Measurement of $\Upsilon(1{\rm S})$ elliptic flow at forward rapidity in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=5.02$ TeV

The first measurement of the $\Upsilon(1{\rm S})$ elliptic flow coefficient ($v_2$) is performed at forward rapidity (2.5 $<$ $y$ $<$ 4) in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV with the ALICE detector at the LHC. The results are obtained with the scalar product method and are reported as a function of transverse momentum ($p_{\rm{T}}$) up to 15 GeV/$c$ in the 5-60% centrality interval. The measured $\Upsilon(1{\rm S})$ $v_2$ is consistent with zero and with the small positive values predicted by transport models within uncertainties. The $v_2$ coefficient in 2 $<$ $p_{\rm T}$ $<$ 15 GeV/$c$ is lower than that of inclusive J/$\psi$ mesons in the same $p_{\rm{T}}$ interval by 2.6 standard deviations. These results, combined with earlier suppression measurements, are in agreement with a scenario in which the $\Upsilon$(1S) production in Pb-Pb collisions at LHC energies is dominated by dissociation limited to the early stage of the collision whereas in the J/$\psi$ case there is substantial experimental evidence of an additional regeneration component.

quarks gives a negligible contribution to the v 2 coefficient due to the small number of available bottom quarks [36]. As a result, the predicted values of ϒ(1S) v 2 coefficient are small in contrast to the charmonium case. It is worth noting that even though the v 2 coefficient of the excited bottomonium state ϒ(2S) is currently beyond experimental reach, it is expected to be significantly higher than that of ϒ(1S). Due to its lower binding energy and other bound-state characteristic differences, the suppression and regeneration occur up to a later stage of the collision. Hence, the path-length dependent suppression induces a larger v 2 , the fraction of regenerated ϒ(2S) is higher and the inherited v 2 is larger [36]. Consequently, the measurement of the bottomonium elliptic flow is a crucial ingredient in the study of heavy-flavor interactions with the QGP, not only to complement the corresponding charmonium measurements, but also in the search for any sizable v 2 beyond the theoretical expectations.
In this Letter, we present the first measurement of ϒ(1S) elliptic flow in Pb-Pb collisions at √ s NN = 5.02 TeV at forward rapidity (2.5 < y < 4). The ϒ mesons are reconstructed via their µ + µ − decay channel. The results are obtained in the momentum interval 0 < p T < 15 GeV/c and the 5-60% collision centrality interval.
General information on the ALICE apparatus and its performance can be found in Refs. [37,38]. The muon spectrometer, which covers the pseudorapidity range −4 < η < −2.5 1 , is used to reconstruct muon tracks. It consists of a front absorber followed by five tracking stations with the third station placed inside a dipole magnet. Two trigger stations located downstream of an iron wall complete the spectrometer. The Silicon Pixel Detector (SPD) [39,40] consists of two cylindrical layers covering the full azimuthal angle and |η| < 2.0 and |η| < 1.4, respectively. The SPD is employed to determine the position of the primary vertex and to reconstruct tracklets, track segments formed by the clusters in the two SPD layers and the primary vertex [41]. Two arrays of 32 scintillator counters each [42], covering 2.8 < η < 5.1 (V0A) and −3.7 < η < −1.7 (V0C), are used for triggering, the event selection and the determination of the collision centrality and the event flow vector. In addition, two neutron Zero Degree Calorimeters [43], installed 112.5 m from the interaction point along the beam line on each side, are employed for the event selection.
The data samples recorded by ALICE during the 2015 and 2018 LHC Pb-Pb runs at √ s NN = 5.02 TeV are used for this analysis. The trigger conditions and the event selection criteria are described in Ref. [24]. The primary vertex position is required to be within ±14 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 [44]. The integrated luminosity of the analyzed data sample is about 750 µb −1 .
