similar values. The uncertainties of the v3coefficients do not allow one to draw firm conclusions about their convergence, although the centralityand pT-integrated J/ψ v3is compatible with that of high-pTcharged particles. The analysis using Event Shape Engineering technique shows that the J/ψ v2coefficients increase (decrease) for classes of events with high (low) reduced event flow vector. – 14 – JHEP02(2019)012 Compared to single muons reconstructed in the same rapidity interval, the J/ψresults are found compatible with the expected variations of the eccentricity of the initial-state geometry. Acknowledgments 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 (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences and Nationalstiftung f¨ur Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Funda¸c˜ao de Amparo `a Pesquisa do Estado de S˜ao Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China; Ministry of Science and Education, Croatia; Centro de Aplicaciones Tecnol´ogicas y Desarrollo Nuclear (CEADEN), Cubaenerg´ıa, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research — Natural Sciences, the Carlsberg Foundation and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat `a l’Energie Atomique (CEA) and Institut National de Physique Nucl´eaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium f¨ur Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnolog´ıa, through Fondo de Cooperaci´on Internacional en Ciencia y Tecnolog´ıa (FONCICYT) and Direcci´on General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), – 15 – JHEP02(2019)012 Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Cat´olica del Per´u, Peru; Ministry of Science and Higher Education and National Science Centre, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Romanian National Agency for Science, Technology and Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; National Science and Technology Development Agency (NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. A Flow coefficients of combinatorial background The azimuthal distribution of the combinatorial background dNB/dϕis a product of the azimuthal distributions of the single muons from which the background dimuons are formed. Thus, using eq. (1.1) one obtains dNB dϕ∝ 1+2 ∞ X n=1 v(1) n(p(1) T,η1)cos[n(ϕ1−Ψn)]! 1+2 ∞ X m=1 v(2) m(p(2) T,η2)cos[m(ϕ2−Ψm)]! ∝1+2 ∞ X n=1 v(1) n(p(1) T,η1)cos[n(∆ϕ1+ϕ−Ψn)] +2 ∞ X m=1 v(2) m(p(2) T,η2)cos[m(∆ϕ2+ϕ−Ψm)] (A.1) +4 ∞ X n=1 ∞ X m=1 v(1) n(p(1) T,η1)v(2) m(p(2) T,η2)cos[n(∆ϕ1+ϕ−Ψn)]cos[m(∆ϕ2+ϕ−Ψm)], where v(1) n(p(1) T, η1) and v(2) m(p(2) T, η2) are the flow coefficients of the two muons as a function of their transverse momenta and pseudorapidities, ϕ1and ϕ2are the azimuthal angles of the two muons, ϕis the azimuthal angle of the dimuon and ∆ϕ1,2=ϕ1,2−ϕ. – 16 – JHEP02(2019)012 The n-th order flow coefficient of the background dimuon is then calculated as vB n(p(1) T, p(2) T, η1, η2, ϕ1, ϕ2) = hcos[n(ϕ−Ψn)]i= 2π R0 dNB dϕcos[n(ϕ−Ψn)]dϕ 2π R0 dNB dϕdϕ .