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

: 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 p s NN = 5.02 TeV at the CERN LHC. The measurement was performed with the ALICE detector in the center of mass rapidity ranges (cid:0) 4 : 46 < y cms < (cid:0) 2 : 96 and 2 : 03 < y cms < 3 : 53, down to zero transverse momentum, by reconstructing the (2S) decay to a muon pair. The (2S) production cross section (cid:27) (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(cid:11)ects on the (2S) and on the corresponding 1S charmonium state J/ is then studied by means of the double ratio of cross sections [ (cid:27) (2S) =(cid:27) J = ] pPb = [ (cid:27) (2S) =(cid:27) J = ] pp between p-Pb and pp collisions, and by the values of the nuclear modi(cid:12)cation factors for the two charmonium states. The results show a large suppression of (2S) production relative to the J/ at backward (negative) rapidity, corresponding to the (cid:13)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.


Introduction
At the LHC, centrality-integrated results on the ψ(2S) and J/ψ resonances for p-Pb collisions at √ s NN = 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/ψ was observed, relative to proton-proton collisions. Again, this result was unexpected, as the τ c values are either at most the same order of magnitude (at negative y cms ) or more than two orders of magnitude smaller (at positive y cms ) than τ f [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/ψ studies were published in [27]. In Sect. 2 we give a brief overview of the experimental apparatus and run conditions. Sect. 3 presents details on the analysis procedure, while Sect. 4 is dedicated to the results. The conclusions are presented in Sect. 5.

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 < η lab < −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 π and K decays, and is followed by two stations of trigger chambers that select muon candidates based on their transverse momentum (p T ). In addition to the muon spectrometer, the first two layers of the Inner Tracking System (SPD, i.e., Silicon Pixel Detectors, the first covering |η lab | < 2.0 and the second |η lab | < 1.4) [30] are used for the determination of the position of the interaction vertex. The two V0 scintillator hodoscopes (covering −3.7 < η lab < −1.7 and 2.8 < η lab < 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 clean-up 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 L pPb int = 5.01 ± 0.19 nb −1 and L Pbp 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 p µ T > 0.5 GeV/c cut 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 < y cms < 3.53 and −4.46 < y cms < −2.96 for the p-Pb and Pb-p configurations, respectively.

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 N coll 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, is expected to be monotonically related to N coll [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 N coll for 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 N part = N coll + 1 [38]. The values of N coll , used in this analysis, are reported in Tab. 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 m µ µ 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/ψ and 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/ψ line 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 Fig. 1.
The quality of the fits is good, with χ 2 /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, N i 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 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 × ε for the ψ(2S) resonance was calculated with the MCbased 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) p T and y input 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 N i where N i 2µ is the number of dimuon-triggered events and F i 2µ/MB is the inverse of the probability of having a dimuon triggered in a MB event for that class. The F i 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 F i 2µ/MB , as detailed in [27].
In the evaluation of the systematic uncertainties on F i 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 Monte-Carlo 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)→µ µ , was calculated with the following expression The ratio N MB /σ MB , where N MB is the total number of minimum bias events and σ MB is the cross section for events satisfying the minimum bias trigger condition, gives the integrated luminosity L int . The σ MB values were evaluated through a van der Meer scan which gives σ pPb MB = 2.09 ± 0.07 b and σ Pbp 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 aČerenkov counter [29], gives a result compatible within 1% [35]. Therefore, an additional 1% uncertainty is added to the σ MB values used in the ψ(2S) cross section determination.
The comparison of the ψ(2S) and J/ψ production cross sections can be performed by calculating the ratio B.R. ψ(2S)→µ + µ − σ ψ(2S) /B.R. J/ψ→µ + µ − σ J/ψ . In this way, the uncertainties related to the cross section normalization and to the reconstruction efficiency cancel out. The J/ψ cross 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 √ s-and 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 Q i,ψ(2S) pPb as a function of centrality is performed as the product of the corresponding Q i,J/ψ pPb for the J/ψ [27] (except for the 2-20% centrality interval where Q i,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/ψ cross sections in p-Pb and pp collisions: The uncertainties are obtained combining those on Q i,J/ψ pPb [27] with those on the double ratio, avoiding a double counting of the J/ψ related uncertainties. The notation Q i,ψ(2S) pPb , rather than the more usual R i,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 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 σ MB is related to the ψ(2S) cross section only.