The muon selection is identical to that used in Refs. [24,27]. 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 15 GeV/c. The alignment of the muon spectrometer is performed based on the MILLEPEDE package [45] and using Pb-Pb data taken with the nominal dipole magnetic field [38]. The presence of the magnetic field limits the precision of the alignment procedure in the track bending direction. Indeed, a study of the reconstructed ϒ mass as a function of the momentum of muon tracks (p µ ) reveals a residual misalignment leading to a systematic shift in the measured muon track momentum ∆(1/p µ ) ≈ ±2.5 × 10 −4 (GeV/c) −1 , where the sign of the shift depends on the muon charge and the magnetic field polarity. A correction of this misalignment effect is obtained via a high-statistics sample of reconstructed J/ψ → µ + µ − decays and the spectra of high-momentum muon tracks. The correction is then applied to the reconstructed muon track momentum, resulting in up to 25% improvement of the ϒ(1S) mass resolution for p T > 6 GeV/c.   Fig. 1. It is worth noting that no statistically significant ϒ(3S) is observed in any of the studied centrality and p T intervals, and thus it is not considered in the further analysis.
The dimuon v 2 is measured using the scalar product method [47,48], correlating the reconstructed dimuons with the second-order harmonic event flow vector Q SPD 2 [5,49] calculated from the azimuthal distribution of the reconstructed SPD tracklets where u 2 = exp(i2ϕ) is the unit flow vector of the dimuon with azimuthal angle ϕ. The brackets · · · µ µ denote an average over all dimuons belonging to a given p T , M µ µ and centrality interval. The Q V0A 2 and Q V0C 2 are the event flow vectors calculated from the azimuthal distribution of the energy deposition measured in the V0A and V0C detectors, respectively, and * is the complex conjugate. The brackets · · · in the denominator denote an average over all events in a sufficiently narrow centrality class which encloses the event containing the dimuon. In order to account for a non-uniform detector response and efficiency, the components of all three event flow vectors are corrected using a recentering procedure [50]. The gaps in pseudorapidity between the muon spectrometer and SPD (|∆η| > 1.0) and between the SPD, V0A, and V0C remove auto-correlations and suppress short-range correlations unrelated to the azimuthal asymmetry in the initial geometry ("non-flow"), which largely come from jets and resonance decays. In the following, the v 2 {SP} coefficient is denoted as v 2 .
The ϒ(1S) v 2 coefficient is obtained by a least squares fit of the superposition of the ϒ(1S) signal and the background to the dimuon flow coefficient as a function of the dimuon invariant mass [51] v where v ground and α(M µ µ ) is the signal fraction, obtained from the fit of the M µ µ distribution described above. The background v B 2 is modeled as a second-order polynomial function of M µ µ . For consistency, and despite its low yield, the ϒ(2S) is included in the fit by restricting the value of its v 2 coefficient within the range between −0.5 and 0.5. In practice, this inclusion has a negligible impact on the ϒ(1S) fit results. An example of v 2 (M µ µ ) fit is presented in the right panel of Fig. 1.