(A.2) The denominator in eq. (A.2) is obtained as 2π+ 2 ∞ X n=1 v(1) n(p(1) T, η1)In(∆ϕ1)+2 ∞ X m=1 v(2) m(p(2) T, η2)Im(∆ϕ2) + 4 ∞ X n=1 ∞ X m=1 v(1) n(p(1) T, η1)v(2) m(p(2) T, η2)Inm(∆ϕ1,∆ϕ2), (A.3) where In(∆ϕ1,2) = 2π Z 0 cos[n(∆ϕ1,2+ϕ−Ψn)]dϕ= 0,(A.4) Imn(∆ϕ1,∆ϕ2) = 2π Z 0 cos[n(∆ϕ1+ϕ−Ψn)] cos[m(∆ϕ2+ϕ−Ψm)]dϕ =(0,n6= m πcos[n(∆ϕ1−∆ϕ2)],n=m.(A.5) The numerator in eq. (A.2) is obtained as 2 ∞ X k=1 v(1) k(p(1) T, η1)Jkn(∆ϕ1)+2 ∞ X m=1 v(2) m(p(2) T, η2)Jmn(∆ϕ2) + 4 ∞ X k=1 ∞ X m=1 v(1) k(p(1) T, η1)v(2) m(p(2) T, η2)Jkmn(∆ϕ1,∆ϕ2), (A.6) where Jkn(∆ϕ1,2) = 2π Z 0 cos[k(∆ϕ1,2+ϕ−Ψk)] cos[n(ϕ−Ψn)]dϕ =(0,k6= n πcos[n∆ϕ1,2],k=n,(A.7) Jkmn(∆ϕ1,∆ϕ2) = 2π Z 0 cos[k(∆ϕ1+ϕ−Ψk)] cos[m(∆ϕ2+ϕ−Ψm)] ×cos[n(ϕ−Ψn)]dϕ= 0.(A.8) – 17 – JHEP02(2019)012 Combining eq. (A.2)–(A.8) yields vB n(p(1) T, p(2) T, η1, η2, ϕ1, ϕ2) = v(1) n(p(1) T, η1) cos[n(ϕ1−ϕ)] + v(2) n(p(2) T, η2) cos[n(ϕ2−ϕ)] 1+2 ∞ P m=1 v(1) m(p(1) T, η1)v(2) m(p(2) T, η2) cos[m(ϕ1−ϕ2)] . (A.9) Finally, the vB nas a function of Mµµ is obtained by averaging the numerator and denominator in eq. (A.9) over all dimuons, which belong to a given Mµµ interval: vB n(Mµµ) = hv(1) n(p(1) T, η1) cos[n(ϕ1−ϕ)] + v(2) n(p(2) T, η2) cos[n(ϕ2−ϕ)]iMµµ h1+2 ∞ P m=1 v(1) m(p(1) T, η1)v(2) m(p(2) T, η2) cos[m(ϕ1−ϕ2)]iMµµ .(A.10) The eq. (A.8) is derived assuming no correlation between different harmonic symmetry plane angles Ψ. While this is in general the case, there are some noticeable exceptions [59]. In fact, the significant correlation between the Ψ2and Ψ4angles leads to non-zero J422. The corresponding contribution to the numerator of eq. (A.10) for vB 2is given approximately by 1 2hcos[4(Ψ4−Ψ2)]ihv(1) 4(p(1) T, η1)v(2) 2(p(2) T, η2) cos[4(ϕ1−ϕ)−2(ϕ2−ϕ)] +v(2) 4(p(2) T, η2)v(1) 2(p(1) T, η1) cos[4(ϕ2−ϕ)−2(ϕ1−ϕ)]iMµµ , (A.11) where the brackets h···i denote an average over all events. The contribution is estimated as described in the following. First, the v2and v4coefficients of single muons are measured with the SP method, averaged over pseudorapidity and parameterized as a function of pT. The obtained parameterizations v2,4(pT) are then combined with opposite-sign dimuons (p(1) T, p(2) T, η1, η2, ϕ1, ϕ2) in the data outside the J/ψmass peak. The values of hcos[4(Ψ4− Ψ2)]i, which ranges from 0 in central collisions to about 0.8 in peripheral collisions, are taken from ref. [59]. Finally, the magnitude of the effect is calculated via interpolation of the results at the J/ψmass peak. In general, the magnitude is found to be at the order of 10−4, reaching at most 7 ×10−4for 0 < pT<2 GeV/cand the 30–50% centrality interval. A similar effect is present in the numerator of eq. (A.10) for vB 3, due to the correlation of the Ψ3and Ψ6angles. In practice, however, this contribution can be certainly neglected, because of the small magnitude of the v6coefficient. Open Access. 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