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Centrality dependence of ψ(2S) suppression in p-Pb collisions at √sNN=5.02 TeV

ALICE Collaboration; González Ferreiro, Elena

Abstract

The inclusive production of the (2S) charmonium state was studied as a function of centrality in p-Pb collisions at the nucleon-nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement was performed with the ALICE detector in the center of mass rapidity ranges -4:46 < ycms < -2:96 and 2:03 < ycms < 3:53, down to zero transverse momentum, by reconstructing the (2S) decay to a muon pair. The (2S) production cross section (2S) is presented as a function of the collision centrality, which is estimated through the energy deposited in forward rapidity calorimeters. The relative strength of nuclear e ects on the (2S) and on the corresponding 1S charmonium state J/ is then studied by means of the double ratio of cross sections [σ ψ(2S) /σJ/ψ ]pPb /[σ ψ(2S) /σJ/ψ ]pp between p-Pb and pp collisions, and by the values of the nuclear modi cation factors for the two charmonium states. The results show a large suppression of ψ(2S) production relative to the J/ψ at backward (negative) rapidity, corresponding to the ight direction of the Pb-nucleus, while at forward (positive) rapidity the suppressions of the two states are comparable. Finally, comparisons to results from lower energy experiments and to available theoretical models are presented.

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JHEP06(2016)050 Published for SISSA by Springer Received:March 11, 2016 Revised:May 13, 2016 Accepted:May 27, 2016 Published:June 8, 2016 Centrality dependence of ψ(2S) suppression in p-Pb collisions at √sNN = 5.02 TeV The ALICE collaboration E-mail: [email protected] Abstract: The inclusive production of the ψ(2S) charmonium state was studied as a function of centrality in p-Pb collisions at the nucleon-nucleon center of mass energy √sNN = 5.02 TeV at the CERN LHC. The measurement was performed with the ALICE detector in the center of mass rapidity ranges −4.46 < ycms <−2.96 and 2.03 < ycms <3.53, down to zero transverse momentum, by reconstructing the ψ(2S) decay to a muon pair. The ψ(2S) production cross section σψ(2S) is presented as a function of the collision centrality, which is estimated through the energy deposited in forward rapidity calorimeters. The relative strength of nuclear effects on the ψ(2S) and on the corresponding 1S charmonium state J/ψis then studied by means of the double ratio of cross sections [σψ(2S)/σJ/ψ]pPb/[σψ(2S)/σJ/ψ]pp between p-Pb and pp collisions, and by the values of the nuclear modification factors for the two charmonium states. The results show a large suppression of ψ(2S) production relative to the J/ψat backward (negative) rapidity, corresponding to the flight direction of the Pb-nucleus, while at forward (positive) rapidity the suppressions of the two states are comparable. Finally, comparisons to results from lower energy experiments and to available theoretical models are presented. Keywords: Heavy Ion Experiments, Quark Gluon Plasma ArXiv ePrint: 1603.02816 Open Access, Copyright CERN, for the benefit of the ALICE Collaboration. Article funded by SCOAP3. doi:10.1007/JHEP06(2016)050 JHEP06(2016)050 Contents 1 Introduction 1 2 Experimental conditions 3 3 Data analysis 3 4 Results 7 5 Conclusions 11 The ALICE collaboration 16 1 Introduction Charmonia are bound states of a charm and an anticharm quark (cc), and represent an important testing ground for the properties of the strong interaction. In high-energy protonproton collisions, the charmonium production process is usually factorized in two steps: the creation of a cc pair followed, on a longer time scale, by the binding and emission of one or more gluons that brings the pair to a colour singlet state. This process is described reasonably by theoretical models inspired by Quantum Chromodynamics (QCD) [1], although a quantitative evaluation of the production cross sections and polarization of the charmonium states still meets difficulties [1,2]. If a charmonium state is produced within the nuclear medium, as can happen in protonnucleus collisions, several effects become important and might influence the charmonium formation. In particular, the modification in the nucleus of the parton distribution functions (shadowing/anti-shadowing) [3–5], can lead to a suppression or an enhancement of the charmonium production. Furthermore, the incoming partons, as well as the outgoing cc pair, may lose energy in the nuclear medium, altering the differential distributions of the produced charmonium state [6]. Finally, once the bound state is formed, it may be dissociated via collisions within nuclear matter [7–9]. However, the formation of the final-state resonance occurs in a finite time τfwhich, depending on the kinematics of the cc pair and on the collision energy, may be longer than its crossing time, τc, in the nucleus. Among the narrow charmonium states, i.e. those