Suppression of $\psi$(2S) production in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV

The ALICE Collaboration has studied the inclusive production of the charmonium state $\psi(2S)$ in proton-lead (p-Pb) collisions at the nucleon-nucleon centre of mass energy $\sqrt{s_{NN}}$ = 5.02 TeV at the CERN LHC. The measurement was performed at forward ($2.03<y_{cms}<3.53$) and backward ($-4.46<y_{cms}<-2.96$) centre of mass rapidities, studying the decays into muon pairs. In this paper, we present the inclusive production cross sections $\sigma_{\psi(2S)}$, both integrated and as a function of the transverse momentum $p_{T}$, for the two $y_{cms}$ domains. The results are compared to those obtained for the 1S vector state (J/$\psi$), by showing the ratios between the production cross sections, as well as the double ratios $[\sigma_{\psi(2S)}/\sigma_{J/\psi}]_{pPb}/[\sigma_{\psi(2S)}/\sigma_{J/\psi}]_{pp}$ between p-Pb and proton-proton collisions. Finally, the nuclear modification factor for inclusive $\psi(2S)$ is evaluated and compared to the measurement of the same quantity for J/$\psi$ and to theoretical models including parton shadowing and coherent energy loss mechanisms. The results show a significantly larger suppression of the $\psi(2S)$ compared to that measured for J/$\psi$ and to models. These observations represent a clear indication for sizeable final state effects on $\psi(2S)$ production.

The physics of charmonia, bound states of the charm (c) and anti-charm (c) quarks, is an extremely broad and interesting field of investigation [1]. The description of the various states and the calculation of their production cross sections in hadronic collisions involve an interplay of perturbative and nonperturbative aspects of Quantum ChromoDynamics (QCD) [2], which still today represent a significant challenge for theory [3]. Charmonium states can have smaller sizes than light hadrons (down to a few tenths of a fm) and large binding energies (> 500 MeV) [4]. These properties make charmonia a useful probe of the hot nuclear matter created in ultrarelativistic heavy-ion collisions, which can be seen as a plasma of deconfined quarks and gluons (QGP) (see [5] for a recent overview of QGP studies). In particular, the cc binding can be screened by the high density of colour charges present in the QGP, leading to a suppression of the yields of charmonia in high-energy nuclear collisions compared to the corresponding production rates in elementary pp collisions at the same energy [6]. In the so-called "sequential suppression" scenario, the melting of a bound cc state occurs when the temperature of the hot medium exceeds a threshold dissociation temperature [7,8], which depends on the binding energy of the state and can be calculated in lattice QCD [9]. At LHC energies, where the number of produced cc pairs is large, this suppression effect can be partly counterbalanced by charmonium "regeneration" processes due to the recombination of charm quarks that occurs as the system cools and hadrons form [10][11][12].
Among the charmonium states, the strongly bound S-wave J/ψ and the weakly bound radially excited ψ(2S) have received most attention in the context of QGP studies. Both decay to lepton pairs with a non-negligible branching ratio (5.93% and 0.77%, respectively, for the µ + µ − channel [13]). The results obtained by the NA50 collaboration at the CERN SPS showed a significant suppression of the J/ψ production in Pb-Pb collisions at √ s NN = 17 GeV [14] and a comparatively larger suppression of the ψ(2S) [15], in qualitative agreement with sequential suppression models. However, the same experiment also detected a significant suppression of both states (although not as strong as in Pb-Pb) in protonnucleus (p-A) collisions [16], where no QGP formation was expected. The same observation was made by other fixed-target experiments studying p-A collisions at Fermilab (E866 [17]) and HERA (HERA-B [18]). It was indeed realized that the charmonium yields are also sensitive to the presence of cold nuclear matter (CNM) in the target nucleus, and various mechanisms (nuclear parton shadowing [19], cc break-up via interaction with nucleons [20][21][22], initial/final state energy loss [23]) were taken into account in order to describe experimental observations. In particular, these experiments observed a stronger suppression for ψ(2S) relative to J/ψ at central rapidity, while at forward rapidity no difference was found within uncertainties. This feature of the results was interpreted in terms of pair break-up: at central rapidity the time spent by the cc state in the nuclear medium (crossing time) is typically larger than the formation time of the resonances (∼ 0.1 fm/c [24,25]), so that the loosely bound ψ(2S) can be more easily dissociated than the J/ψ. Conversely, in forward production the crossing time is smaller than the formation time and the influence of the nucleus on the pre-hadronic state is the same, independent of the particular resonance being produced [26].
