Measurement of prompt ψ (2S) to J/ ψ yield ratios in Pb-Pb and p-p collisions at √ sNN = 2.76 TeV

The ratio between the prompt ψ(2S) and J/ψ yields, reconstructed via their decays into μ+ μ-, is measured in Pb-Pb and p-p collisions at sqrt[sNN]=2.76  TeV. The analysis is based on Pb-Pb and p-p data samples collected by CMS at the Large Hadron Collider, corresponding to integrated luminosities of 150  μb(-1) and 5.4  pb(-1), respectively. The double ratio of measured yields (Nψ(2S)/N(J/ψ))(Pb-Pb)/(Nψ(2S)/N(J/ψ))(p-p) is computed in three Pb-Pb collision centrality bins and two kinematic ranges: one at midrapidity, |y|<1.6, covering the transverse momentum range 6.5<pT<30  GeV/c, and the other at forward rapidity, 1.6<|y|<2.4, extending to lower pT values, 3<pT<30  GeV/c. The centrality-integrated double ratio changes from 0.45±0.13(stat)±0.07(syst) in the first range to 1.67±0.34(stat)±0.27(syst) in the second. This difference is most pronounced in the most central collisions.

1 matched to tracks in the silicon tracker, using an algorithm optimized for the heavy-ion environment [24,25]. In addition, an iterative track reconstruction algorithm [26] is applied to the PbPb data, limited to cone regions defined by the standalone muons. The pp reconstruction algorithm includes an iterative tracking step in the full silicon tracker. The final parameters of the muon trajectory are obtained from a global fit of the standalone muon with a track in the silicon tracker. The single muon acceptance and identification criteria are the same as in Ref. [6]. Opposite-sign muon pairs are fitted with a common vertex constraint and are kept if the fit χ 2 probability is greater than 1%. Most of the non-prompt J/ψ and ψ(2S) mesons, originating from b-hadron decays, are rejected using the pseudo-proper decay length, ψ = L xy m ψ /p T , where L xy is the transverse distance between the µ + µ − vertex and the interaction point and m ψ is the J/ψ or ψ(2S) mass. The ψ selection condition is tuned with Monte Carlo (MC) simulation studies, separately for the pp and PbPb collision systems, such that 90% of the prompt J/ψ and ψ(2S) are kept, typically rejecting 80% of the non-prompt ones. For these studies, unpolarized prompt and non-prompt J/ψ and ψ(2S) mesons are generated with PYTHIA 6.424 [27] and decayed with EVTGEN [28], while the final-state bremsstrahlung is simulated with PHOTOS [29]. The signal events are embedded in underlying heavy-ion events, generated with HYDJET 1.8 [30], at the level of detector hits and with matching vertices. The detector response is simulated with GEANT4 [31] and the resulting information is processed through the full event reconstruction chain, including trigger emulation. The selection efficiency cancels in the double ratio and the remaining non-prompt contamination is accounted for as a systematic uncertainty.
The analysis is performed in two dimuon kinematic domains: the "midrapidity" domain covers the range |y| < 1.6, where the J/ψ and ψ(2S) mesons are only reconstructed for p T > 6.5 GeV/c, while the "forward rapidity" domain covers the range 1.6 < |y| < 2.4, where the acceptance extends down to p T = 3 GeV/c. Dimuons are restricted to p T < 30 GeV/c in order to have a well defined kinematic interval. The available PbPb data at forward rapidity could not be fitted reliably when split into the intervals 3 < p T < 6.5 GeV/c and 6.5 < p T < 30 GeV/c. Therefore, this analysis cannot differentiate between p T and rapidity dependent effects on the measured double ratios. The PbPb sample is split in three bins of collision centrality, defined using fractions of the inelastic hadronic cross section where 0% denotes the most central collisions: 40-100%, 20-40%, and 0-20%. This fraction is determined from the HF energy distribution [32]. Related variables, such as the number of nucleons participating in the collision (N part ), are evaluated using a Glauber-model calculation [33] and are only used to display the centrality dependence of the measurements. The average N part values corresponding to the three centrality bins above are N part = 32.8, 158.7, and 308.4, respectively. Figure 1 shows the dimuon invariant-mass (m µ + µ − ) distributions measured in central (0-20%) PbPb and pp collisions, for the midrapidity and forward rapidity bins. The results of unbinned maximum likelihood fits are also shown. Each charmonium resonance is described by the sum of a Gaussian function and a Crystal Ball (CB) function [34], with common mean m 0 , independent widths σ G and σ CB , and relative contribution of the Gaussian to the signal yield f G . In all cases, the fitted J/ψ mean agrees within 0.3% with the world average [35]. The resolution, after averaging the Gaussian and CB widths, is about 30 MeV/c 2 at midrapidity and 50 MeV/c 2 at forward rapidity, both for pp and PbPb data. The CB radiative tail parameters α and n, common to both charmonia, are fixed to the values obtained in fits to simulated distributions. The m 0 , σ G , and σ CB parameters of the ψ(2S) resonance shape match the J/ψ parameters, scaled by the ratio of their masses, m ψ(2S) /m J/ψ [35]. This scaling assumption has been validated in analyses of larger event samples [21,36]. The same value for f G is used in the definition of the ψ(2S) and J/ψ signal shapes. Six parameters are left free in the pp fit: m 0 , σ G , σ CB , f G , the J/ψ yield, and the ψ(2S) to J/ψ yield ratio. In the PbPb fits, instead, the double ratio replaces collisions, for |y| < 1.6 and 6.5 < p T < 30 GeV/c (top) as well as 1.6 < |y| < 2.4 and 3 < p T < 30 GeV/c (bottom). The results of unbinned maximum likelihood fits are also shown. The ψ(2S) region is magnified in the insets.
the ψ(2S) to J/ψ ratio as one of the free parameters. In addition, given their smaller signal-tobackground ratio, the PbPb data are fitted fixing the σ G /σ CB ratio to the value obtained in fits to MC distributions.
The background is described by Chebychev polynomials, of order (0 ≤ N ≤ 3) determined for each analysis bin with log-likelihood ratio (LLR) tests. The background shape is mostly determined by the kinematic distributions of the muons produced in meson decays, which are expected to change with collision centrality [6, 37, 38]. Once the background functions are selected, the pp and three PbPb centrality samples are fitted simultaneously. Since the signal shape does not depend on the collision centrality [6], the three PbPb centrality bins are fitted with common signal shape parameters, which are independent of the pp values; the four background shapes are independent. The simultaneous fit directly provides the three double ratios (one per centrality class), for each rapidity interval.
The systematic uncertainties from the fitting method are studied by varying the signal and background shapes as well as the fitted invariant-mass range. As an alternative signal shape, the sum of two CB functions with common mean and tail parameters is used, leaving all parameters free in the fit except for the mass scaling between the J/ψ and ψ(2S) means and widths. The uncertainty on the background is evaluated by considering three fit variations: (i) use as background shape an exponential function with a Chebychev polynomial of order 1 ≤ N ≤ 3 (determined with a LLR test) as an argument; (ii) extend the fitted mass region to 1.8 < m µ + µ − < 5 GeV/c 2 ; (iii) fit the J/ψ and ψ(2S) regions (below 3.5 GeV/c 2 and above 3.3 GeV/c 2 , respectively) with independent background functions. The maximum deviation from the nominal fit is added in quadrature with the signal shape uncertainty to obtain the fit systematic uncertainty in the double ratio, which varies between 8% at midrapidity and 28% at forward rapidity. The dominant contribution to this uncertainty changes from bin to bin because of the strongly varying signal-to-background ratio. Adding in quadrature the uncertainties mentioned above leads to total systematic uncertainties of 13-30%, values smaller than the corresponding statistical uncertainties.
The double ratio of measured yields, (N ψ(2S) /N J/ψ ) PbPb /(N ψ(2S) /N J/ψ ) pp , is shown in Fig. 2 as a function of centrality, for both kinematic bins. The quadratic sum of the pp statistical and systematic uncertainties (≈6%) is common to all centralities. The centrality-integrated results are also displayed, in the right panel. In the most peripheral PbPb collisions, no significant ψ(2S) signal has been observed in the midrapidity bin and an upper limit of 0.47 at 95% confidence level (CL) is set on the double ratio, using the Feldman-Cousins method [42].
In the midrapidity bin, restricted to p T > 6.5 GeV/c, the double ratio is below unity in all cen-  trality bins, with a centrality-integrated value of 0.45 ± 0.13 (stat) ± 0.07 (syst), including the global pp uncertainties. In the forward rapidity bin, which extends down to p T = 3 GeV/c, the centrality-integrated double ratio increases to 1.67 ± 0.34 (stat) ± 0.27 (syst). While the forward-rapidity double ratio is consistent with unity in peripheral PbPb collisions, it becomes 2.31 ± 0.53 (stat) ± 0.37 (syst) ± 0.15 (pp) in the 20% most central collisions, indicating that the ψ(2S) to J/ψ yield ratio is enhanced in central PbPb collisions with respect to pp collisions (the hypothesis of being compatible with unity has a p-value of only 0.011).
Nuclear modification factors for prompt ψ(2S) production, R AA (ψ(2S)), can be derived by multiplying the centrality-integrated double ratios by the corresponding prompt J/ψ R AA which can be found in Ref. [6]. The resulting centrality-integrated R AA values for ψ(2S) are 0.13 ± 0.04 (stat) ± 0.02 (syst) ± 0.01 (pp) at midrapidity and 0.67 ± 0.16 (stat) ± 0.11 (syst) ± 0.07 (pp) at forward rapidity. While the ψ(2S)/J/ψ ratio at low p T (forward rapidity) is enhanced in central PbPb collisions, as compared to pp, the yield of ψ(2S) itself in PbPb collisions is still suppressed in comparison to the yield in pp collisions scaled by the number of inelastic nucleonnucleon collisions.
In summary, the CMS measurements reported in this Letter show two interesting observations. First, ψ(2S) production is suppressed in PbPb collisions with respect to pp collisions, in both kinematic regions investigated. Second, in comparison to J/ψ production and in the most central PbPb collisions, ψ(2S) production is suppressed in the range |y| < 1.6 and 6.5 < p T < 30 GeV/c, as expected in the sequential melting scenario and matching the corresponding bottomonia pattern [21], while it is enhanced in the range 1.6 < |y| < 2.4 and 3 < p T < 30 GeV/c. Such behavior implies the presence of physics processes that either cause the p T dependence of R AA (ψ(2S)) to be weaker than for the R AA (J/ψ) or cause the R AA (ψ(2S)) to start decreasing at higher p T . Alternatively, these processes would have to have the opposite dependence with increasing rapidity. Larger event samples are needed to evaluate in more detail how these observations depend separately on the p T and rapidity of the charmonium states.