Measurement of prompt ψ(2S) production cross sections in proton–lead and proton–proton collisions at √sNN=5.02 TeV

Article history: Received 6 May 2018 Received in revised form 2 January 2019 Accepted 29 January 2019 Available online 1 February 2019 Editor: M. Doser


Introduction
The study of quarkonium production in nuclear collisions has a long and rich history, dating back to the original proposal by Matsui and Satz predicting J/ψ suppression in heavy ion collisions due to Debye screening in the quark-gluon plasma (QGP) [1]. After this proposal, the first J/ψ measurements in heavy ion collisions were performed in fixed target experiments at the CERN SPS, at a nucleon-nucleon center-of-mass energy of √ s NN ≈ 20 GeV [2,3].
A similar level of suppression was later observed in gold-gold collisions at the BNL RHIC, at √ s NN = 200 GeV [4,5]. At the CERN LHC, the production of charmonium (J/ψ , ψ(2S)) and bottomonium (ϒ(1S), ϒ(2S), ϒ(3S)) states has been studied in lead-lead (PbPb) collisions at √ s NN = 2.76 and 5.02 TeV [6][7][8][9][10][11][12], bringing new elements for the understanding of the medium produced in highenergy heavy ion collisions. The quarkonium yields can be modified in heavy ion collisions because of several effects [13], including suppression [1] and recombination of charm quark pairs [14] inside the hot matter (QGP), and cold nuclear matter effects. An unambiguous interpretation of the nucleus-nucleus LHC results requires a quantitative understanding of cold nuclear matter effects. The nuclear parton distribution functions (nPDFs) are known to be different from those in a E-mail address: cms -publication -committee -chair @cern .ch. free proton [15,16]. In addition, gluon radiation induced by multiple parton scattering in the nucleus leads to transverse momentum (p T ) broadening and coherent energy loss, resulting in a significant quarkonium suppression in nuclear collisions at all available energies [17,18]. These phenomena are best studied in proton-nucleus collisions, in which hot medium effects, such as those due to the QGP, are likely to be limited.
Many charmonium production measurements have been performed in proton-induced collisions, on several nuclei, at the SPS [19][20][21][22], HERA [23], and Tevatron [24]. A global analysis of the fixed-target measurements can be found in Ref. [25]. At RHIC, J/ψ and ψ(2S) data in deuteron-gold collisions have been reported by the PHENIX [26] and STAR [27] Collaborations. At the LHC, the cross section of J/ψ in proton-lead (pPb) collisions at √ s NN = 5.02 TeV has been measured by the ALICE [28,29], ATLAS [30], CMS [31], and LHCb [32] Collaborations. A significant suppression of the prompt J/ψ yield in pPb collisions has been observed at forward rapidity ( y) and low p T , while no strong nuclear effects are reported at backward rapidity, where forward and backward indicate, respectively, the directions of the proton and Pb beams. the ground states and might suffer stronger suppression in heavy ion collisions. At the LHC, the ALICE [36] and CMS [11] Collaborations have reported a stronger suppression of the ψ(2S) state compared to the J/ψ in PbPb collisions. In pPb collisions, ALICE [37], ATLAS [34], and LHCb [38] data show that ψ(2S) suppression, integrated over transverse momentum, is more pronounced than that of the J/ψ . This observation suggests final-state effects for the excited states, possibly due to inelastic interactions with the medium produced in pPb collisions [39]. In the bottomonium sector, the double yield ratios ϒ(3S)/ϒ(1S) and ϒ(2S)/ϒ(1S) in pPb relative to pp collisions have been measured by CMS [40] and found to be less than unity, again indicating stronger final-state effects in the production of excited quarkonium states.
This Letter reports measurements of the cross sections for prompt ψ(2S) production in pp and pPb collisions at √ s NN = 5.02 TeV, with the ψ(2S) decaying to μ + μ − , over the p T range 4-30 GeV/c and center-of-mass rapidity range −2.4 < y CM < 1.93.
The data were collected with the CMS detector at the LHC, in 2013 for the pPb sample and in 2015 for the pp sample, corresponding to integrated luminosities of 34.6 ± 1.2 nb −1 [41] and 28.0 ± 0.6 pb −1 [42], respectively. In addition, the modification of quarkonium production in pPb collisions is quantified by the nuclear modification factor, R pPb , which is defined as the ratio of the cross sections in pPb and pp collisions divided by the Pb mass number, A = 208. The ψ(2S) R pPb is determined as a function of y CM and p T , and is compared to that of the J/ψ mesons measured at the same center-of-mass energy [31]. This is the first measurement of ψ(2S) R pPb at √ s NN = 5.02 TeV in differential bins of p T and y CM that uses the pp data measured at the same center-ofmass energy.