The main systematic uncertainty of the measurement arises from the choice of the background fit function v B 2 (M µ µ ). In order to estimate this uncertainty, linear and constant functions are also used instead of the second-order polynomial. In addition, the signal CB2 tail parameters and background fit functions are varied [35]. The systematic uncertainty is then derived as the standard deviation with respect to the default choice of fitting functions. The absolute uncertainty increases from 0.004 to 0.016 with increasing collision centrality and decreasing p T , which is due to the decreasing signal-to-background ratio. The dimuon trigger and reconstruction efficiency depends on the detector occupancy. This, coupled to the muon flow, could lead to a bias in the measured v 2 . The corresponding systematic uncertainty is obtained by embedding simulated ϒ(1S) decays into real Pb-Pb events [24]. It is found to be at most 0.0015 and is conservatively assumed to be the same in all transverse momentum and centrality intervals. The variations of the fit range and invariant-mass binning do not lead to deviations beyond the expected statistical fluctuations. The uncertainty related to the magnitude of the Q SPD 2 flow vector is found to be negligible. Furthermore, the absence of any residual non-uniform detector acceptance and efficiency in the SPD flow vector determination after applying the recentering procedure is verified via the imaginary part of the scalar product (see Eq. (1)) [50].  [52]. The TAMU model incorporates in addition a regeneration component originating from the recombination of (partially) thermalized bottom quarks [36]. Given that the regeneration component gives practically negligible contribution to the total ϒ(1S) v 2 , the differences between the two models are marginal. It is worth noting that although the quoted model predictions are for mid-rapidity, they remain valid also for the rapidity range of the measurement within the theoretical uncertainties. Indeed the fractions of regenerated and initially-produced ϒ(1S) are very close at midand forward rapidities [36]. In addition, the QGP medium evolution is also similar between mid-and forward rapidities, given the weak rapidity dependence of the charged-particle multiplicity density [53]. The presented ϒ(1S) v 2 result is coherent with the measured ϒ(1S) suppression in Pb-Pb collisions [35], as the level of suppression is also fairly well reproduced by the BBJS model and the TAMU model including or excluding a regeneration component. Therefore, the result is in agreement with a scenario in which the predominant mechanism affecting ϒ(1S) production in Pb-Pb collisions at the LHC energies is the dissociation limited to the early stage of the collision. It is interesting to note that the presented ϒ(1S) v 2 results are reminiscent of the corresponding charmonia measurements in Au-Au collisions at RHIC [54], where so far non-observation of significant v 2 is commonly interpreted as a sign of a small regeneration component from recombination of thermalized charm quarks at lower RHIC energies.
The ϒ(1S) v 2 values in the three p T intervals shown in Fig. 2 are found to be lower, albeit with large uncertainties, compared to those of the inclusive J/ψ measured in the same centrality and p T intervals using the data sample and analysis procedure described in Ref. [24].
Given that any v 2 originating either from recombination or from path-length dependent dissociation ϒ v 2 in Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration vanishes at zero p T , the observed difference between ϒ(1S) and J/ψ v 2 is quantified by performing the p Tintegrated measurement excluding the low p T range. Figure 3 presents the ϒ(1S) v 2 coefficient integrated over the transverse momentum range 2 < p T < 15 GeV/c for three centrality intervals compared with that of the inclusive J/ψ. The ϒ(1S) v 2 is found to be −0.003 ± 0.030(stat) ± 0.006(syst) in the 2 < p T < 15 GeV/c and 5-60% centrality interval. This value is lower than the corresponding J/ψ v 2 by 2.6σ . This observation, coupled to the different measured centrality and p T dependence of the ϒ(1S) and J/ψ suppression in Pb-Pb collisions at the LHC [17, 35], can be interpreted within the models used for comparison as a sign that unlike ϒ(1S), J/ψ production has a significant regeneration component. Nevertheless, no firm conclusions can be drawn, given that currently the transport models can not explain the significant J/ψ v 2 for p T > 4-5 GeV/c observed in the data [23].
In summary, the first measurement of the ϒ(1S) v 2 coefficient in Pb-Pb collisions at √ s NN = 5.02 TeV is presented. The measurement is performed in the 5-60% centrality interval within 0 < p T < 15 GeV/c range at forward rapidity. The v 2 coefficient is compatible with zero and with the model predictions within uncertainties. Excluding low p T (0 < p T < 2 GeV/c), ϒ(1S) v 2 is found to be 2.6σ lower with respect to that of inclusive J/ψ. The presented measurement opens the way for further studies of bottomonium flow using the future data samples from the LHC Runs 3 and 4 with an expected ten-fold increase in the number of the ϒ candidates [55,56].

Acknowledgements
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration.  [20] P. Braun-Munzinger and J. Stachel, "(Non)thermal aspects of charmonium production and a new look at J/ψ suppression", Phys.      [39] ALICE Collaboration, G. Dellacasa et al., "ALICE technical design report of the inner tracking system (ITS)", tech. rep., CERN, 1999. https://cds.cern.ch/record/391175.  ϒ v 2 in Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration

A The ALICE Collaboration
ϒ v 2 in Pb-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration