Inclusive, prompt and non-prompt J/$\psi$ production at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV

The transverse momentum ($p_{\rm T}$) dependence of the nuclear modification factor $R_{\rm AA}$ and the centrality dependence of the average transverse momentum $\langle p_{\rm T}\rangle$ for inclusive J/$\psi$ have been measured with ALICE for Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV in the e$^+$e$^-$ decay channel at mid-rapidity ($|y|<0.8$). The $\langle p_{\rm T}\rangle$ is significantly smaller than the one observed for pp collisions at the same centre-of-mass energy. Consistently, an increase of $R_{\rm AA}$ is observed towards low $p_{\rm T}$. These observations might be indicative of a sizable contribution of charm quark coalescence to the J/$\psi$ production. Additionally, the fraction of non-prompt J/$\psi$ from beauty hadron decays, $f_{\rm B}$, has been determined in the region $1.5<p_{\rm T}<10$ GeV/c in three centrality intervals. No significant centrality dependence of $f_{\rm B}$ is observed. Finally, the $R_{\rm AA}$ of non-prompt J/$\psi$ is discussed and compared with model predictions. The nuclear modification in the region $4.5<p_{\rm T}<10$ GeV/c is found to be stronger than predicted by most models.

In this paper we present a differential measurement of the inclusive J/ψ production at mid-rapidity in Pb-Pb collisions at √ s NN = 2.76 TeV. The p T dependence of the nuclear modification factor and the centrality dependence of the average transverse momentum of J/ψ have been obtained, extending the set of results presented in [12]. A measurement of the prompt and non-prompt contributions to the inclusive J/ψ production is also presented. The nuclear modification factor of non-prompt J/ψ is determined down to p T = 1.5 GeV/c and compared to model predictions.

Data Analysis
A detailed description of the ALICE detector can be found in [38]. For the analysis presented here the detectors of the central barrel have been used, in particular the Inner Tracking System (ITS) and the Time Projection Chamber (TPC). These detectors are located inside a large solenoidal magnet with a field strength of 0.5 T. They allow the measurement of J/ψ mesons via the dielectron decay channel in the central rapidity region down to zero p T . The ITS [39] consists of six layers of silicon detectors surrounding the beam pipe at radial positions between 3.9 cm and 43.0 cm. Its two innermost layers are composed of Silicon Pixel Detectors (SPD), which provide the spatial resolution to separate on a statistical basis the non-prompt J/ψ. The active volume of the TPC [40] covers the range along the beam direction −250 < z < 250 cm relative to the Interaction Point (IP) and extends in radial direction from 85 cm to 247 cm. It is the main tracking device in the central barrel and is in addition used for particle identification via the measurement of the specific ionization (dE/dx) in the detector gas.
Triggering and event characterization is performed via forward detectors, the V0 [41] and two Zero Degree Calorimeters (ZDC) [42]. The V0 detectors consist of two scintillator arrays positioned at z = −90 cm and z = +340 cm and cover the pseudo-rapidity ranges −3.7 ≤ η ≤ −1.7 and 2.8 ≤ η ≤ 5.1. The ZDCs, each one consisting of two quartz fiber sampling calorimeters, are placed at a distance of 114 m relative to the IP in both directions along the beam axis and are used to detect spectator nucleons.
The results presented in this article are based on data samples collected during the Pb-Pb data taking periods of the LHC in the years 2010 and 2011. In the case of the 2011 data sample the Minimum Bias (MB) Level-0 (L0) trigger condition was defined by the coincidence of signals in both V0 detectors along with a valid bunch crossing trigger. For the 2010 data sample, in addition, the detection of at least two hits in the ITS was required. Both MB trigger definitions lead to trigger efficiencies larger than 95% for inelastic Pb-Pb collisions. Electromagnetic interactions were rejected by the Level-1 (L1) trigger, which required a minimum energy deposition in the ZDC by spectator neutrons. The beam-induced background was further reduced during the offline analysis by selecting events according to the relative timing of signals in V0 and ZDC. The offline centrality selection is done using the sum of the two V0 signal amplitudes. By fitting the corresponding distribution with the results of Glauber model simulations, the average number of participants N part and the average nuclear overlap function T AA = N coll /σ inel NN for a given centrality class can be determined as described in [43]. Here, N coll is the average number of binary nucleon-nucleon collisions and σ inel NN the inelastic nucleon-nucleon cross section. The numerical values for N part , N coll , and T AA are tabulated in [12].
The 2010 data sample consists of 1.5 × 10 7 events, taken with the corresponding MB trigger. The 2011 event sample was enriched with central and semi-central Pb-Pb collisions by using thresholds on the V0 multiplicity at the L0 trigger. From the latter data set we analyzed 1.9 × 10 7 central (0-10% of the centrality distribution) and 1.7 × 10 7 semi-central (10-50%) events. The summed 2010 and 2011 data samples correspond to an integrated luminosity of L int = 26.4 ± 0.3(stat.) +2.1 −1.7 (syst.) µb −1 [12].  The left panels show the interval 0 < p T < 2.5 GeV/c and the right ones 2.5 < p T < 6 GeV/c. The upper panels display the opposite sign distributions together with the result of the mixed event procedure. In the lower panels the background subtracted distributions are shown and compared to the simulated line shape. Also, the signal-to-background ratio S/B and the significance of the signal are given.

Inclusive J/ψ
J/ψ candidates are reconstructed by combining opposite-sign (OS) pairs of electron/positron candidates and calculating their invariant mass m ee . These candidates are selected from tracks reconstructed in the ITS and the TPC by employing the set of quality criteria described in [12,44]. In order to reject the background from photon conversions in the detector material, tracks are required to have a hit in one of the SPD layers. In addition, at least 70 out of a maximum of 159 space points reconstructed in the TPC must be assigned to a given track, which also needs to fulfill a quality criterion of the track fit (χ 2 /nd f < 4). The tracks are required to be in the range |η| < 0.8, where the tracking and particle identification performance of the TPC is optimal, and to have p T > 0.85 GeV/c to improve the signalto-background ratio in the J/ψ mass region.
Electron candidates are selected by requiring that the dE/dx measurement in the TPC lies within a band [−1σ , +3σ ] around the momentum-dependent parameterization of the expected signal, where σ is the phase space dependent dE/dx resolution (details can be found in [45]). The selection is asymmetric in order to minimize the contribution from pions. To further suppress the hadron contamination, tracks that are compatible within ±4σ with the proton expectation are rejected. A side effect of this cut is that tracks below p T = 1 GeV/c are effectively removed.

Measurement of the inclusive J/ψ yield
The J/ψ signal counts N J/ψ are obtained from the number of entries in the background subtracted invariant mass distributions in the range 2.92 < m ee < 3.16 GeV/c 2 . The uncorrelated background is evaluated with a mixed event (ME) technique. In order to achieve a good description of the background only electrons and positrons from events with similar properties in terms of centrality, primary vertex position, and event plane angle are combined. The ME distributions are scaled to the same event (SE) distributions in the mass ranges 1.5 < m ee < 2.5 GeV/c 2 and 3.2 < m ee < 4.2 GeV/c 2 , so that the J/ψ signal region is excluded. The normalization area contains the ψ(2S) signal, but its contribution is negligible and can therefore be safely ignored. Also, contributions from the tail of the J/ψ signal shape to this mass interval are below the percent level and will thus not significantly affect the normalization. Figure 1 shows a comparison of the SE and ME invariant mass distributions for the 0-40% most central Pb-Pb collisions for electron-positron pairs at mid-rapidity (|y| < 0.8) in two p T intervals: 0 -2.5 GeV/c and 2.5 -6 GeV/c. The agreement between the SE and ME distributions outside the signal region is very good and allows signal extraction with significances larger than eight.
The J/ψ yield per MB event in a given p T interval, Y J/ψ , is obtained as Here BR ee is the branching ratio for the decay J/ψ → e + e − , N evts the number of events, and A × ε the phase space dependent product of acceptance A and reconstruction efficiency ε. The latter is calculated from Monte Carlo (MC) simulations as the ratio between the number of reconstructed and generated MC J/ψ, which are assumed to be unpolarized. In pp collisions at √ s = 7 TeV the J/ψ polarization has been measured and was found to be compatible with zero at mid-rapidity (p T > 10 GeV/c) and forward rapidity (p T > 2 GeV/c) [46][47][48]. In heavy-ion collisions no measurement exists, but J/ψ mesons produced from the recombination of charm quarks in the medium are expected to be unpolarized 1 . The MC events used for the calculation of A × ε are constructed by adding to background events, generated with the HIJING model [49], J/ψ mesons decaying into e + e − pairs, whose phase space distribution is obtained from extrapolations of other measurements [50], taking into account shadowing effects as parameterized in EKS98 [51]. The dielectron decay is simulated with the EvtGen [52] package, using the PHOTOS model [53] to describe the influence of final state radiation. This choice, together with the simulation of bremsstrahlung in the detector material, is mandatory for a proper description of the low mass tail in the measured J/ψ mass distribution and ensures that the fraction of the signal outside of the m ee integration window is properly accounted for in the correction A × ε . The propagation of the simulated particles is done by GEANT3 [54] and a full simulation of the detector response is performed. The same reconstruction procedure and cuts are applied to MC events and to real data. The quality of the simulation is illustrated by the good agreement of the background-subtracted invariant mass distributions with the MC simulation of the J/ψ signal shape, after normalizing it to the same integral as the measured signal (see Fig. 1).

Determination of the pp reference for R AA
From the corrected J/ψ yield Y J/ψ (p T ) the nuclear modification factor R AA (p T ) is calculated as . (2) Since no differential J/ψ measurement at mid-rapidity at low p T is available for pp collisions at √ s = 2.76 TeV [55], the reference needed for the construction of R AA is based on an interpolation of the midrapidity measurements by PHENIX at √ s = 0.2 TeV [56], CDF at √ s = 1.96 TeV [57], and ALICE at Here, z T is defined as p T / p T , a = Γ(3/2) Γ(n − 3/2)/Γ(n − 1), and c = 2(n − 1) a, where n is the only free fit parameter. The value for p T (calculated in the p T range 0 -10 GeV/c) at √ s = 2.76 TeV, which is needed to translate this parameterization into dσ /dp T , is determined by interpolating between the existing p T measurements for pp and pp collisions [55][56][57]. This interpolation is done using various functional forms for the √ s dependence to determine the systematic uncertainty. For the absolute normalization of the parametrized spectrum, the same interpolated value dσ /dy = 4.25 ± 0.28(stat.) ± 0.43(syst.) µb as in [12] is used.
The main sources of systematic uncertainties for the p T dependent R AA of inclusive J/ψ are the signal reconstruction procedure, the MC input kinematics, the uncertainties on the interpolated pp reference and on the nuclear overlap function. The corresponding values are summarized in Tab. 1. While the first two components are uncorrelated between the p T intervals (type II), the uncertainty due to the nuclear overlap function is fully correlated (type I). The pp reference on the other hand introduces both uncorrelated and correlated contributions. To determine the uncertainty related to the signal reconstruction, the normalization range of the ME background and the size and positions of the m ee bins have been varied. All track and electron selection criteria, such as the electron inclusion cut and the SPD hit requirement, have been relaxed and/or tightened in order to test the stability of the result, as was performed in [12]. The value of the systematic uncertainty is determined as the standard deviation of the distribution of all results obtained with the listed variations. The evaluation of the uncertainties associated with the MC input kinematics is also described in [12], while the uncertainty of the pp reference is estimated from the differences between the cross-section values obtained with the fitting procedure based on Eq. (3) and the measured values used for the fit at the various energies.

Determination of p T and p 2 T
Since the collected Pb-Pb statistics would allow the extraction of the J/ψ yield in a few p T intervals only, the average transverse momentum p T is determined by a fit to the distribution of the p T of e + e − pairs as a function of m ee . When building such a distribution, the individual e + e − pairs are weighted by the inverse of their acceptance times efficiency (A × ε) −1 , assuming that they come from the decay of a J/ψ. The resulting p T distributions are fitted by the expression Both factors S and B depend on m ee and correspond to the distribution of the J/ψ signal and of the background. For S the same background subtracted signal distribution S(m ee ) is used as for the extraction of the yield (see lower panels of Fig. 1), while the background B is generated from the ME sample, as The normalization factor is determined by fitting c B B ME (m ee ) to the corresponding m ee distribution of e + e − pairs excluding the signal region. For the sum S(m ee ) + B(m ee ) in the denominator of Eq. (4), the measured OS pair m ee distribution is used. The p T Bkg , defined as the p T of the combinatorial background pairs, is also calculated from the ME sample. This analysis is performed in three different centrality intervals: 0-10%, 10-40%, and 40-90%. Figure 2 shows the measured p T of the e + e − pairs in the p T range 0 -10 GeV/c together with the results of the fit procedure. In addition, with an equivalent method, the mean square transverse momentum p 2 T is also calculated for the same centrality intervals.
The systematic uncertainties of the p T measurement for inclusive J/ψ are mainly determined by the signal extraction, the stability of track and electron selection criteria and the fit procedure (see Tab. 2). While the first two components are not correlated between the different centrality intervals (type II), the systematic uncertainty intrinsic to the fit procedure can affect the data points in a correlated way (type I).
The uncertainties related to the signal extraction have been evaluated by varying the normalization range of the ME background, the size and positions of the m ee bins, the fit region and by using in addition to the ME background a linear function for the background description. In addition, the stability of the fit procedure was tested by modifying the approach, e.g. by using in the fit the direct sum of S and B, instead of the OS pair m ee distribution, or by using a fit function for B, instead of ME. It was also verified by applying the above described method to MC events, which were constructed by combining signal with background events with a realistic S/B ratio. It turned out that the procedure allows to recover the p T of the simulated J/ψ mesons within a 2% difference. This value is assumed as correlated (type I) uncertainty. Finally, the uncertainty in the signal-to-background ratio is propagated into the statistical uncertainty of the p T J/ψ .

Non-prompt J/ψ
The candidate selection for the non-prompt J/ψ analysis includes, in addition to the previously described criteria, the condition that at least one of the two decay tracks has a hit in the first SPD layer, in order to enhance the resolution of secondary vertices.  The non-prompt J/ψ fraction has been determined using an unbinned two-dimensional log-likelihood fit described in detail in [37], which is performed by maximizing the quantity where N is the total number of OS candidates in the range 2.2 < m ee < 4 GeV/c 2 and x is the pseudoproper decay length of the candidate Here L is the vector pointing from the primary vertex to the J/ψ decay vertex. F Sig (x) and F Bkg (x) (M Sig (m ee ) and M Bkg (m ee )) are Probability Density Functions (p.d.f.) describing the pseudo-proper decay length (invariant mass) distribution for signal and background candidates, respectively.
where F prompt (x) and F B (x) are the p.d.f. for prompt and non-prompt J/ψ, respectively, and f ′ B is the fraction of reconstructed J/ψ coming from beauty hadron decays A correction due to different average A × ε values, in a given p T interval, for prompt and non-prompt J/ψ, is necessary to obtain from f ′ B the fraction of produced non-prompt J/ψ, f B The various ingredients for the determination of f B are described in the following:

Monte Carlo p T distributions and polarization assumptions
Assuming both prompt and non-prompt J/ψ to be unpolarized, at a given p T their acceptance times efficiency values A × ε are the same. However, the p T distributions of prompt and non-prompt J/ψ can be different, resulting in different average A × ε computed over a p T range of finite size. Different hypotheses for the kinematical (p T ) distributions of both prompt and non-prompt J/ψ are considered, i.e. including or excluding shadowing or suppression effects as, e.g., those predicted in references [58][59][60] for non-prompt J/ψ. Due to the weak p T dependence of A × ε , the resulting uncertainty on f B is small, being ∼ 5% at low p T and ∼ 3% in the highest p T bin, and is independent of centrality.
At a given p T , prompt and non-prompt J/ψ can have different polarization and therefore a different acceptance. However, the polarization of J/ψ from b-hadron decays is expected to be small due to the averaging effect caused by the admixture of various exclusive B → J/ψ + X decay channels. Indeed, in more elementary colliding systems, the sizable polarization, which is observed when the polarization axis refers to the B-meson direction [61], is strongly smeared when calculated with respect to the direction of the daughter J/ψ [62], as observed by CDF [63]. The central values of the fraction of non-prompt J/ψ are evaluated with Eq. (9) assuming unpolarized prompt J/ψ and a polarization of non-prompt J/ψ as predicted by EVTGEN [52]. The assumption of a null polarization for non-prompt J/ψ results in a relative decrease of f B by only 1% at high p T (4.5 -10 GeV/c) and 3% at low p T (1.5 -4.5 GeV/c). The relative variations of f B expected in extreme scenarios for the polarization of prompt J/ψ was studied in [44]. The uncertainties related to the polarization of prompt and non-prompt J/ψ are are not further propagated to the results.
P.d.f. for prompt J/ψ: F prompt (x) The x distribution F prompt (x) for prompt J/ψ, which decay at the primary vertex, coincides with the resolution function R(x), which describes the accuracy by which x can be reconstructed. It also enters in the p.d.f. describing the x distributions of non-prompt J/ψ, F B (x), and of the background candidates, F Bkg (x). The determination of R(x) is based on the same MC data sample as used for the inclusive J/ψ analysis (see Sect. 2.1). The systematic uncertainty on R(x) was estimated with a MC approach by propagating the maximum observed discrepancies of the track parameters (space and momentum variables) between data and MC to the x variable [45, 64,65] and was found to be at most 10%. To propagate this systematic uncertainty to the final results the fits are repeated after modifying in the loglikelihood function the resolution to (1/(1 + δ )) × R (x/(1 + δ )). In this expression δ parameterizes the relative variation of the RMS of the resolution function and is varied between −10% and +10%. The systematic uncertainty due to the resolution function is smaller in the highest p T bin, because of the better resolution in the x variable and the higher values of the signal-to-background ratio.

