J/Psi Elliptic Flow in Pb-Pb Collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

We report on the first measurement of inclusive J/$\psi$ elliptic flow, $v_2$, in heavy-ion collisions at the LHC. The measurement is performed with the ALICE detector in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV in the rapidity range $2.5<y<4.0$. The dependence of the J/$\psi$ $v_2$ on the collision centrality and on the J/$\psi$ transverse momentum is studied in the range $0<p_{\rm T}<10$ GeV/$c$. For semi-central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV, an indication of non-zero $v_2$ is observed with a maximum value of $v_2 = 0.116 \pm 0.046 {\rm (stat.)} \pm 0.029 {\rm (syst.)}$ for J/$\psi$ in the transverse momentum range $2<p_{\rm T}<4$ GeV/$c$. The elliptic flow measurement complements the previously reported ALICE results on the inclusive J/$\psi$ nuclear modification factor and favors the scenario of a significant fraction of J/$\psi$ production from charm quarks in a deconfined partonic phase.

J/ψ Elliptic Flow in Pb-Pb Collisions at √ s NN = 2.76 TeV The ALICE Collaboration In this Letter, we report ALICE results on inclusive J/ψ elliptic flow in Pb-Pb collisions at √ s NN = 2.76 TeV at forward rapidity, measured via the µ + µ − decay channel. The results are presented as a function of transverse momentum and collision centrality.
The ALICE detector is described in [17]. At forward rapidity (2.5 < y < 4) the production of quarkonia is measured in the muon spectrometer 2 down to p T = 0. The spectrometer consists of an absorber stopping the hadrons in front of five tracking stations comprising two planes of cathode pad chambers each, with the third station inside a dipole magnet. The tracking apparatus is completed by a triggering system made of four planes of resistive plate chambers downstream of an iron wall, which absorbs secondary hadrons escaping from the front absorber and low momentum muons. Also used in this analysis are two cylindrical layers of silicon pixel detectors, to determine the location of the interaction point, and two scintillator arrays (VZERO). The VZERO counters consist of two arrays of 32 scintillator sectors each distributed in four rings covering 2.8 ≤ η ≤ 5.1 (VZERO-A) and −3.7 ≤ η ≤ −1.7 (VZERO-C). All of these detectors have full azimuthal coverage. The data sample used for this analysis, collected in 2011, amounts to 17×10 6 dimuon unlike sign (MU) triggered Pb-Pb collisions and corresponds to an integrated luminosity L int ≈ 70 µb −1 . The MU trigger requires a minimum bias (MB) trigger and at least a pair of opposite-sign (OS) track segments, each with a p T above the threshold of the on-line trigger algorithm. This p T threshold was set to provide 50% efficiency for muon tracks with p T = 1 GeV/c. The MB trigger requires a signal in both VZERO-A and VZERO-C. The beam-induced background was further reduced offline using the VZERO and the zero degree calorimeter (ZDC) timing information. The contribution from electromagnetic processes was removed by requiring a minimum energy deposited in the neutron ZDCs [18]. The centrality determination is based on a fit of the VZERO amplitude distribution [19,20]. The average number of participating nucleons N part for the centrality classes used in this analysis (see Table. 1) are derived from a Glauber model calculation [19,20].
J/ψ candidates are formed by combining pairs of OS tracks reconstructed in the geometrical acceptance of the muon spectrometer. To improve the muon identification, the reconstructed tracks in the tracking chambers are required to match a track segment in the trigger system above the p T threshold aforementioned.
The J/ψ v 2 is calculated using event plane (EP) based methods. The azimuthal angle Ψ of the second harmonic EP is used to estimate the reaction plane angle [21]. Ψ is determined from the azimuthal distribution of the VZERO amplitude. A two step flattening procedure of the EP azimuthal distribution was applied as described in [22] and [23], respectively. It results in an EP azimuthal distribution uniform to better than 2% for all centrality classes under study. The VZERO-C has a common acceptance region with the muon spectrometer. Therefore, only the VZERO-A was used for the EP determination to avoid autocorrelations. The J/ψ v 2 results were obtained determining v 2 = cos 2(φ − Ψ) versus the invariant mass (m µ µ ) [24], where φ is the OS dimuon azimuthal angle. The resulting v 2 (m µ µ ) distribution is fitted where v sig 2 and v bkg 2 correspond to the v 2 of the J/ψ signal and of the background, respectively (see Fig. 1 was parametrized using a second order polynomial. Here, α(m µ µ ) = S/(S + B) is the ratio of the signal over the sum of the signal plus background of the m µ µ distributions. It is extracted from fits to the OS invariant mass distribution (see Fig. 1 (a)) in each p T and centrality class. The J/ψ line shape was described with a Crystal Ball (CB) function and the underlying continuum with either a third order polynomial or a Gaussian with a width linearly varying with mass. The CB function connects a Gaussian core with a power-law tail [25] at low mass to account for energy loss fluctuations and radiative decays. An extended CB function with an additional power-law tail at high mass, to account for alignment and calibration biases, was also used. The combination of several CB and underlying  continuum parametrizations described before were tested to assess the signal and the related systematic uncertainties. The J/ψ v 2 and its statistical uncertainty in each p T and centrality class were determined as the average of the v sig 2 obtained by fitting v 2 (m µ µ ) using Eq. 1 with the various α(m µ µ ), while the corresponding systematic uncertainties were defined as the RMS of these results. Figure 1 shows typical fits of the OS invariant mass distribution (a) and of the cos 2(φ − Ψ) as a function of m µ µ (b) in the 20%-40% centrality class. The procedure above was repeated using either a first order polynomial or its inverse as v bkg 2 parametrization. The largest deviation of the results obtained with the three different v bkg 2 parametrizations was conservatively adopted as the systematic uncertainty related to the unknown shape of the v bkg 2 (m µ µ ). This turns out to be often the dominant source of systematic uncertainties with the uncertainty from the signal extraction being the second one. It was checked that different choices of invariant mass binnings yield v 2 values that are consistent within uncertainties. A similar method was used to extract the uncorrected (for detector acceptance and efficiency) average transverse momentum ( p T uncor ) of the reconstructed J/ψ in each centrality and p T class. The p T uncor is used to locate the data points when plotted as a function of p T . Consistent v 2 values were obtained using an alternative method [21] in which the J/ψ raw yield is extracted, as described before, in bins of (φ − Ψ) and v 2 is evaluated by fitting the data with the function dN where A is a normalization constant. As an additional check the first analysis procedure [24] was also applied to the same-sign (SS) dimuons. As expected, no J/ψ signal is seen in either the invariant mass distribution or the cos 2(φ − Ψ) as a function of m µ µ of SS dimuons. In both cases the SS dimuons exhibit the same trend as the continuum of the OS dimuons.
The finite resolution in the EP determination smears out the azimuthal distributions and lowers the value of the measured anisotropy [21]. The VZERO-A EP resolution as a function of the centrality was determined using MB events and the 3 sub-event method [21]. To estimate the systematic uncertainty from the EP determination two sets of 3 sub-events were used: first, VZERO-A, VZERO-C and Table 1: N part and VZERO-A EP resolution for the centrality classes expressed in percentages of the nuclear cross section [19].
The J/ψ reconstruction efficiency depends on the detector occupancy, which could bias the v 2 measurement. This effect was evaluated by embedding azimuthally isotropic simulated J/ψ → µ + µ − decays into real events. The measured v 2 of those embedded J/ψ does not deviate from zero by more than 0.015 in the centrality and p T classes considered. This value is used as a conservative systematic uncertainty on all measured v 2 values.   shape and the reconstruction efficiency. The global correlated relative systematic uncertainty on the EP resolution is 1.3%. A non-zero v 2 is observed in the intermediate p T range 2 ≤ p T < 6 GeV/c. Including statistical and systematic uncertainties the combined significance of a non-zero v 2 in this p T range is 2.7σ . At lower and higher p T the inclusive J/ψ v 2 is compatible with zero within uncertainties.
To study the centrality dependence of the v 2 we select J/ψ with 1.5 ≤ p T < 10 GeV/c. Indeed, below 1.5 GeV/c the v 2 of the J/ψ is expected to be small [14] and the signal to background ratio is also low. Since the initial spatial anisotropy for head-on collisions is small, the expected v 2 is also small. In addition, for the 0%-5% centrality range the VZERO-A EP resolution is quite low and has higher systematic uncertainties. Therefore, the 0%-5% centrality range was excluded. Figure 3 (a) shows v 2 for inclusive J/ψ with 1.5 ≤ p T < 10 GeV/c as a function of N part in Pb-Pb collisions at √ s NN = 2.76 TeV. Here, the point-to-point uncorrelated systematic uncertainties (boxes) also include, in addition to those discussed above, the uncertainty from the EP resolution determination. The measured v 2 depends on the p T distribution of the reconstructed J/ψ, which could vary with the collision centrality. Therefore, p T uncor of the reconstructed J/ψ is also shown in Fig. 3 (b). The error bar indicates the statistical uncertainties while the boxes show the systematic uncertainties due to the J/ψ signal extraction. For the most central collisions, 5%-20% and 20%-40% the inclusive J/ψ v 2 for 1.5 ≤ p T < 10 GeV/c are 0.101 ± 0.044(stat.) ± 0.032(syst.) and 0.116 ± 0.045(stat.) ± 0.041(syst.), respectively. The combined significance of a non-zero v 2 is 2.9σ . For more peripheral Pb-Pb collisions, the v 2 is consistent with zero within uncertainties. Although there is a small variation with centrality, the p T uncor stays in the  all centralities. Thus, the observed centrality dependence of the v 2 for inclusive J/ψ with 1.5 ≤ p T < 10 GeV/c does not result from any bias in the sampled p T distributions. For J/ψ with p T < 1.5 GeV/c (not shown), the v 2 is compatible with zero within one standard deviation for the four centrality classes. The p T uncor ranges from about 0.75 to 0.9 GeV/c.
To allow a direct comparison with current model calculations, the inclusive J/ψ v 2 (p T ) was also calculated in a broader centrality range, namely 20%-60%, and it is shown in Fig. 4. In this broader centrality range, the measured v 2 signal in the p T range 2-4 GeV/c deviates from zero by 2σ . The same trend of v 2 (p T ) is observed in the 20%-60% and in the 20%-40% centrality classes. This trend seems qualitatively different from that of the STAR measurement [16] at lower collision energy, which is compatible with zero for p T ≥ 2 GeV/c albeit in somewhat different (10%-40% and 0%-80%) centrality ranges. Also shown in Fig. 4 are two transport model calculations that include a J/ψ regeneration component from deconfined charm quarks in the medium [14,26]. In both models about 30% of the measured J/ψ in the 20%-60% centrality range are regenerated. First, thermalized charm quarks in the medium transfer a significant elliptic flow to regenerated J/ψ. Second, primordial J/ψ emitted out-of-plane traverse a longer path through the medium than those emitted in-plane resulting in a small apparent v 2 . The predicted maximum v 2 at p T ∼ 2.5 GeV/c results from an interplay between the regeneration component, dominant at lower p T , and the primordial J/ψ component which takes over at higher p T .