Results
The ψ(2S) production cross sections as a function of the centrality of the collision, expressed via N coll , are plotted in Fig. 2 (left). As expected, their values increase with N coll . In Fig. 2 (right) the ratio B.R. ψ(2S)→µ + µ − σ ψ(2S) /B.R. J/ψ→µ + µ − σ J/ψ is shown as a function of N coll and 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 Sect. 3, the pp cross section ratio measured at √ s = 7 TeV has been used, including an 8% additional uncertainty to account for its possible √ s-and y-dependence.
The degree of suppression of ψ(2S) is directly quantified in Fig. 3 where the double ratio between the ψ(2S) and J/ψ cross 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 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 σ co−J/ψ = 0.65 mb and σ co−ψ(2S) = 6 mb, these values being fixed from fits to low-energy experimental data [41]. The effect of co-movers 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/c 2 [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 Fig. 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 Fig. 3. Remarkably, in spite of the very different √ s NN and y cms 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].  Fig. 3: Double ratio [σ ψ(2S) /σ J/ψ ] pPb /[σ ψ(2S) /σ J/ψ ] pp for p-Pb and Pb-p collisions, shown as a function of N coll (Pb-p points are slightly shifted in N coll to improve visibility). The data are compared to PHENIX mid-rapidity results [19] and to the theoretical calculations of Ref. [11] and [26]. The boxes around unity correspond to the global systematic uncertainties at forward (red box) and backward (blue box) rapidities. The grey box is a global systematic uncertainty common to both p-Pb rapidity ranges, while the green box refers to the PHENIX results.
In Fig. 4 the nuclear modification factor for ψ(2S) mesons is shown as a function of centrality, separately for forward and backward rapidities. In both regions, a trend towards an increasing suppression can be seen when moving from peripheral to central collisions. The corresponding Q J/ψ pPb values [27] are also shown. At forward-y there is an indication for a smaller Q ψ(2S) pPb with respect to Q J/ψ pPb . The difference between the ψ(2S) and the J/ψ nuclear modification factors amounts, for central events, to 1.9σ , while, integrating over centrality, the corresponding quantity is 2.3σ . At backward-y the suppression patterns for the J/ψ and the ψ(2S) are different, with Q J/ψ pPb ∼ 1 (or even slightly larger), and a strong suppression for the ψ(2S). In the most central collisions, the difference between the measured Q pPb corresponds to 4.3σ , while, integrating over centrality, suppressions differ by 4.1σ . The results are compared to calculations including either only shadowing (EPS09 LO [11], EPS09 NLO [44]) or only coherent energy loss [45] and to models implementing final state interactions (co-movers [11], QGP+HRG [26]). While the J/ψ results are reproduced by shadowing/energy loss calculations, additional final state effects, as those discussed in the context of Fig. 3, are needed to describe the ψ(2S) results, in particular at backward rapidity.
Finally, the double ratios are shown in Fig. 5 as a function of the pair crossing time τ c in nuclear matter [9]. This quantity can be calculated as τ c = L /(β z γ) where L is the average thickness of nuclear matter crossed by the pair, which was evaluated, for each centrality class, using the Glauber model [46], β z = tanh y rest cc is the velocity of the cc along the beam direction in the nucleus rest frame, γ = E cc /m cc and E cc = m T,cc cosh y rest cc . The value m cc = 3.4 GeV/c 2 was chosen for the (average) mass of the evolving cc pair [9,47], while m T,cc was calculated in each centrality bin starting from the measured J/ψ p T values [27]. We use the J/ψ p T as a proxy for the average p T of the cc pair, as the ψ(2S) statistics is too low to extract a corresponding p T value. If we assume instead that p  [27] and ψ(2S) nuclear modification factors, Q pPb , shown as a function of N coll for the backward (left) and forward (right) rapidity regions and compared to theoretical models [11,26,44,45]. The boxes around unity correspond to the global ψ(2S) systematic uncertainties at forward (red box) and backward (blue box) rapidities. The grey box is a global systematic uncertainty common to both J/ψ and ψ(2S).
than 1%, and those on L , which are dominant and of the order of 10%. In Fig. 5 we show the double ratio as a function of τ c in the two rapidity regions. Different τ c intervals can also be selected by slicing the events in bins of p T (see Ref. [36]), varying, in this way, the γ values of the cc. The double ratio results, obtained in [36], are therefore also shown in Fig. 5 at their corresponding average τ c values. In the double ratio one effectively removes, as discussed above, initial state effects, so that Fig. 5 shows the τ c dependence of final state effects on ψ(2S) compared to J/ψ. The two sets of results, corresponding to a slicing of the events in centrality or in p T , are in good agreement. At backward-y, where the largest τ c values are reached, a clearly decreasing trend can be observed. The average resonance formation time τ f is, according to most theory estimates [9,20,21], larger by at least a factor ∼ 2 than the accessible τ c range. On the other hand, the width of the τ f distribution is expected to be non-negligible [21], and it cannot be excluded that at least a fraction of the cc pairs hadronizes inside the nucleus. Therefore, the observed behaviour is likely due to a combination of final state effects which take place outside the nucleus, as e.g. interaction with a hadronic resonance gas, and dissociation effects on the fully formed resonance, due to nuclear matter, and taking place inside the nucleus. The relative importance of the two mechanisms is difficult to quantify in such a simple analysis and quantitative theoretical studies, also exploring alternative mechanisms, are needed. At forward rapidity, where τ c becomes smaller than τ f by about 2-3 orders of magnitude, the interaction with nuclear matter is not expected to play any significant role. The results of a similar analysis carried out on PHENIX mid-rapidity data [19] are also shown in Fig. 5. Within uncertainties, a scaling of the ALICE and PHENIX double ratio values with τ c is observed.