The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume there are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity (η) coverage provided by the barrel and endcap detectors. The forward hadron (HF) calorimeter uses steel as absorber and quartz fibers as the sensitive material. The two halves of the HF are located at ±11.2 m from the nominal interaction point. Together they provide coverage in the range 3.0 < |η| < 5.2 and also serve as luminosity monitors. Muons are detected in gasionization chambers embedded in the steel flux-return yoke outside the solenoid, in the range |η| < 2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive-plate chambers. Matching muons to tracks measured in the silicon tracker results in a relative p T resolution for typical muons in this analysis of 1.3-2.0% in the barrel and better than 6% in the endcaps [43]. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [44].

Event selection
The pPb collisions at √ s NN = 5.02 TeV correspond to a proton beam energy of 4 TeV and a lead beam energy of 1.58 TeV per nucleon. The proton beam traveled in the −η direction (in the detector coordinate system) in the first part of the run, corresponding to an integrated luminosity L int = 20.7 nb −1 , and in the opposite direction in the second part of the run, corresponding to L int = 13.9 nb −1 . Particles emitted at |η CM | = 0 in the nucleonnucleon center-of-mass frame are detected in the laboratory frame at η lab = ±0.465 depending on the proton beam direction. In this paper, data for half of the run were reflected so that positive η always corresponds to the direction of the proton beam. The pp data set, collected at the same collision energy as the pPb sample, corresponds to L int = 28.0 pb −1 . In the pp sample, the dimuons from ψ(2S) decays are reconstructed within |y CM | < 2.4 and in the same p T range as the pPb data, 4 < p T < 30 GeV/c.
Inelastic hadronic collisions are selected by requiring at least one HF tower with more than 3 GeV of total energy in each of the two HF calorimeters. This is not required in pp collisions, which suffer less from photon-induced interactions compared to pPb collisions. The pp and pPb events are further selected to have at least one reconstructed primary vertex composed of two or more associated tracks, excluding the two muons, within 25 cm from the nominal interaction point along the beam axis and within 2 cm in the transverse plane. To reject the beam-gas background events, the fraction of good-quality tracks associated with the primary vertex is required to be larger than 25% when there are more than 10 tracks per event.
The dimuon events are selected by the level-1 trigger, a hardware-based trigger system requiring two muon candidates in the muon detectors with no explicit limitations on their p T or η. In the offline analysis, muons are required to be within the following kinematic regions, which ensure single-muon reconstruction efficiencies above 10%: (1) The oppositely charged muon pairs are further selected to originate from a common vertex with a χ 2 probability greater than 1%, and to survive standard identification criteria [43]. In order to remove cosmic-ray muons, the transverse and longitudinal distances of closest approach between the muon trajectory and the reconstructed primary vertex are required to be less than 0.3 cm and 20 cm, respectively. All of these selections are common to both the pp and the pPb data sets.

Yield extraction
The prompt ψ(2S) signal extraction procedure is similar to that in previous CMS analyses [8,11], and is the same for the pp and pPb data sets. The dimuon mass distribution is fitted with signal (including both the J/ψ and ψ(2S) resonances) and background contributions using an extended unbinned maximum likelihood procedure [45]. While the scope of the present Letter is the measurement of the prompt ψ(2S) production, the J/ψ resonance was included in the ψ(2S) fit to increase the peak fitting stability. It has been checked that the prompt J/ψ results obtained in this analysis agree with the ones in Ref. [31], which used a different method for separating prompt from nonprompt charmonia. The prompt J/ψ results of Ref.
The CB and Gaussian functions have independent widths, σ CB and σ G , to accommodate the dependence of the dimuon invariant mass resolution on the dimuon rapidity and p T , but share a common mean m 0 representing the J/ψ mass. The signal models and J/ψ signal shapes. The underlying background is described by a Chebyshev polynomial of degree N (1 ≤ N ≤ 3). The degree of the Chebyshev polynomial is obtained in each (p T , y CM ) bin of the analysis using a log-likelihood ratio test. Several alternative fitting procedures have been tested, and the yield variations with respect to the nominal result are included as a systematic uncertainty, as explained in Section 6. The two pPb data sets, corresponding to each proton beam direction, are merged and analyzed together after having verified that the independent results are compatible with each other.
The J/ψ and ψ(2S) coming from b hadron decays (nonprompt charmonia) are evaluated using the displacement of the μ + μ − vertex from the primary collision vertex. This secondary μ + μ − vertex is characterized by the pseudo-proper decay length, where L xy is the transverse distance between the primary and dimuon vertices, m J/ψ is the mass of the J/ψ [47] (assumed for all muon pairs), and p T is the transverse momentum of the dimuon. Prompt charmonia are selected by requiring J/ψ to be smaller than a threshold value l 0 , which is tuned using simulation separately for the pp and pPb collisions systems, in order to keep 90% of the total prompt charmonia [11]. Since the J/ψ resolution improves with increasing dimuon p T , the l 0 values also depend on p T . The l 0 values used remove between 70% and 90% (80% and 90%) of the nonprompt ψ(2S) in pPb (pp) collisions, from low-to high-p T .
The yields so obtained have a small nonprompt contamination, which is corrected using the number of simulated events passing and failing the J/ψ threshold criteria [11]. The full value of this correction is also propagated as a source of systematic uncertainty. Fig. 1 shows the dimuon invariant mass distributions with the J/ψ and ψ(2S) peaks in pPb and pp data, for one of the bins with the smallest signal-to-background ratio (lowest p T and most backward y), after applying the J/ψ selection, together with the curves resulting from the fits. The raw prompt ψ(2S) yield extracted in these bins is ∼300 for the pPb, and twice as much for the pp samples.

Acceptance and efficiency corrections
Simulated events are used to obtain the acceptance and efficiency correction factors for the measured ψ(2S) yields. The events are generated using pythia 6.424 [48] for The acceptance in a given (p T , y CM ) bin is defined as the fraction of generated ψ(2S) mesons resulting in a detectable muon pair, i.e., passing the single muon selection criteria defined in Eq. (1). The efficiency is given by the fraction of generated and detectable muon pairs that result in a reconstructed muon pair, also passing the trigger and offline selections. The combined ψ(2S) acceptance and efficiency for pPb (pp) results ranges between 13% (14%) in the lowest p T region (4.0 < p T < 6.5 GeV/c) and 66% (67%) in the highest p T region (10.0 < p T < 30.0 GeV/c). It is maximum in the overlap region between barrel and endcap detectors, and decreases to minimum values for |y CM | > 2.
The individual components of the simulation-based dimuon efficiency (track reconstruction, muon identification and selection, and triggering) are probed using single muons from J/ψ meson decays in both simulated and collision data, with the tag-and-probe (T&P) method [31,54]. The data-to-simulation ratios of single muon efficiencies obtained from T&P, calculated as a function of muon η and p T , are used as weights (scale factors) to correct event-by-event the dimuon efficiency. The effect of this correction on the dimuon efficiency is similar for pp and pPb events and ranges from 0.99 to 1.33, with larger corrections at lower p T and more forward/backward rapidities.