P.d.f. for non-prompt J/ψ: F B (x)
The shape of the x distribution of non-prompt J/ψ is estimated by using PYTHIA 6.4.21 [66] in the Perugia-0 tune [67] to generate beauty hadrons at √ s = 2.76 TeV, and the EvtGen package [52] to describe their decays. The systematic uncertainty related to this shape is estimated by assuming a softer p T distribution for the non-prompt J/ψ which is obtained by adding the suppression effects as predicted in [60] and a harder one taken from the same PYTHIA event generator at √ s = 7 TeV instead of 2.76 TeV. The resulting systematic uncertainty is within 3 -4%.

P.d.f. for the background: F Bkg (x)
The main difference of the analysis presented in this section, with respect to previous work on pp collisions [37], concerns the description of F Bkg (x). In this analysis such a function includes an extra symmetric exponential tail (∝ e −|x|/λ sym ) [57] and depends on the invariant mass and the p T of the dielectron pair. It is determined, for each centrality class, by a fit to the data in three p T regions (1.5 -3, 3 -4.5, 4.5 -10 GeV/c) and in four invariant mass regions on the side-bands of the J/ψ mass peak (2.2 -2.6, 2.6 -2.8, 3.16 -3.5, 3.5 -4 GeV/c 2 , labelled with the indices 1, 2, 3 and 4, respectively), for a total of 3 × 4 combinations. The background function in the invariant mass region 2.8 -3.16 GeV/c 2 and in each of the three p T ranges are obtained by an interpolation procedure as the weighted combination of the p.d.f. determined in the other four invariant mass regions. The weights are chosen inversely proportional to the absolute difference (or its square) between the mean of the invariant mass distribution in the given mass interval and that in the interpolated region Optionally, only the two adjacent mass regions can be considered in the interpolation procedure, corresponding to the condition w 1 = w 4 = 0. The central value of f B has been determined as the average of the values obtained with the different assumptions (n = 1 or n = 2, with or without the condition w 1 = w 4 = 0). The RMS of the distributions of the relative variations obtained for f B is used to define the systematic uncertainty. It becomes larger for central events and in the lowest p T interval, where the signal-to-background ratio S/B is lower. This approach allows to cope with the much lower S/B ratio in Pb-Pb than in pp collisions.

P.d.f. for the invariant mass distribution of the signal: M Sig (m ee )
The shape of the invariant mass distribution for the signal is determined by the same MC simulations described in Sect. 2.1. The influence of detector material budget is studied with dedicated MC simulations, where the material budget is varied within its uncertainty (±6%) [68]. The resulting contribution to the systematic uncertainty on f B slightly increases for central events, and ranges from 2 to 4%.