with a mass smaller than twice the mass of the lightest D mesons, we address in this paper the vector states (JPC = 1−−) J/ψ, characterized by a binding energy ∆E∼650 MeV (corresponding to the mass gap to the open charm threshold), and the weakly bound ψ(2S), with ∆E∼50 MeV [10]. A comparison of the production cross section of the two states in proton-nucleus collisions offers interesting insights into the size of the various cold nuclear matter (CNM) effects outlined above. In particular, shadowing acts on the initial state partons and has a nearly identical size for the two resonances [11,12]. Therefore, its effect largely cancels out – 1 – JHEP06(2016)050 when studying the ratio of their production cross sections. Also coherent energy loss mechanisms [6], have a similar effect on the two resonances, due to the fact that they act on a compact cc pair not yet evolved into a final color singlet state. On the contrary, the break-up probability of the final resonance inside the nucleus should be much larger for the weakly bound ψ(2S) [13]. Early results on J/ψand ψ(2S) production in proton-nucleus collisions were obtained at fixed target experiments by E866 [14] at FNAL (√sNN = 63 GeV), by HERA-B [15] at HERA (√sNN = 39 GeV) and by NA38, NA50, NA60 [16–18] at the CERN SPS (√sNN = 17–29 GeV). At mid-rapidity, i.e., close to ycms = 0, the relative production cross section σψ(2S)/σJ/ψ was found to decrease rather strongly for increasing mass number of the nuclear target. Since part of the kinematic domain accessed at fixed target energies is characterized by τf< τc[9], such an observation can indeed be related to a stronger break-up effect on the weakly bound ψ(2S). At collider energies, it becomes technically more difficult to have data samples corresponding to various nuclear colliding species. Therefore, in order to vary the thickness of CNM crossed by the cc pair, one can rather select classes of events based on estimators of the geometry (centrality) of the collision, corresponding to various ranges in the number of nucleon-nucleon collisions Ncoll. This procedure was followed by the PHENIX experiment at RHIC, which studied the nuclear modification factors, defined as the ratio between the measured yields in d-Au and proton-proton collisions, normalized to Ncoll, for the J/ψand ψ(2S) resonances at mid-rapidity [19]. At √sNN = 200 GeV, the nuclear modification factors were smaller by a factor ∼3 for ψ(2S) relative to J/ψfor central events, indicating a stronger suppression for ψ(2S). However, such an observation is surprising since for mid-rapidity production at RHIC energies the time spent by the cc pair in the nucleus (τc<0.05 fm/c) is below the formation time of the final-state resonance (most theory estimates [9,20,21] give τf>0.15 fm/c). In such a situation, one would rather expect a similar suppression for the J/ψand ψ(2S) states. At the LHC, centrality-integrated results on the ψ(2S) and J/ψresonances for p-Pb collisions at √sNN = 5.02 TeV were obtained by ALICE [22,23] and LHCb [24,25]. At both forward (positive) and backward (negative) rapidities, corresponding to the p-going and Pb-going directions respectively, a significantly larger suppression of ψ(2S) compared to J/ψwas observed, relative to proton-proton collisions. Again, this result was unexpected, as the τcvalues are either at most the same order of magnitude (at negative ycms) or more than two orders of magnitude smaller (at positive ycms) than τf[22]. Therefore, additional effects, as the interaction of the loosely bound ψ(2S) with a hadronic or partonic medium produced in the collision, might be necessary in order to explain the results [11,26]. As outlined above, a differential measurement as a function of the collisions centrality is equivalent to a study of the propagation of the cc pairs over various thicknesses of CNM. In this Letter, we go in that direction by showing results obtained by the ALICE Collaboration on ψ(2S) studies in p-Pb collisions as a function of centrality, estimated through the energy deposited at very forward rapidity by the remnants of the Pb-nucleus. The corresponding J/ψstudies were published in [27]. In section 2 we give a brief overview of the experimental apparatus and run conditions. Section 3 presents details on the analysis procedure, while section 4 is dedicated to the results. The conclusions are presented in section 5. – 2 – JHEP06(2016)050 2 Experimental conditions The analysis presented in this Letter is based on the detection of the ψ(2S)→µ+µ−decay in the forward muon spectrometer of ALICE, described in detail elsewhere [28,29]. This detector covers the pseudorapidity range −4< ηlab <−2.5 and includes a 3 T·m dipole magnet and five stations of tracking chambers, the central one being inside the magnet gap. A main absorber (10 interaction lengths thick) is positioned between the ALICE interaction point and the tracking system, in order to remove hadrons. A second absorber is placed downstream of the