Systematic uncertainties
The following sources of point-to-point systematic uncertainties are considered for both pp and pPb data: the yield extraction method, given the choice of signal and background models; acceptance and efficiency corrections, including T&P scale factors and the possible difference in the dimuon p T spectrum between data and simulation; and the nonprompt charmonia contamination. The evaluation of these systematic uncertainties is described below.
• Signal shape variation. This systematic uncertainty is obtained by changing the fitting constraints on the CB shape parameters. In the nominal fits, the CB parameter n is fixed from simulation, n = 2.1, and the parameter α is left free. In a first variation, the parameter α is fixed to the MC-based value 1.7, and n is left free. A second variation consists in fixing both parameters to the values extracted from MC, n = 2.1 and α = 1.7.
The maximum difference, in each analysis bin, between the yields extracted with the nominal fit and either of these variations, is taken as a systematic uncertainty.
The systematic uncertainty is estimated as the absolute difference in the yields with respect to the nominal case.
• Simulated dimuon p T spectrum. The acceptance and efficiency correction factors depend on the shape of the simulated ψ(2S) p T distribution; the difference between data and simulation is a source of systematic uncertainty. The ratio of the corrected yields in data and simulation is evaluated as a function of p T , for each rapidity bin. Continuous weighting factors are obtained by fitting these data-to-simulation ratios with a linear function in p T . The acceptance and efficiency values are evaluated again after weighting the p T distribution of the generated ψ(2S) mesons in the simulation by the function obtained. The difference between the reweighed simulation and the nominal yields is taken as a systematic uncertainty.
• T&P scale factors. The statistical uncertainty on the T&P scale factors, as well as systematic uncertainties in their derivation, are accounted for as a systematic uncertainty. These uncertainties are further described in Ref. [31].
• Nonprompt contamination. The difference between the prompt meson yields with and without the correction for the residual nonprompt contamination is propagated as a systematic uncertainty.
The systematic uncertainty in the yield extraction, determined by summing the uncertainties from the signal and background shape variations in quadrature, is in the range 1.0-22% and 0.4-6.5% for the pPb and pp results, respectively. This large range is mostly driven by the variation of the signal over background ratio across the analysis bins. The dominant part in this uncertainty is from background modeling, with an average over all the p T and y CM bins of 3.9 (2.4)% and a maximum of 22 (4.9)% for the pPb (pp) results. The average signal modeling contribution is 1.9% and 1.4%, for the pPb and pp results, respectively.
The systematic uncertainty in the acceptance and efficiency correction factors, combining the dimuon p T spectrum reweighting and T&P uncertainties, lies within 2.0-7.4% and 1.9-8.1% for the pPb and pp results, respectively. The prompt selection method induces an uncertainty of 4.5-15% (0.2-8.0%) for the pPb (pp) results, with the maximum value in the lowest p T bin in the backward y region. The total systematic uncertainty, calculated as the sum in quadrature of the individual uncertainties, is in the range 5-26% (4-11%) for the pPb (pp) cross section measurements. In general, the uncertainty is minimum in the highest p T bins in the central y region, and increases when going to lower p T and forward/backward y regions. For the R pPb measurement, the pp and pPb uncertainties are considered independent and added in quadrature point-by-point. The total systematic uncertainty in this case is in the range 5.0-22.6%. The global (common to all points) systematic uncertainty due to the uncertainty in the integrated luminosity of the pPb and pp data sets is 3.5% [41] and 2.3% [42], respectively. For the cross section results, this uncertainty is not included to the point-topoint uncertainties, while for the R pPb results the two numbers are added in quadrature and displayed as a box around R pPb = 1.
The dominant source of uncertainty for the R pPb measurement is the statistical uncertainty in the pPb data.