More generally, the study of charmonia in p-A collisions can be used as a tool for a quantitative investigation of the aforementioned processes, relevant in the context of studies of the strong interaction. Therefore, measurements at high energies are important to test our understanding of the various mechanisms. In particular, the pair break-up cross sections discussed above are expected to be strongly reduced due to the increasingly shorter time spent by the cc pair in CNM. On the other hand, the other effects listed above (shadowing, energy loss) are not expected to depend on the final quantum numbers of the charmonium states. In such a situation, a similar suppression for the two charmonium states should be observed in high-energy p-A collisions.
In the context of comparative studies between the resonances, the PHENIX experiment at RHIC has recently published results on the ψ(2S) suppression at central rapidity for d-Au collisions at √ s NN = 200 GeV [27], by studying the nuclear modification factor R ψ(2S) /dy), which corresponds to the ratio of the production yields in d-Au and pp at the same energy, normalized by the number of nucleon-nucleon collisions in d-Au. The ratio of the nuclear modification factors R ψ(2S) dAu /R J/ψ dAu is found to be smaller than 1, and strongly decreasing from peripheral to central d-Au events. The observation of a ψ(2S) suppression stronger than that of the J/ψ is in contrast to the expectation of a similar suppression as described above. Data from the LHC can be useful to shed further light on this observation, as nuclear crossing times [25] may be as low as 10 −4 fm/c for charmonium production at forward rapidity, implying a negligible influence of pair break-up processes and, in more general terms, to test our understanding of charmonium propagation in CNM.
In this Letter, we present the first measurement of inclusive ψ(2S) production in √ s NN = 5.02 TeV p-Pb collisions at the LHC, carried out by the ALICE Collaboration, and we compare the results with those for J/ψ. The resonances were measured in the dimuon decay channel using the Muon Spectrometer (MS) [28], which covers the pseudorapidity range −4 < η lab < −2.5. The other detectors involved in this analysis are: (i) the two innermost layers of the Inner Tracking System (Silicon Pixel Detectors, SPD), used for the determination of the primary vertex of the interaction and covering |η lab | < 2.0 (first layer) and |η lab | < 1.4 (second layer) [29]; (ii) the two VZERO scintillator hodoscopes, used mainly for triggering purposes and covering −3.7 < η lab < −1.7 and 2.8 < η lab < 5.1 [30]; (iii) the Zero Degree Calorimeters (ZDC), at 112.5 m from the interaction point [31], used to remove collisions outside the nominal timing of the LHC bunches. Details of the ALICE experimental setup are provided elsewhere [32].
Due to the LHC design, the colliding beams have different energies per nucleon (E p = 4 TeV, E Pb = 1.58 · A Pb TeV, where A Pb = 208 is the mass number of the Pb nucleus). As a consequence, the centre of mass of the nucleon-nucleon collision is shifted by ∆y = 0.465 with respect to the laboratory frame in the direction of the proton beam. Data were taken in two configurations, by inverting the sense of the orbits of the two beams. In this way, both forward (2.03 < y cms < 3.53) and backward (−4.46 < y cms < −2.96) centre of mass rapidities were covered, with the positive rapidity defined by the direction of the proton beam. We refer to the two data samples as p-Pb and Pb-p respectively. The integrated luminosities for the two data samples are L pPb int = 5.01 ± 0.17 nb −1 and L Pbp int = 5.81 ± 0.18 nb −1 [33]. Data were collected with a dimuon trigger, defined as the coincidence of the minimum-bias (MB) condition with the detection of two opposite-sign muon candidates in the trigger system of the MS. The MB condition is a coincidence between signals in the two VZERO hodoscopes and has > 99% efficiency for non-single diffractive events [34]. For the muon candidates, a transverse momentum p T,µ = 0.5 GeV/c trigger threshold is applied. The effect of this threshold is not sharp, and the single muon trigger efficiency reaches its plateau value (∼ 96%) for p T,µ ∼ 1.5 GeV/c. The offline event selection, the muon reconstruction and identification criteria and the kinematic cuts applied at the single and dimuon levels are identical to those described in [35]. In addition, a cut on the transverse distance from the primary vertex of each of the reconstructed muon tracks, weighted with its momentum (pDCA), was performed. Tracks with pDCA> 6 × σ pDCA were rejected. The pDCA resolution is obtained from data, taking into account the resolution on track momentum and slope [36]. Such a track cut reduces the background continuum by a few percent without affecting the resonances.
The extraction of the resonance signals is carried out by means of a fit to the dimuon invariant mass spectrum, as illustrated in Fig. 1 for the two rapidity ranges under study. The J/ψ and ψ(2S) line shapes are described either by Crystal Ball (CB) functions [37], with asymmetric tails on both sides of the peak, or by pseudo-Gaussian functions [38]. The parameters of the resonance shapes are obtained by means of a Monte-Carlo (MC) simulation, generating charmonia which are then tracked and reconstructed in the experimental setup with the same procedure applied to real data. Due to the large signal to background ratio (S/B) in the J/ψ mass region and in order to account for small deviations between MC and data, the position of the J/ψ mass peak and the width are left as free parameters in the fit. For the ψ(2S), due to the less favourable S/B, the mass and widths are constrained by those for the J/ψ using the following relations, which involve the corresponding MC quantities: Alternative values of the ψ(2S) mass resolution have also been tested, allowing the ratio (σ MC ψ(2S) /σ MC J/ψ ) to vary within 10% [36]. Finally, the parameters of the asymmetric tails, which can hardly be constrained by the data, are kept fixed to their MC values. Additional sets of tails, obtained from the MC, but sampling the y cms and p T phase space, have also been tested. The dependence of the extracted J/ψ and ψ(2S) yields on the variation of the tails and on the ψ(2S) mass resolution is included in the systematic uncertainty on the signal extraction. The background continuum under the resonances is parameterized by empirical shapes, using a polynomial times an exponential function or a Gaussian having a width increasing with mass. In order to assess the systematic uncertainty on signal extraction, fits with various combinations of the signal and background shapes are performed, and the start/end point of the fit range is also varied. The raw ψ(2S) yields and their statistical uncertainty is finally obtained as the average of the results of the various fits performed, while the systematic uncertainty is calculated as the root-mean-square (RMS) of their distribution. This results in N ψ(2S) pPb = 1069 ± 130 ± 102 and N ψ(2S) Pbp = 697 ± 111 ± 65, where the first uncertainty is statistical and the second is systematic. As a cross-check, an alternative approach for signal extraction, based on event counting, was also tested. More precisely, after fitting the invariant mass distribution and subtracting the background contribution, the number of ψ(2S) was obtained by integrating the background subtracted spectrum in the region 3.5 < m µ µ < 3.8 GeV/c 2 . Corrections were applied to the measured number of counts to account for the fraction of ψ(2S) outside of the integration region (∼15%) and for the number of J/ψ falling inside the ψ(2S) mass range (∼8%). The results were found to be stable within 1% with respect to 0.  The acceptance times efficiency values (A × ε) for the ψ(2S) were evaluated using MC simulations in a similar way as detailed in [35] for the J/ψ. The input p T distributions were obtained from those used for the J/ψ [35], scaled such that p T , and using the √ s = 7 TeV pp values from LHCb [39,40] obtained in the slightly larger range 2 < y cms < 4.5. The input y distributions were obtained from those used for the J/ψ assuming a scaling of the widths with y is the maximum rapidity for the resonance i at the √ s value under study. An unpolarized distribution for the ψ(2S) was assumed, according to the results obtained in pp collisions at √ s = 7 TeV by the CMS and LHCb experiments [41,42]. The systematic uncertainty for the ψ(2S) acceptance was calculated as the maximum spread of the values obtained by assuming as alternative input distributions those used for the J/ψ itself and amounts to 1.8% (2.5%) for p-Pb (Pb-p). The efficiency of the tracking and trigger detectors of the MS was taken into account in the MC simulations by means of a map of dead channels (tracking) and by building efficiency tables for the detector elements (trigger). The evolution of the detector performance was matched in the MC throughout the data taking, and the ψ(2S) signal was simulated on a run-by-run basis by generating a number of events proportional to the number of offline-selected triggered events. The systematic uncertainties on the efficiencies were obtained with algorithms based on real data, with the same procedure adopted in [35], and they are identical for J/ψ and ψ(2S). A small uncertainty related to the efficiency of the matching between tracking and triggering information was also included [35].
The p T -integrated A × ε values for ψ(2S) production, obtained with this procedure, are 0.270 ± 0.014 (p-Pb) and 0.184 ± 0.013 (Pb-p), where the lower value for Pb-p is mainly due to a smaller detector efficiency in the corresponding data taking period. The quoted uncertainties are systematic and are obtained as the quadratic sum of the uncertainties on MC input, tracking, triggering and matching efficiencies. The statistical uncertainties are negligible.
The cross section times the branching ratio B.R.(ψ(2S) → µ µ) for inclusive ψ(2S) production in p-Pb collisions (and similarly for Pb-p) is: where N cor ψ(2S)→µ µ is the number of ψ(2S) corrected for A × ε, N MB is the number of MB events, obtained as the number of dimuon triggers times the probability of having a triggered dimuon in a MB event, and σ MB pPb is the cross section for the occurrence of the MB condition. The numerical values of N MB and σ MB pPb , and their uncertainties, are the same as those quoted in [35]. We obtain in this way the following cross section values:  Table 1. The splitting between uncorrelated and (partially) correlated sources is also summarized there. The corresponding values for the J/ψ can be found in [35].
Suppression of ψ(2S) production in p-Pb collisions at √ s NN = 5.02 TeV 7 The study of the cross section ratio between ψ(2S) and J/ψ, and the comparison of this ratio between different systems, offers a powerful tool to investigate nuclear effects on charmonium production. In addition, several systematic uncertainties cancel, or are significantly reduced, when studying such ratios. In particular, in the present analysis, the tracking, trigger and matching efficiencies, as well as the normalization-related quantities, cancel out. For the MC input, the fraction of the uncertainty related to the choice of the J/ψ kinematical distribution [35] cancels in the cross section ratios, and a remaining 1% (2%) uncertainty for p-Pb (Pb-p) is assigned to this source. Finally, the uncertainty on signal extraction is considered as uncorrelated between J/ψ and ψ(2S), and its value for the cross section ratios amounts to 10% for both p-Pb and Pb-p. The resulting values are: In Fig. 2 we compare these ratios with the corresponding ALICE results for pp collisions [36], obtained in slightly different centre of mass energy and rapidity regions, √ s = 7 TeV, 2.5 < |y| < 4, as no LHC pp results are available in the same kinematic conditions of proton-nucleus collisions. The pp ratios are significantly higher than those for p-Pb and Pb-p, which are compatible within uncertainties. The double ratio [σ ψ(2S) /σ J/ψ ] pPb /[σ ψ(2S) /σ J/ψ ] pp is a useful quantity to directly compare the relative suppression of the two states between various experiments. For this analysis, since the collision energy and the y-coverage of the p-Pb (Pb-p) and pp measurements are different, we have estimated the possible dependence of the σ ψ(2S) /σ J/ψ vs √ s and y in pp collisions. We start from the empirical observation that this ratio is very similar at collider energies over a rather broad range of y and √ s. In particular, from the LHCb data ( √ s = 7 TeV, 2 < y < 4.5) [39,40] one gets 2.11% for the inclusive ratio integrated over p T , while the corresponding value from CDF data (pp at √ s = 1.96 TeV, |y| < 0.6) [43] is 2.05%, i.e., only 3% smaller (the latter quantity was obtained by extrapolating the CDF ψ(2S) measurement to p T = 0 with the phenomenological function f (p T ) = (p T )/[1 + (p T /a) 2 ] b ) [44]. The LHCb result can be extrapolated to central rapidity at √ s = 7 TeV, assuming a Gaussian y-distribution for both resonances, with the width of the J/ψ distribution tuned directly on data [39] and that for ψ(2S) obtained from the former assuming a scaling of the widths with y ψ(2S) max /y J/ψ max . The effect of this rescaling is small, leading to a 3% increase of the ratio. The central-rapidity ratio σ ψ(2S) /σ J/ψ at √ s = 5.02 TeV is then obtained by means of an interpolation between the CDF and LHCb-rescaled values, assuming a linear dependence of the ratio vs √ s. Finally, one can extrapolate the ratio to the p-Pb and Pb-p rapidity ranges by using for the J/ψ the Gaussian shape obtained with the interpolation procedure described in [45] and for the ψ(2S) the corresponding shape scaled with y The difference between the measured value of σ ψ(2S) /σ J/ψ for √ s = 7 TeV, 2 < y cms < 4.5 and the results of the interpolation procedure to √ s = 5.02 TeV, 2.03 < y cms < 3.53 (−4.46 < y cms < −2.96) is -1.6% (-3.7%). When calculating the double ratio [σ ψ(2S) /σ J/ψ ] pPb /[σ ψ(2S) /σ J/ψ ] pp , we choose to use for pp the measured value at √ s = 7 TeV, 2.5 < y cms < 4 [36] (rather than the interpolated one at √ s = 5.02 TeV) and to include a 8% systematic uncertainty on this quantity, i.e., about twice the maximum difference between the measured values of the ratio in pp and the results of the interpolation procedure. A similar uncertainty would be obtained using as an input for the calculation, instead of the LHCb data, the more recent pp result from ALICE on σ ψ(2S) /σ J/ψ [36].
The values of the double ratio are shown in Fig. 3, where they are also compared with the corresponding results obtained by the PHENIX experiment at √ s NN = 200 GeV, for |y| < 0.35 [27]. When forming the double ratio, the systematic uncertainties on the pp ratio, including the 8% contribution described in the previous paragraph, are considered as correlated between forward and backward rapidity, while the other systematic uncertainties are treated as uncorrelated. The ALICE results show that, compared to pp, the ψ(2S) is more suppressed than the J/ψ to a 2.1σ (3.5σ ) level in p-Pb (Pb-p). The PHENIX result shows a similar feature, at a 1.3σ level.
The suppression of charmonium states with respect to the corresponding pp yield can be quantified using the nuclear modification factor. For ψ(2S), R ψ(2S) pPb is obtained by combining R J/ψ pPb [35] with the double ratio evaluated above: In Fig. 4, R ψ(2S) pPb is shown and compared with R J/ψ pPb . For the double ratios, the difference in the √ s and y domains between p-Pb and pp is taken into account by the inclusion of the 8% systematic uncertainty described above. The other quoted uncertainties combine those from R J/ψ pPb [35] with those for the double ratio, avoiding a double counting of the J/ψ related uncertainties. Figure 4 indicates that the ψ(2S) suppression is much stronger than for the J/ψ and reaches a factor ∼2 with respect to pp. The results are compared with theoretical calculations including either nuclear shadowing only [46] or coherent energy loss, with or without a shadowing contribution [47]. For the former mechanism, the values correspond to calculations performed for the J/ψ. However, due to the relatively similar kinematic distributions of gluons that produce the cc pair which will then hadronize to a J/ψ or a ψ(2S), the shadowing effects are expected to be the same, within 2-3% [48], for the two charmonium states. No sensitivity to the final quantum numbers of the charmonium state is expected for coherent energy loss [49], implying that the calculations shown in Fig. 4 are valid for both resonances. As a consequence, all three models would predict an almost identical suppression for the ψ(2S) and the J/ψ over the full rapidity range, with negligible theoretical uncertainties. This prediction is in strong disagreement with our data and Suppression of ψ(2S) production in p-Pb collisions at √ s NN = 5.02 TeV 9 clearly indicates that other mechanisms must be invoked in order to describe the ψ(2S) suppression in proton-nucleus collisions.
The break-up cross section of the final state resonance due to interactions with CNM is expected to depend on the binding energy of the charmonium and such a mechanism would be a natural explanation for the larger suppression of ψ(2S). However, this process becomes relevant only if the charmonium formation time τ f is smaller than the time τ c spent by the cc pair inside the nucleus. One can evaluate the average proper time τ c spent in CNM as τ c = L /(β z γ) [25], where L is the average length of nuclear matter crossed by the pair, which can be calculated in the framework of the Glauber model [50], β z = tanh y rest cc is the velocity of the cc along the beam direction in the nucleus rest frame, and γ = E cc /m cc . For cc pairs in the charmonium mass range emitted at p T = 0 in the forward acceptance, one gets τ c ∼ 10 −4 fm/c, while the corresponding value at backward rapidity is ∼ 7 · 10 −2 fm/c. Estimates for the formation time τ f range between 0.05 and 0.15 fm/c [24,25]. In this situation, no break-up effects depending on the final charmonium state should be expected at forward rapidity, and even for backward production one has at most τ f ∼ τ c which would hardly accomodate the strong difference observed between ψ(2S) and J/ψ suppression. As a consequence, other final state effects should be considered, including the interaction of the cc pair with the final state hadronic system created in the proton-nucleus collision.
The sizeable ψ(2S) statistics collected in proton-nucleus collisions allows for a differential study of the various observables as a function of p T , in the range 0 < p T < 8 GeV/c. We have chosen a transverse momentum binning which leads to similar relative statistical uncertainties in each bin over the p T range covered. The analysis is carried out with the same procedure adopted for the integrated data samples. In particular, the systematic uncertainties are evaluated differentially in p T , and their range is also reported in Table 1. In Fig. 5 the differential cross sections at forward and backward rapidity are presented. The systematic uncertainties on signal extraction, MC input and efficiencies are considered as bin-tobin uncorrelated. The uncertainties associated with the cross section normalization (N MB , σ MB pPb ) are correlated between the various p T bins, and partially correlated between p-Pb and Pb-p. The nuclear modification factor for ψ(2S), compared to the corresponding quantity for J/ψ [35]. The horizontal bars correspond to the width of the rapidity regions under study. The vertical error bars correspond to statistical uncertainties, the boxes to uncorrelated systematic uncertainties, and the shaded areas to partially correlated uncertainties. The filled box on the right, centered on R pPb = 1, shows uncertainties that are fully correlated between J/ψ and ψ(2S). Model calculations tuned on J/ψ, and including nuclear shadowing [46] and coherent energy loss [47] are also shown. The corresponding calculations for ψ(2S) produce identical values for the coherent energy loss mechanisms and a 2-3% larger result for nuclear shadowing and therefore are not shown. In Fig. 6 we present the p T dependence of the double ratio [σ ψ(2S) /σ J/ψ ] pPb /[σ ψ(2S) /σ J/ψ ] pp , with the p-Pb J/ψ cross sections taken from [35] and the pp values from [36]. As for the integrated double ratio, the systematic uncertainties related to efficiencies and to normalizations cancel out for both protonnucleus and pp, while the uncertainties on signal extraction and Monte-Carlo input are considered as uncorrelated. The 8% uncertainty related to the √ s and y mismatch between the two systems is correlated as a function of p T , while the uncertainties on the ratio in pp collisions are correlated, for each p T bin, between forward and backward rapidity. Finally, in Fig. 7 the p T dependence of the ψ(2S) nuclear modification factor, calculated using Eq. 2, is presented and compared with the corresponding result for J/ψ [51]. The uncertainties are obtained with the procedure used in Fig. 4, and the results are compared to the same models quoted there.
Within uncertainties, no p T dependence of the double ratio can be seen, and consequently as a function of transverse momentum R ψ(2S) pPb has qualitatively a similar shape as that exhibited by R J/ψ pPb , but systematically characterized by smaller values. Theoretical models, which in this case also yield the same prediction for J/ψ and ψ(2S), are in fair agreement with J/ψ results, but clearly overestimate the ψ(2S) nuclear modification factor values.
It is interesting to note that different values of transverse momentum for the resonances correspond to different τ c , with the crossing times decreasing with increasing p T . In particular, for backward production, τ c varies by about a factor 2, between ∼0.07 (at p T = 0) and ∼0.03 fm/c (at p T = 8 GeV/c). As a consequence, a larger fraction of cc pairs may form the final resonance state inside CNM at low p T , and one might expect smaller values of the double ratio in that transverse momentum region due to the weaker binding energy of ψ(2S). Although the results shown in Fig. 6 could be suggestive of such a trend, no firm conclusion can be reached due to the current experimental uncertainties.
In summary, we have presented results on inclusive ψ(2S) production in proton-nucleus collisions at the LHC. Measurements were performed with the ALICE Muon Spectrometer in the p-going (2.03 < y cms < 3.53) and Pb-going (−4.46 < y cms < −2.96) directions, and the production cross sections, the double ratios with respect to the J/ψ in p-Pb and pp and the nuclear modification factors were estimated. The The nuclear modification factor for ψ(2S), compared to the corresponding quantity for J/ψ [51], as a function of p T . Plots correspond to p-Pb (left) and Pb-p (right) collisions. The horizontal bars correspond to the width of the transverse momentum bins. The vertical error bars correspond to statistical uncertainties, the boxes to uncorrelated systematic uncertainties, and the shaded areas to partially correlated uncertainties. The filled box on the right, centered at R pPb = 1, shows uncertainties that are fully correlated between J/ψ and ψ(2S). For details on model comparisons, see the caption of Fig. 4. results show that ψ(2S) is significantly more suppressed than J/ψ in both rapidity regions, and that no p T dependence of this effect is found within uncertainties. This observation implies that initial state nuclear effects alone cannot account for the modification of the ψ(2S) yields, as also confirmed by the poor agreement of the ψ(2S) R pPb with models based on shadowing and/or energy loss. Final state effects, such as the pair break-up by interactions with cold nuclear matter, might in principle lead to the observed effect, but the extremely short crossing times for the cc pair, in particular at forward rapidity, make such an explanation unlikely. Consequently, other final state effects should be considered, including the interaction of the cc pair with the final state hadronic system created in the proton-nucleus collision.