tracking detectors. It removes the remaining hadrons and low-momentum muons produced predominantly from πand Kdecays, and is followed by two stations of trigger chambers that select muon candidates based on their transverse momentum (pT). In addition to the muon spectrometer, the first two layers of the Inner Tracking System (SPD, i.e., Silicon Pixel Detectors, the first covering |ηlab|<2.0 and the second |ηlab|<1.4) [30] are used for the determination of the position of the interaction vertex. The two V0 scintillator hodoscopes (covering −3.7< ηlab <−1.7 and 2.8< ηlab < 5.1, respectively) are used for triggering purposes [31]. Finally, two sets of Zero-Degree Calorimeters (ZDC), positioned at 112.5 m on the two sides of the interaction point, each one including a neutron calorimeter (ZN) and a proton calorimeter (ZP), are used to cleanup the event sample from interactions occurring out of the nominal bunches and for the centrality estimate [32,33]. The data-taking conditions were described in [23,34] and are briefly stated here. Two data samples were taken, corresponding to the p-beam or the Pb-beam going in the direction of the muon spectrometer, and labelled in the following as p-Pb and Pb-p, respectively. The integrated luminosities were LpPb int = 5.01 ±0.19 nb−1and LPbp int = 5.81 ± 0.20 nb−1[35]. The events used in this analysis were collected requiring a coincidence between a minimum bias (MB) trigger condition, defined by the logical AND of signals on the two V0 hodoscopes (>99% efficiency for non-single diffractive events), and the detection of two candidate opposite-sign tracks in the trigger system of the muon spectrometer. A pµ T>0.5 GeV/ccut on such tracks was also imposed at the trigger level. The offline event selection, the muon reconstruction and identification criteria and the kinematic and quality cuts applied at the single-muon and dimuon levels have already been described in refs. [22,23,27,36]. In particular, the covered dimuon rapidity ranges were 2.03 < ycms < 3.53 and −4.46 < ycms <−2.96 for the p-Pb and Pb-p configurations, respectively. 3 Data analysis In this section, the evaluation of the various elements that enter the cross section measurements and the nuclear modification factor calculations are described. The centrality selection and the determination of Ncoll are based on a hybrid method described in detail in ref. [33]. Events are selected according to the energy deposited at very large rapidity in the ZN positioned in the Pb-going direction, which mainly detects slow neutrons emitted by the Pb-nucleus as the result of the interaction. Their emission, according to results obtained in the analysis of lower energy proton-nucleus experiments, – 3 – JHEP06(2016)050 ZN centrality class hNcolli 2–20% 11.3 ±0.6 ±0.9 20–40% 9.6 ±0.2 ±0.8 40–60% 7.1 ±0.3 ±0.6 60–80% 4.3 ±0.3 ±0.3 80–100% 2.1 ±0.1 ±0.2 Table 1. Average numbers of binary nucleon-nucleon collisions, Ncoll, evaluated in the ZN centrality classes used in this analysis. The first quoted systematic uncertainty is uncorrelated, while the second is global. is expected to be monotonically related to Ncoll [37]. A centrality selection based on the ZN energy is found to be less biased than other centrality estimators, based on the charged particle multiplicity measurements at central (SPD) or forward (V0) pseudorapidity [33]. The average number of nucleon-nucleon collisions hNcollifor each ZN-selected centrality class is then obtained by assuming that the charged particle multiplicity measured at central rapidity is proportional to the number of participants Npart =Ncoll + 1 [38]. The values of hNcolli, used in this analysis, are reported in table 1, together with their uncertainties. The centrality classes used in this analysis correspond to 2–20%, 20–40%, 40–60%, 60–80% and 80–100% of the measured cross section corresponding to the MB trigger. Very central events (0–2%) are discarded from the event sample due to a large contamination from pile-up interactions. The estimate of the ψ(2S) signal is based on binned likelihood fits to the dimuon invariant mass spectra mµµ corresponding to events in the centrality ranges defined above. Details on the procedure, on the fitting functions and on the estimate of systematic uncertainties are discussed in [22]. The function used in the fit is the sum of a continuum background, mainly related to uncorrelated decays from pions and kaons and to semi-leptonic decays of pairs of hadrons with open heavy flavor, and of resonance shapes corresponding to the J/ψand ψ(2S) mesons. The background is parameterized by various empirical shapes, directly fitted to the data. The resonances are described by either a Crystal Ball function or a pseudo-gaussian with a mass-dependent width [39]. The main parameters of the J/ψline shapes, i.e. mass position and width, are left as free parameters, while the non-gaussian tail parameters are fixed to Monte-Carlo (MC) estimates. The ψ(2S) line shape parameters, given the less favourable signal over background, are fixed relative to those of the J/ψ, assuming that the mass difference and the widths scale according to the MC result. The results of the fits are shown in figure 1. The quality of the fits is good, with χ2/ndf ranging from 0.7 to 1.3. The ψ(2S) signal is visible in all the centrality bins, and the signal over background ratio increases from central (0.06 for p-Pb and 0.04 for Pb-p) to peripheral events (0.15 and 0.28, respectively). The number of reconstructed ψ(2S) for the various centrality bins, Ni ψ(2S)→µ+µ−, ranges from 265±73±32 (i= 2–20%) to 100±29±9 (i= 80–100%) in p-Pb, where the first uncertainty is statistical and the second one is systematic. The corresponding values for Pb-p are – 4 – JHEP06(2016)050 2 cCounts per 50 MeV/ 2 10 3 10 4 10 2-20% = 5.02 TeV NN sALICE, p-Pb >0 T p<3.53, cms y2.03< /ndf = 1.0 2 χ ) = 0.06σS/B (3 2 3 420-40% /ndf = 1.2 2 χ ) = 0.08σS/B (3 2 3 440-60% /ndf = 1.1 2 χ ) = 0.10σS/B (3 2 3 460-80% /ndf = 0.9 2 χ ) = 0.07σS/B (3 2 3 480-100% /ndf = 1.2 2 χ ) = 0.15σS/B (3 2.5 3 3.5 4 4.5 2 10 3 10 4 10 2-20% >0 T p<-2.96, cms y-4.46< /ndf = 1.2 2 χ ) = 0.04σS/B (3 2.5 3 3.5 4 4.5 2 3 420-40% /ndf = 1.1 2 χ ) = 0.05σS/B (3 2.5 3 3.5 4 4.5 2 3 440-60% /ndf = 1.3 2 χ ) = 0.06σS/B (3 2.5 3 3.5 4 4.5 2 3 460-80% /ndf = 0.7 2 χ ) = 0.12σS/B (3 ) 2 c (GeV/ - µ + µ m 2.5 3 3.5 4 4.5 2 3 480-100% /ndf = 1.2 2 χ ) = 0.28σS/B (3 Figure 1. Opposite-sign dimuon invariant mass spectra in ZN centrality classes at forward (top) and backward (bottom) rapidities. The fit curves shown in red in the figure correspond to the sum of signal and background shapes, the former being also shown separately in blue. 141 ±64 ±13 (i= 2–20%) and 65 ±20 ±7 (i= 80–100%). The systematic uncertainties on the signal extraction are given by the root mean square of the number of ψ(2S) obtained in 72 fits corresponding to various fitting functions for background and signal, to different fitting ranges, to variations of the non-gaussian tails of the resonance shape, and of the ψ(2S) mass resolution values. In p-Pb, the systematic uncertainties range between 11 and 13% from peripheral to central events (11–21% for Pb-p). The product of acceptance times efficiency A×for the ψ(2S) resonance was calculated with the MC-based procedure described in refs. [22,23]. The values are the same as quoted there for the centrality integrated production (0.270 ±0.014 for p-Pb and 0.184 ±0.013 for Pb-p), since it was verified that the tracking efficiency does not depend on the centrality of the collision [27]. The quoted errors are the quadratic sum of the systematic uncertainties on tracking, trigger and matching efficiencies and on the choice of the ψ(2S) pTand yinput shapes used in the MC simulations. The normalization of the ψ(2S) yield was calculated according to the procedure described in ref. [27]. It is based on the evaluation, for each centrality class, of the number of minimum bias events as Ni MB =Fi 2µ/MB ·Ni 2µ, where Ni 2µis the number of dimuontriggered events and Fi 2µ/MB is the inverse of the probability of having a dimuon triggered in a MB event for that class. The Fi 2µ/MB-values increase from central to peripheral events and are 287 ±3 and 694 ±8 for the 2–20% centrality class in p-Pb and Pb-p respectively. The corresponding values for the 80–100% class are 3291 ±36 and 3338 ±35. The systematic uncertainties quoted above (statistical uncertainties are negligible) come from the comparison obtained with two slightly different approaches in the calculation of Fi 2µ/MB, as detailed in [27]. – 5 – JHEP06(2016)050 In the evaluation of the systematic uncertainties on Fi 2µ/MB, the presence of interaction pile-up was considered. Pile-up can lead to a bias in the evaluation of the centrality of the collision since, for example, the superposition of the signals from two peripheral events in the ZN can fake a more central event. The contribution of pile-up was calculated by detecting events with multiple interaction vertices in the SPD, and checking via a MonteCarlo that the ZN energy distribution can be reproduced assuming a pile-up probability corresponding to the observed interaction rate. Events in the 0–2% centrality interval were rejected, as the pile-up contribution becomes significant (∼30%) in that region. The effect is small but not negligible in the 2–20% range, where it amounts to 2.1% (2.6%) for p-Pb (Pb-p), and becomes <1% going towards more peripheral events. From the quantities described above, the inclusive cross section for ψ(2S) production in the centrality bin i, times its branching ratio to dimuons B.R.ψ(2S)→µµ, was calculated with the following expression B.R.ψ(2S)→µ+µ−σi,ψ(2S) pPb =Ni ψ(2S)→µ+µ− (A×)·Ni MB ×σMB (3.1) The ratio NMB/σMB, where NMB is the total number of minimum bias events and σMB is the cross section for events satisfying the minimum bias trigger condition, gives the integrated luminosity Lint. The σMB values were evaluated through a van der Meer scan which gives σpPb MB = 2.09 ±0.07 b and σPbp MB = 2.12 ±0.07 b [35]. A determination of the luminosity which makes use of a different reference process, based on the signals released in aˇ Cerenkov counter [29], gives a result compatible within 1% [35]. Therefore, an additional 1% uncertainty is added to the σMB values used in the ψ(2S) cross section determination. The comparison of the ψ(2S) and J/ψproduction cross sections can be performed by calculating the ratio B.R.ψ(2S)→µ+µ−σψ(2S)/B.R.J/ψ→µ+µ−σJ/ψ. In this way, the uncertainties related to the cross section normalization and to the reconstruction efficiency cancel out. The J/ψcross section values that enter this ratio are those reported in [27], with the value for the centrality interval 2–20% obtained by summing the 2–10% and 10–20% results. This ratio can be further normalized to the corresponding measurement in pp collisions. This quantity, called double ratio in the following, gives direct access to modifications in the ψ(2S) production relative to that of the J/ψ, going from pp to p-Pb collisions. Due to the lack of precise pp data at √s= 5.02 TeV, the results obtained at √s= 7 TeV [40] were used instead. This choice is justified from the fact that the √sand y-dependence of the cross section ratio is known to be weak in the TeV beam energy range. An 8% systematic uncertainty has been included, corresponding to the maximum estimated size of the variation of the ratio between the two energies [22]. The estimate of the nuclear modification factors Qi,ψ(2S) pPb as a function of centrality is performed as the product of the corresponding Qi,J/ψ pPb for the J/ψ[27] (except for the 2–20% centrality interval where Qi,J/ψ pPb was re-computed by merging the 2–10% and 10–20% bins) and the double ratio between the ψ(2S) and J/ψcross sections in p-Pb and pp collisions: Qi,ψ(2S) pPb =Qi,J/ψ pPb ·σi,ψ(2S) pPb σi,J/ψ pPb ·σJ/ψ pp σψ(2S) pp (3.2) – 6 – JHEP06(2016)050 Source of uncertainty σψ(2S) pPb ,Qψ(2S) pPb σψ(2S) Pbp ,Qψ(2S) Pbp 2.03< ycms <3.53 -4.46< ycms <-2.96 Tracking efficiency (I) 4 6 Trigger efficiency (I) 3 3.4 Matching efficiency (I) 1 1 Signal extraction 10.8 −13.4 10.8 −20.9 MC input 1.8 2.5 σMB (I) 3.3 3.0 σMB (I,II) 1.6 1.6 Table 2. Systematic uncertainties, in percentage, on the ψ(2S) cross sections and nuclear modification factors. For centrality-dependent quantities, the range of variation is given. Type I uncertainties are correlated over centrality, while type II are correlated between the forward and the backward rapidity regions. When no indication is given, the uncertainties are uncorrelated. The uncertainty on σMB is related to the ψ(2S) cross section only. The uncertainties are obtained combining those on Qi,J/ψ pPb [27] with those on the double ratio, avoiding a double counting of the J/ψrelated uncertainties. The notation Qi,ψ(2S) pPb , rather than the more usual Ri,ψ(2S) pPb , is used in this Letter, to draw attention to possible residual biases in the centrality determination, related to the loose correlation between the centrality estimators and the corresponding collision geometry [33]. Table 2summarizes the values of the systematic uncertainties on the various ingredients that enter the cross section determination and the calculation of the nuclear modification factor. 4 Results The ψ(2S) production cross sections as a function of the centrality of the collision, expressed via hNcolli, are plotted in figure 2(left). As expected, their values increase with hNcolli. In figure 2(right) the ratio B.R.ψ(2S)→µ+µ−σψ(2S)/B.R.J/ψ→µ+µ−σJ/ψ is shown as a function of hNcolliand compared with the corresponding value for pp collisions. Despite the large uncertainties, the data suggest a decreasing trend from peripheral to central events, in particular at backward rapidity, indicating a suppression of the ψ(2S) production relative to the J/ψ. While for peripheral collisions the cross section ratios are consistent with the pp value, they become a factor 2–3 smaller for central events, in both rapidity ranges. As remarked in section 3, the pp cross section ratio measured at √s= 7 TeV has been used, including an 8% additional uncertainty to account for its possible √sand y-dependence. The degree of suppression of ψ(2S) is directly quantified in figure 3where the double ratio between the ψ(2S) and J/ψcross sections in p-Pb and pp collisions is shown. The result is compared with two theoretical calculations. The first is based on a scenario where – 7 – JHEP06(2016)050 〉 coll N〈 0 2 4 6 8 10 12 14 b)µ (y/d (2S)ψ cent σ d⋅B.R. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 = 5.02 TeV NN sALICE, p-Pb - µ + µ →(2S) ψInclusive < 3.53, global unc.= 6% cms y2.03 < < -2.96, global unc.= 8% cms y-4.46 < 〉 coll N〈 0 2 4 6 8 10 12 14 ψJ/ σ - µ + µ→ψJ/ /B.R. (2S)ψ σ - µ + µ→(2S)ψ B.R. 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 - µ + µ →(2S) ψ, ψALICE, inclusive J/ < 3.53, global unc.= 1% cms y= 5.02 TeV, 2.03 < NN sp-Pb < -2.96, global unc.= 2% cms y= 5.02 TeV, -4.46 < NN sp-Pb < 4 (Eur. Phys. J. C74 (2014)) cms y= 7 TeV, 2.5 <spp Figure 2. Left: ψ(2S) production cross sections shown as a function of hNcollifor both p-Pb and Pb-p collisions. Right: B.R.ψ(2S)→µ+µ−σψ(2S)/B.R.J/ψ→µ+µ−σJ/ψ shown as a function of hNcolliand compared to the pp value (line), with a band representing its uncertainty. In both figures, vertical error bars correspond to statistical uncertainties, while the open boxes represent the systematic uncertainties. The Pb-p points are slightly shifted in hNcollito improve visibility. the resonances may be dissociated via interactions with the partons or hadrons produced in the collision in the same rapidity region (co-movers) [11]. The model includes contributions from nuclear shadowing, based on the EPS09 LO parameterization [3], and a co-mover interaction term, with dissociation cross sections σco−J/ψ = 0.65 mb and σco−ψ(2S) = 6 mb, these values being fixed from fits to low-energy experimental data [41]. The effect of comovers is larger at backward rapidity since their density is larger in that region. The calculated co-mover densities are compatible with the measured experimental charged particle multiplicities [42]. The calculation reproduces well the measured values of the double ratio. Shadowing effects are very similar for the two mesons and in this model they are assumed to cancel out in the double ratio, so that only co-mover absorption plays a role. The second model (QGP+HRG) is based on a thermal-rate equation framework [43] which also implements the dissociation of charmonia in a hadron resonance gas, including a total of 52 non-strange and single-strange meson species, up to a mass of 2 GeV/c2[26]. The fireball evolution includes the transition from a short QGP phase into the hadron resonance gas, through a mixed phase. The shadowing effects, implemented through the EPS09 parametrization, cancel out in the double ratio, as in the previous model. The result of the calculation, also shown in figure 3, is in fair agreement with the measured values, in particular for central collisions. The model uncertainties are dominated by the evaluation of the charmonium dissociation rates. The ALICE result is also compared to mid-rapidity (|y|<0.35) PHENIX data [19] in figure 3. Remarkably, in spite of the very different √sNN and ycms values, the observed patterns as a function of centrality are similar. It should also be noted that the PHENIX result can be qualitatively described in a hadronic dissociation scenario, as discussed in [11,26]. In figure 4the nuclear modification factor for ψ(2S) mesons is shown as a function of centrality, separately for forward and backward rapidities. 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Sinha133 , T. Sinha100 , B. Sitar38 , M. Sitta31 , T.B. Skaali21 , M. Slupecki123 , N. Smirnov137 , R.J.M. Snellings53 , T.W. Snellman123 , J. Song96 , M. Song138 , Z. Song7, F. Soramel29 , S. Sorensen125 , R.D.de Souza121 , F. Sozzi97 , M. Spacek39 , E. Spiriti72 , I. Sputowska117 , M. Spyropoulou-Stassinaki89 , J. Stachel93 , I. Stan58 , P. Stankus85 , E. Stenlund33 , G. Steyn65 , J.H. Stiller93 , D. Stocco113 , P. Strmen38 , A.A.P. Suaide120 , T. Sugitate46 , C. Suire51 , M. Suleymanov16 , M. Suljic25 ,i, R. Sultanov54 , M. ˇ Sumbera84 , S. Sumowidagdo49 , A. Szabo38 , I. Szarka38 , A. Szczepankiewicz35 , M. Szymanski134 , U. Tabassam16 , J. Takahashi121 , G.J. Tambave22 , N. Tanaka128 , M. Tarhini51 , M. Tariq18 , M.G. Tarzila78 , A. Tauro35 , G. Tejeda Mu˜noz2, A. Telesca35 , K. Terasaki127 , C. Terrevoli29 , B. Teyssier130 , J. Th¨ader74 , D. Thakur48 , D. Thomas118 , R. Tieulent130 , A. Tikhonov52 , A.R. Timmins122 , A. Toia60 , S. Trogolo26 , G. Trombetta32 , V. Trubnikov3, W.H. Trzaska123 , T. Tsuji127 , A. Tumkin99 , R. Turrisi107 , T.S. Tveter21 , K. Ullaland22 , A. Uras130 , G.L. Usai24 , A. Utrobicic129 , M. Vala55 , L. Valencia Palomo70 , S. Vallero26 , J. Van Der Maarel53 , J.W. Van Hoorne35 , M. van Leeuwen53 , T. Vanat84 , P. Vande Vyvre35 , D. Varga136 , A. Vargas2, M. Vargyas123 , R. Varma47 , M. Vasileiou89 , A. Vasiliev80 , A. Vauthier71 , O. V´azquez Doce36 ,94 , V. Vechernin132 , A.M. Veen53 , M. Veldhoen53 , A. Velure22 , E. Vercellin26 , S. Vergara Lim´on2, R. Vernet8, M. Verweij135 , L. Vickovic116 , J. Viinikainen123 , Z. Vilakazi126 , O. Villalobos Baillie101 , A. Villatoro Tello2, A. Vinogradov80 , L. Vinogradov132 , Y. Vinogradov99 ,i, T. Virgili30 , V. Vislavicius33 , Y.P. Viyogi133 , A. Vodopyanov66 , M.A. V¨olkl93 , K. Voloshin54 , S.A. Voloshin135 , G. Volpe32 ,136 , B. von Haller35 , I. Vorobyev36 ,94 , D. Vranic35 ,97 , J. Vrl´akov´a40 , B. Vulpescu70 , B. Wagner22 , J. Wagner97 , H. Wang53 , M. Wang7,113 , D. Watanabe128 , Y. Watanabe127 , M. Weber35 ,112 , S.G. Weber97 , D.F. Weiser93 , J.P. Wessels61 , U. Westerhoff61 , A.M. Whitehead90 , J. Wiechula34 , J. Wikne21 , G. Wilk77 , J. Wilkinson93 , M.C.S. Williams104 , B. Windelband93 , M. Winn93 , P. Yang7, S. Yano46 , Z. Yasin16 , Z. Yin7, H. Yokoyama128 , I.-K. Yoo96 , J.H. Yoon50 , V. Yurchenko3, I. Yushmanov80 , A. Zaborowska134 , V. Zaccolo81 , A. Zaman16 , C. Zampolli35 ,104 , H.J.C. Zanoli120 , S. Zaporozhets66 , N. Zardoshti101 , A. Zarochentsev132 , P. Z´avada56 , N. Zaviyalov99 , H. Zbroszczyk134 , I.S. Zgura58 , M. Zhalov86 , H. Zhang22 , X. Zhang7,74 , Y. Zhang7, C. Zhang53 , Z. Zhang7, C. Zhao21 , N. Zhigareva54 , D. Zhou7, Y. Zhou81 , Z. Zhou22 , H. Zhu22 , J. Zhu7,113 , A. Zichichi12 ,27 , A. Zimmermann93 , M.B. Zimmermann35 ,61 , G. Zinovjev3, M. Zyzak42 iDeceased ii Also at: Georgia State University, Atlanta, Georgia, United States iii Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India iv Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia 1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2Benem´erita Universidad Aut´onoma de Puebla, Puebla, Mexico 3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine 4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India 5Budker Institute for Nuclear Physics, Novosibirsk, Russia 6California Polytechnic State University, San Luis Obispo, California, United States – 19 – JHEP06(2016)050 7Central China Normal University, Wuhan, China 8Centre de Calcul de l’IN2P3, Villeurbanne, France 9Centro de Aplicaciones Tecnol´ogicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 10 Centro de Investigaciones Energ´eticas Medioambientales y Tecnol´ogicas (CIEMAT), Madrid, Spain 11 Centro de Investigaci´on y de Estudios Avanzados (CINVESTAV), Mexico City and M´erida, Mexico 12 Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Rome, Italy 13 Chicago State University, Chicago, Illinois, U.S.A. 14 China Institute of Atomic Energy, Beijing, China 15 Commissariat `a l’Energie Atomique, IRFU, Saclay, France 16 COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan 17 Departamento de F´ısica de Part´ıculas and IGFAE, Universidad de Santiago de Compostela, Santiago de Compostela, Spain 18 Department of Physics, Aligarh Muslim University, Aligarh, India 19 Department of Physics, Ohio State University, Columbus, Ohio, United States 20 Department of Physics, Sejong University, Seoul, South Korea 21 Department of Physics, University of Oslo, Oslo, Norway 22 Department of Physics and Technology, University of Bergen, Bergen, Norway 23 Dipartimento di Fisica dell’Universit`a ‘La Sapienza’ and Sezione INFN Rome, Italy 24 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Cagliari, Italy 25 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Trieste, Italy 26 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Turin, Italy 27 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Bologna, Italy 28 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Catania, Italy 29 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Padova, Italy 30 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Universit`a and Gruppo Collegato INFN, Salerno, Italy 31 Dipartimento di Scienze e Innovazione Tecnologica dell’Universit`a del Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy 32 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy 33 Division of Experimental High Energy Physics, University of Lund, Lund, Sweden 34 Eberhard Karls Universit¨at T¨ubingen, T¨ubingen, Germany 35 European Organization for Nuclear Research (CERN), Geneva, Switzerland 36 Excellence Cluster Universe, Technische Universit¨at M¨unchen, Munich, Germany 37 Faculty of Engineering, Bergen University College, Bergen, Norway 38 Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia 39 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 40 Faculty of Science, P.J. ˇ Saf´arik University, Koˇsice, Slovakia 41 Faculty of Technology, Buskerud and Vestfold University College, Vestfold, Norway 42 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany 43 Gangneung-Wonju National University, Gangneung, South Korea 44 Gauhati University, Department of Physics, Guwahati, India 45 Helsinki Institute of Physics (HIP), Helsinki, Finland 46 Hiroshima University, Hiroshima, Japan 47 Indian Institute of Technology Bombay (IIT), Mumbai, India 48 Indian Institute of Technology Indore, Indore (IITI), India 49 Indonesian Institute of Sciences, Jakarta, Indonesia 50 Inha University, Incheon, South Korea 51 Institut de Physique Nucl´eaire d’Orsay (IPNO), Universit´e Paris-Sud, CNRS-IN2P3, Orsay, France 52 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia 53 Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands 54 Institute for Theoretical and Experimental Physics, Moscow, Russia – 20 – JHEP06(2016)050 55 Institute of Experimental Physics, Slovak Academy of Sciences, Koˇsice, Slovakia 56 Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 57 Institute of Physics, Bhubaneswar, India 58 Institute of Space Science (ISS), Bucharest, Romania 59 Institut f¨ur Informatik, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany 60 Institut f¨ur Kernphysik, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany 61 Institut f¨ur Kernphysik, Westf¨alische Wilhelms-Universit¨at M¨unster, M¨unster, Germany 62 Instituto de Ciencias Nucleares, Universidad Nacional Aut´onoma de M´exico, Mexico City, Mexico 63 Instituto de F´ısica, Universidad Nacional Aut´onoma de M´exico, Mexico City, Mexico 64 Institut Pluridisciplinaire Hubert Curien (IPHC), Universit´e de Strasbourg, CNRS-IN2P3, Strasbourg, France 65 iThemba LABS, National Research Foundation, Somerset West, South Africa 66 Joint Institute for Nuclear Research (JINR), Dubna, Russia 67 Konkuk University, Seoul, South Korea 68 Korea Institute of Science and Technology Information, Daejeon, South Korea 69 KTO Karatay University, Konya, Turkey 70 Laboratoire de Physique Corpusculaire (LPC), Clermont Universit´e, Universit´e Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France 71 Laboratoire de Physique Subatomique et de Cosmologie, Universit´e Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 72 Laboratori Nazionali di Frascati, INFN, Frascati, Italy 73 Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy 74 Lawrence Berkeley National Laboratory, Berkeley, California, United States 75 Moscow Engineering Physics Institute, Moscow, Russia 76 Nagasaki Institute of Applied Science, Nagasaki, Japan 77 National Centre for Nuclear Studies, Warsaw, Poland 78 National Institute for Physics and Nuclear Engineering, Bucharest, Romania 79 National Institute of Science Education and Research, Bhubaneswar, India 80 National Research Centre Kurchatov Institute, Moscow, Russia 81 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 82 Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands 83 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom 84 Nuclear Physics Institute, Academy of Sciences of the Czech Republic, ˇ Reˇz u Prahy, Czech Republic 85 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States 86 Petersburg Nuclear Physics Institute, Gatchina, Russia 87 Physics Department, Creighton University, Omaha, Nebraska, United States 88 Physics Department, Panjab University, Chandigarh, India 89 Physics Department, University of Athens, Athens, Greece 90 Physics Department, University of Cape Town, Cape Town, South Africa 91 Physics Department, University of Jammu, Jammu, India 92 Physics Department, University of Rajasthan, Jaipur, India 93 Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany 94 Physik Department, Technische Universit¨at M¨unchen, Munich, Germany 95 Purdue University, West Lafayette, Indiana, United States 96 Pusan National University, Pusan, South Korea 97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum f¨ur Schwerionenforschung, Darmstadt, Germany 98 Rudjer Boˇskovi´c Institute, Zagreb, Croatia 99 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia 100 Saha Institute of Nuclear Physics, Kolkata, India 101 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 102 Secci´on F´ısica, Departamento de Ciencias, Pontificia Universidad Cat´olica del Per´u, Lima, Peru – 21 – JHEP06(2016)050 103 Sezione INFN, Bari, Italy 104 Sezione INFN, Bologna, Italy 105 Sezione INFN, Cagliari, Italy 106 Sezione INFN, Catania, Italy 107 Sezione INFN, Padova, Italy 108 Sezione INFN, Rome, Italy 109 Sezione INFN, Trieste, Italy 110 Sezione INFN, Turin, Italy 111 SSC IHEP of NRC Kurchatov institute, Protvino, Russia 112 Stefan Meyer Institut f¨ur Subatomare Physik (SMI), Vienna, Austria 113 SUBATECH, Ecole des Mines de Nantes, Universit´e de Nantes, CNRS-IN2P3, Nantes, France 114 Suranaree University of Technology, Nakhon Ratchasima, Thailand 115 Technical University of Koˇsice, Koˇsice, Slovakia 116 Technical University of Split FESB, Split, Croatia 117 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 118 The University of Texas at Austin, Physics Department, Austin, Texas, U.S.A. 119 Universidad Aut´onoma de Sinaloa, Culiac´an, Mexico 120 Universidade de S˜ao Paulo (USP), S˜ao Paulo, Brazil 121 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 122 University of Houston, Houston, Texas, United States 123 University of Jyv¨askyl¨a, Jyv¨askyl¨a, Finland 124 University of Liverpool, Liverpool, United Kingdom 125 University of Tennessee, Knoxville, Tennessee, United States 126 University of the Witwatersrand, Johannesburg, South Africa 127 University of Tokyo, Tokyo, Japan 128 University of Tsukuba, Tsukuba, Japan 129 University of Zagreb, Zagreb, Croatia 130 Universit´e de Lyon, Universit´e Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, France 131 Universit`a di Brescia 132 V. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, Russia 133 Variable Energy Cyclotron Centre, Kolkata, India 134 Warsaw University of Technology, Warsaw, Poland 135 Wayne State University, Detroit, Michigan, United States 136 Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, Hungary 137 Yale University, New Haven, Connecticut, United States 138 Yonsei University, Seoul, South Korea 139 Zentrum f¨ur Technologietransfer und Telekommunikation (ZTT), Fachhochschule Worms, Worms, Germany – 22 –