P.d.f. for the invariant mass distribution of the background: M Bkg (m ee )
The shape of the invariant mass distribution for the background candidates is determined from ME pairs. The related systematic uncertainty on f B is evaluated using the like-sign distribution, instead of the ME one. The uncertainty increases at higher centrality and in the lowest p T interval due to the decrease of the S/B ratio.  Table 3: Systematic uncertainties (in percent) on the measurement of the fraction f B of J/ψ from the decay of beauty hadrons, for different centrality intervals in the transverse momentum range 1.5 < p T < 10 GeV/c, and in the two p T intervals for the most central collisions. The contributions which are fully correlated between the different centrality classes are denoted as type I, the uncorrelated ones as type II.
As an example in Fig. 3 the projections of the best fit function for n = 1 and w 1 = w 4 = 0 are shown superimposed to the invariant mass (upper panel) and x (lower panel) distributions of the candidates in the centrality range 10-50% for 1.5 < p T < 10 GeV/c.
A summary of the systematic uncertainties on the determination of the non-prompt J/ψ fraction is provided in Tab. 3 for the three centrality intervals in the integrated p T range and, in the two p T ranges where the results will be given, for the most central collisions (0-10%).
The value of f B is determined in two p T bins (1.5 -4.5 and 4.5 -10 GeV/c) for the 0-50% centrality range and in three centrality classes (0-10%, 10-40% and 40-90%) for 1.5 < p T < 10 GeV/c. The f B measurements are then combined with the nuclear modification factors of inclusive J/ψ to get the non-prompt and prompt J/ψ R AA

pp interpolation
The value of f B in pp collision at √ s = 2.76 TeV, f pp B , is needed to compute the R AA for prompt and non-prompt J/ψ mesons, see Eq. (11). It is determined by an interpolation procedure. Therefore, a fit is performed to the existing measurements of f B as a function of p T in mid-rapidity pp collisions at √ s = 7 TeV (ALICE [37], ATLAS [35] and CMS [69]). The function used to fit the data is chosen as which is the ratio of the differential cross section for non-prompt J/ψ obtained by an implementation of pQCD calculations at fixed order with next-to leading-log resummation (FONLL) [70] to that for inclusive J/ψ, parameterized by the phenomenological function defined in Eq. (3). A similar fit is then performed to the CDF results [57] in pp collisions at √ s = 1.96 TeV. Finally, the f pp B (p T ) value at √ s = 2.76 TeV is determined by an energy interpolation, which gives f pp B = 0.122 ± 0.010 in the integrated p T range 1.5 -10 GeV/c. The quoted uncertainty includes: (i) a component from the fit procedure, which depends on the uncertainties of both data and FONLL predictions; (ii) the systematic uncertainty due to the energy interpolation, which has been estimated by considering different functional forms of the √ s dependency (linear, exponential and power law); (iii) an additional systematic uncertainty, which has been obtained by repeating the whole fitting procedure after excluding, one at a time, the data samples used for the f B fit in pp collisions at √ s = 7 TeV.

Centrality
p T (GeV/c) p 2 T (GeV 2 /c 2 ) 0-10% 2.23 ± 0.10 ± 0.08 5.50 ± 0.58 ± 0.25 10-40% 2.01 ± 0.12 ± 0.08 4.97 ± 0.65 ± 0.34 40-90% 2.02 ± 0.19 ± 0.29 5.15 ± 1.05 ± 1.23 pp 2.54 ± 0.02 ± 0.01 9.07 ± 0.15 ± 0.07 The numerical values of p T and p 2 T calculated in the range 0 < p T < 10 GeV/c for the three analyzed centrality intervals in Pb-Pb collisions (the first uncertainty is the statistical and the second is the uncorrelated systematic (type II), the correlated uncertainty has a value of 2%, see Tab. 2). The values for pp collisions obtained by the interpolation procedure are given as a reference. Figure 4 shows the p T of inclusive J/ψ for the three analyzed centrality intervals. The numerical values for p T are summarized in Tab. 4. As a reference, the p T in pp collisions at the same centreof-mass energy, as determined by the interpolation method described in Sect. 2.1, is also presented. The p T for Pb-Pb collisions is significantly smaller than that for pp collisions. Such a behaviour is not observed at smaller centre-of-mass energies (see left panel of Fig. 4), for which no significant system size dependence of p T is seen. This might indicate the onset of processes which either deplete the high p T region or enhance the J/ψ production at low p T in heavy-ion collisions at the LHC. The latter effect would be expected as a consequence of a significant contribution from cc coalescence.

Results
It has been suggested [76] that the observable r AA = p 2 T AA / p 2 T pp should be particularly sensitive to  [74,75] in the right panels of Figs. 4 and 5. This model includes regeneration and dissociation processes, based on in-medium J/ψ spectral functions, throughout the evolution of a thermally expanding fireball. It also incorporates nuclear shadowing by reducing the input charm cross section by a factor of up to 1/3, with a centrality dependence as estimated in [77]. There is a fair agreement between our p T results and the model calculation, while the r AA is poorly reproduced by the model. Our p T and r AA results are also compared with the calculations by Zhou et al. [73]. These calculations are also based on a transport approach and incorporate dissociation and regeneration of J/ψ and heavier charmonia, as well as nuclear shadowing according to EKS98 [51]. The agreement with the r AA measurement is rather poor. It must be noted that our results from Pb-Pb collisions at forward rapidity [78] exhibit a continuous decrease of p T and r AA from peripheral towards central events and are thus closer to the theory predictions, while the behaviour of mid-rapidity Pb-Pb results is more compatible with a flat N part dependence.
The R AA of inclusive J/ψ in three p T intervals is shown in Fig. 6 along with the results by the CMS collaboration for the interval 6.5 < p T < 30 GeV/c [13], and 0.58 ± 0.06(stat.) ± 0.08(syst.) for 2.5 < p T < 6 GeV/c, where the systematic uncertainties quoted here are the uncorrelated (type II) ones, as listed in Tab. 1. The data point for 4.5 < p T < 10 GeV/c corresponds to the R AA value given in Tab. 5 (centrality range 0-50%). Note that the binning and centrality selection chosen for the R AA values in Tab. 5 is optimized for the extraction of non-prompt J/ψ and therefore differs from the one used for the inclusive J/ψ analysis. The results obtained with the two binnings are in very good agreement. Table 5 also contains the R AA values for prompt J/ψ, which are numerically identical to the ones for inclusive J/ψ. The inclusive R AA values below p T = 6 GeV/c are significantly higher than those measured at higher p T , corresponding to a decrease of R AA with increasing p T , while the high p T data point is close to the CMS measurement. This p T dependence is similar to the one observed at forward rapidity [12], and is in clear contrast to the p T dependence measured at lower centre-of-mass energies by the PHENIX collaboration for √ s NN = 0.2 TeV [9]. Figure 6 also shows the model predictions by Zhou et al. [73]. The value of the predicted R AA is systematically below the measurement and exhibits a p T dependence similar to the one in the data. The prediction by Zhao et al. [74,75] is close to our result. In both models, the rise of R AA towards p T = 0 is due to the dominant contribution from J/ψ regeneration via coalescence.
The fraction of non-prompt J/ψ in the p T range 1.5 -10 GeV/c is shown as a function of the number of participants for the centrality intervals 40-90% ( N part = 38), 10-40% ( N part = 192), and 0-10% ( N part = 356) in the left panel of Fig. 7. Within uncertainties, no centrality dependence is observed.
The p T dependence of f B (centrality: 0-50%) is shown in the right panel of Fig. 7 and compared with the measurements by CMS in the centrality interval 0-100% and p T > 6.5 GeV/c (for the numerical values see Tab [69]) and in pp collisions at √ s = 1.96 TeV (CDF [57]). Considering the ALICE and CMS results in Pb-Pb collisions together, a similar p T dependence as in pp is observed. However, this similarity could be coincidental, being due to a compensation of the medium effects on the prompt component (J/ψ dissociation and recombination) and on the non-prompt part (b-quark energy loss).
In Fig. 8 the nuclear modification factor for non-prompt J/ψ for 1.5 < p T < 4.5 GeV/c and 4.5 < p T < 10 GeV/c is shown together with the result by CMS for 6.5 < p T < 30 GeV/c [13] and with theoretical model predictions [30,31,[58][59][60][79][80][81][82]. One should note that the centrality ranges are not the same for ALICE (0-50%) and CMS (0-20% and 20-100%). However, the results obtained by CMS for these two centrality bins are compatible with each other, and also compatible with our measurement in the high p T interval (4.5 < p T < 10 GeV/c). The model by Uphoff et al. [60] follows a partonic transport approach based on the Boltzmann equation, which allows interactions among all partons. It does not include radiative processes for heavy quarks. The calculation has been performed for a fixed impact parameter b = 5 fm. In the model of Alberico et al. [58,59] the propagation of the heavy quarks in the medium is described by the relativistic Langevin equation. The   shown as filled boxes at unity. Results by CMS for higher p T in the centrality range 0-20% and 20-100% [13] are also shown (the two points have been slightly displaced horizontally for better visibility). The data are compared to theoretical predictions at mid-rapidity (see text for details). In the right panel, the ALICE result in the p T interval 4.5 < p T < 10 GeV/c is compared to theoretical predictions integrated over the same p T range.
of R AA is strongly influenced by the choice of transport coefficients. Two values are considered, either as provided by a perturbative calculation (hard thermal loop approach) or extracted from lattice-QCD simulations. The calculations have been provided for the centrality range 0-50%. A transport approach, which is based on a strong-coupling scheme, is employed in the model of He et al. [79]. The transport is implemented using non-perturbative interactions for heavy quarks and mesons through the QGP, hadronization and hadronic phases of a nuclear collision. In particular, the elastic heavy-quark scattering in the QGP is evaluated within a thermodynamic T-matrix approach, by generating resonances close to the critical temperature that can in turn recombine into B mesons, followed by hadronic diffusion using effective hadronic scattering amplitudes. The hydrodynamic evolution of the system is quantitatively constrained by the measured transverse momentum distributions and elliptic flow of light hadrons. Radiative processes, which should improve the description at high p T , are not included in this approach. The calculations have been performed in the centrality range 0-50%. The model of Vitev et al. [30,31] assumes the existence of open heavy flavour bound-state solutions in the QGP in the vicinity of the critical temperature. A description of beauty quark quenching is combined with B meson inelastic breakup processes. Furthermore, modified beauty parton distribution functions and beauty fragmentation functions in a co-moving plasma are implemented in this calculation. The prediction is shown for a fixed centrality, corresponding to N part = 200, a value very close to the average number of participants in the centrality range 0-50%. In the model, a sizable fraction of the suppression is ascribed to the inelastic break-up processes (collisional dissociation), as can be deduced from Fig. 8 by comparing the full model prediction with and without the contribution of this specific process. The model of Djordjevic [80], shown in Fig. 8 for the centrality range 0-50%, uses a formalism that takes into account finite size dynamical QCD medium with finite magnetic mass effects and running coupling. In the WHDG model [81] (centrality range 0-50%) the energy loss is computed using perturbative QCD and considering both elastic and inelastic partonic collisions and path length fluctuations. Finally, in the model of Horowitz and Gyulassy [82], also applied to the centrality interval 0-50%, the string inspired AdS/CFT gravity-gauge theory correspondence [83,84] is applied to the case of heavy quark energy loss. In the right hand inset of Fig. 8, the ALICE R AA value, integrated over the range 4.5 < p T < 10 GeV/c, is compared to theoretical predictions computed in the same p T range. Most of the models predict a larger value of R AA than observed in the measurement. However, more precise data are needed to discriminate among the different models. The next LHC run will provide increased statistics for this measurement.

Conclusions
A study of J/ψ production at mid-rapidity in Pb-Pb collisions at √ s NN = 2.76 TeV has been presented.
A reduction of the inclusive J/ψ p T between pp and Pb-Pb collisions is observed. The ratio r AA = p 2 T AA / p 2 T pp is found to be significantly below unity, corresponding to a medium-induced change in the shape of the p T spectra. The nuclear modification factor R AA depends on p T . It is around 0.8 for p T < 2.5 GeV/c and reaches, at higher p T , almost the same level of suppression as observed at RHIC energies at low p T . These observations might be indicative of a sizable contribution of charm quark coalescence to the J/ψ production at low p T . Transport models including this additional component are able to qualitatively describe the features seen in the data.
The fraction of J/ψ from beauty hadron decays is determined as a function of centrality and p T . No significant centrality dependence is observed. By combining this measurement with the inclusive J/ψ results the R AA of non-prompt J/ψ is obtained in the region 1.5 < p T < 10 GeV/c, thus extending the coverage of CMS to the low p T region. The nuclear modification in the region 4.5 < p T < 10 GeV/c is found to be stronger than predicted by most of the models.