Conclusions
The centrality dependence of the ψ(2S) production in p-Pb collisions at √ s NN = 5.02 TeV was measured in five intervals, using the ZN energy as an estimator. The ratio B.R. ψ(2S)→µ + µ − σ ψ(2S) /B.R. J/ψ→µ + µ − σ J/ψ is compatible with pp measurements in peripheral events, whereas a decrease is observed towards central events, showing that the ψ(2S) state is suppressed with respect to the J/ψ state. The results on the nuclear modification factors, together with the corresponding model comparisons, show that effects such as shadowing or energy loss are enough to explain the J/ψ behaviour, while additional mechanisms are needed to describe the ψ(2S) suppression. Theoretical models that include final state interactions are able to reproduce such a suppression. A study of the double ratio [σ ψ(2S) /σ J/ψ ] pPb /[σ ψ(2S) /σ J/ψ ] pp , as a function of the crossing time τ c , shows that at forward-y the τ c values are much shorter than the resonance formation time τ f , excluding any significant role of final state interactions with nuclear matter. Effects occurring at later times, such as the break-up by co-movers in the hadronic gas, are suitable can- For each y-range, the two sets of points were obtained from the centrality analysis and from the p T -dependent analysis of Ref. [22]. Statistical uncertainties are shown as lines, while the total systematic uncertainties are shown as boxes around the points. The results of a corresponding analysis carried out on the PHENIX mid-rapidity data [19] is also shown. The box around unity represents the PHENIX global systematic uncertainty. For the ALICE results, the global uncertainties are different for the various data sets, and are included in the boxes around the points didates for an explanation of the observed ψ(2S) suppression. At backward-y the τ c values, although significantly larger, are still smaller than τ f . However, the observed scaling of the double ratios with τ c may be suggestive of an effect at least partly related to a dissociation of the fully-formed resonance in nuclear matter.

Acknowledgements
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the