Results
The prompt ψ(2S) production cross section (multiplied by the ψ(2S) branching fraction to μ + μ − , B(ψ(2S) → μ + μ − )) in the dimuon decay channel is determined as  spectively. The results are given as a function of p T and in four rapidity bins, separately for forward (the direction of the proton beam) and backward (the direction of the Pb beam) rapidities in the case of the pPb measurements. The second observable considered is the nuclear modification factor, defined as In the absence of any nuclear effects the measured yield in pPb collisions would be just a superposition of A = 208 (the number of nucleons in the Pb nucleus) pp collisions, and the R pPb would be one. In the forward rapidity region, the R pPb is consistent with unity for all p T bins (although systematically smaller). For comparison, the prompt J/ψ nuclear modification factor [31] is also shown in Fig. 4.
The measured value of R pPb for prompt ψ(2S) mesons, when integrated over p T and rapidity (6.5 < p T < 30 GeV/c, |y| < 1.6), is 0.852 ± 0.037stat ± 0.062syst. The prompt J/ψ R pPb in the same kinematic range is 1.108 ± 0.021stat ± 0.055syst. The R pPb for prompt J/ψ mesons lies systematically above that of the ψ(2S) state. The difference between the two sets of results was quan-  tified, separately for the backward and forward regions, by comparing the two distributions with a χ 2 -test, removing the correlated uncertainties from the integrated luminosity. The p-values are < 0.05 for the lowest two p T ranges in the backward rapidity region, and > 0.37 in all the other rapidity and p T intervals. This shows that, with a p-value cutoff of 0.05, the two sets of results are incompatible with each other in the backward rapidity region for p T < 10 GeV/c, but are compatible in the rest. This suggests the presence of different nuclear effects at play in the production of the excited charmonium state compared to the ground state, in the region of backward rapidity and for p T < 10 GeV/c. Fig. 5 shows the p T dependence of the prompt ψ(2S) R pPb in seven rapidity bins, from the most backward −2.4 < y CM < −1.93 to the most forward 1.5 < y CM < 1.93 accessible regions. Also in this case, a χ 2 -test was used to quantify the significance of the difference of the results from unity, in which the fully correlated global uncertainty, displayed as a box around R pPb = 1, was not included. The p-values are below 0.05 only in the most backward region. This points to the presence of nuclear effects affecting the ψ(2S) production in the most backward region that persists at large transverse momentum.
The suppression of prompt ψ(2S) mesons as compared to prompt J/ψ mesons, seen in Fig. 4, is compatible with what was measured by the ALICE [37], ATLAS [34], and LHCb [38] Collaborations for p T integrated charmonium production in pPb collisions at the same collision energy. While nPDFs [15,16] and coherent energy loss [17,18] are the most discussed effects to explain prompt J/ψ meson suppression, these two phenomena are expected to affect the R pPb of prompt J/ψ and ψ(2S) mesons by a similar amount. On the contrary, the final-state interaction with hadrons moving along with the produced charmonium might lead to a stronger suppression of the ψ(2S) meson, due to its larger size [39,55]. The present measurements, covering wide transverse momentum (4 < p T < 30 GeV/c) and rapidity (−2.4 < y CM < 1.93) ranges, will help understand the origin of the suppression of excited quarkonium states in pPb collisions at the LHC.

Summary
The data collected by CMS in pp and pPb collisions at √ s NN = 5.02 TeV are used to investigate prompt ψ(2S) meson production.
The results are based on data samples corresponding to integrated luminosities of 28.0 pb −1 for pp collisions and 34.6 nb −1 for pPb collisions. The nuclear modification factor (R pPb ) of prompt ψ(2S), in the kinematic range 4 < p T < 30 GeV/c and −2.4 < y CM < 1.93, is determined and compared to that of prompt J/ψ mesons, reported in Ref. [31]. The prompt ψ(2S) production is suppressed in the intermediate 6.5-10 GeV/c p T interval in the region of backward rapidity. The R pPb is consistent with unity everywhere else (although systematically smaller). The R pPb values of prompt J/ψ when compared to those of prompt ψ(2S) mesons, point to different nuclear effects at play in the production of the excited charmonium state compared to the ground state, in the region of backward rapidity and for p T < 10 GeV/c. The effects of nuclear parton distribution functions or coherent energy loss are expected to affect the R pPb of prompt J/ψ and ψ(2S) by a similar amount, thus the results hint the presence of final-state interactions with the medium (partonic or hadronic) produced in pPb collisions.

Acknowledgements
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses.