Measurement of prompt $\psi$(2S) production cross sections in proton-lead and proton-proton collisions at $\sqrt{s_{_\mathrm{NN}}} =$ 5.02 TeV

Measurements of prompt $\psi$(2S) meson production cross sections in proton-lead (pPb) and proton-proton (pp) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{_\mathrm{NN}}} =$ 5.02 TeV are reported. The results are based on pPb and pp data collected by the CMS experiment at the LHC, corresponding to integrated luminosities of 34.6 nb$^{-1}$ and 28.0 pb$^{-1}$, respectively. The nuclear modification factor $R_\mathrm{pPb}$ is measured for prompt $\psi$(2S) in the transverse momentum range 4 $<$ p$_\mathrm{T}$ $<$ 30 GeV$/c$ and the center-of-mass rapidity range $-$2.4 $<y_\mathrm{cm}<$ 1.93. The results on $\psi$(2S) $R_\mathrm{pPb}$ are compared to the corresponding modification factor for prompt J$/\psi$ mesons. The results 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$_\mathrm{T}$ $<$ 10 GeV$/c$.


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 at the CERN SPS, at a nucleonnucleon 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 high-energy heavy ion collisions.
The quarkonium yields can be modified in heavy ion collisions because of several effects [13], including suppression inside the QGP [1], recombination of charm quark pairs [14], and cold nuclear matter effects. An unambiguous interpretation of the 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 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 protonnucleus 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. Measurements of the Υ(1S) in pPb collisions at √ s NN = 5.02 TeV have also been performed by the ALICE [33], ATLAS [34], and LHCb [35] experiments, indicating that the Υ(1S) state is less suppressed than the J/ψ.
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. Additional information can be obtained by studying the behavior of the excited states, which are less tightly bound compared to 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. 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 using the pp data measured at the same center-of-mass 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 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 gas-ionization 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 nucleon-nucleon center-of-mass frame are detected at η lab = ±0.465 depending on proton beam direction. In this paper, data for half of the run was 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.
In order to remove beam-related background, 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 goodquality 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%: 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.

Yield extraction
The signal extraction procedure is similar to that in previous CMS analyses [8,11]. The J/ψ results obtained in this analysis agree with the ones previously published [31], presented in this Letter along with the new analysis of ψ(2S) production. 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]. Both resonance shapes are modeled by the weighted sum of a Crystal Ball (CB) [46] and a Gaussian function. The CB function, g CB (m), combines a Gaussian core and a power law tail with exponent n, accounting for energy loss due to final-state photon radiation, with a parameter α defining the transition between the Gaussian and the power law functions: (2) 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 used for the ψ(2S) and J/ψ share the same α and n parameters. The mean and the width of the Gaussian model for the ψ(2S) are obtained from those of the J/ψ, scaled by their mass ratio (m ψ(2S) /m J/ψ = 1.1903 [47]). The following parameters are left free in the fit: m 0 , σ CB , σ G , N J/ψ (the J/ψ yield), N ψ(2S) (the ψ(2S) yield), f (the relative contribution of the Gaussian and CB functions), and α. Based on simulation studies, the value of the parameter n is fixed to 2.1. The parameter α is left free, covering the variation of signal shapes in each of the p T and rapidity bins. The same value for f is used in the definition of the ψ(2S) 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 [11], which is tuned using simulation in order to keep 90% of the total prompt charmonia. 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. Figure 1 shows the dimuon invariant mass distributions with the J/ψ and ψ(2S) peaks, for two kinematic ranges in the dimuon p T and rapidity in pPb data, after applying the J/ψ selection, together with the curves resulting from the fits. after applying the J/ψ selection, for −2.4 < y CM < −1.93 and 4 < p T < 6.5 GeV/c (left panel), and 0 < y CM < 0.9 and 10 < p T < 30 GeV/c (right panel). The fits to the distributions are also shown.

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 pPb collisions and PYTHIA 8.209 [49] for pp collisions. The generated particles in the pPb Monte Carlo (MC) are boosted by the β of the center-of-mass system in the laboratory frame, resulting in ∆y = ±0.465. The prompt J/ψ and ψ(2S) are assumed to be produced unpolarized in both pp and pPb collisions, which is supported by measurements in pp collisions at √ s = 7 TeV [50,51]. The final-state QED radiation of the decay muons is simulated using PHOTOS 215.5 [52]. Finally, the CMS detector response is simulated using GEANT4 [53].
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 single muon efficiencies obtained from simulation are corrected using J/ψ data, with the data driven tag-and-probe (T&P) technique [31,54]. The data-to-simulation ratios of single muon efficiencies obtained from T&P, as a function of η and p T , are applied to each of the two muons as scale factors to reweight, event-by-event, the number of reconstructed dimuons in the simulation. The dimuon efficiency scale factors are similar for pp and pPb events, and range from 0.99 to 1.33, with the largest factor found in the lowest p T bin.

Systematic uncertainties
The following sources of systematic uncertainties are considered: 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 method for selecting prompt charmonia. 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.
• Background shape variation. The degree N of the Chebyshev polynomial is changed to N + 1 if N < 3, and to N − 1 if N = 3. 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].
• Prompt selection method. 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 2-25%. This large range is mostly driven by the variation of the signal over background ratio across the analysis bins. The systematic uncertainty in the acceptance and efficiency correction factors, combining the dimuon p T spectrum reweighting and T&P uncertainties, lies within 3-10%. The prompt selection method induces an uncertainty of 1 to 10%. The total systematic uncertainty is in the range 5-27%, depending on the (p T , y CM ) bin. In addition, for R pPb measurements there is a global systematic uncertainty of 4.2%, due to the uncertainty in the integrated luminosity of the pp (2.3% [42]) and pPb (3.5% [41]) data sets, combined in quadrature.

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 where N ψ(2S) fit is the extracted raw yield of prompt ψ(2S) mesons in a given (p T , y CM ) bin, (acc ε) is the product of the dimuon acceptance and efficiency described in Section 5, and ∆p T and ∆y CM are the widths of the kinematic bin considered. The second observable considered is the nuclear modification factor, defined as R pPb (p T , y CM ) ≡ (d 2 σ/dp T dy CM ) pPb A(d 2 σ/dp T dy CM ) pp .
If R pPb = 1, there are no nuclear effects present in the pPb measurements. Figure 4 shows the rapidity dependence of the prompt ψ(2S) R pPb in three p T ranges: 4-6.5, 6.5-10, and 10-30 GeV/c. In the two lowest p T bins, R pPb remains below unity independently of rapidity, while in the highest p T bin R pPb is consistent with unity (although systematically smaller). For comparison, the prompt J/ψ nuclear modification factor [31] is also shown in Fig. 4. Interestingly, the R pPb for prompt J/ψ mesons lies systematically above that of the ψ(2S) state, indicating different nuclear effects in the production of the two states. There are hints of more suppression of ψ(2S) mesons in the region of backward rapidity and for p T < 10 GeV/c.
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 ± 0.037 (stat) ± 0.062 (syst). For comparison, the prompt J/ψ R pPb in the same kinematic range is 1.108 ± 0.021 (stat) ± 0.055 (syst). Figure 5 shows the p T dependence of the prompt ψ(2S) R pPb in four rapidity bins. The R pPb values in the lowest p T bins are found to be below unity in all rapidity bins. The suppression of prompt ψ(2S) mesons as compared to prompt J/ψ mesons, seen in Fig. 4 Figure 4: Rapidity dependence of the prompt ψ(2S) R pPb in three p T ranges. For comparison, the prompt J/ψ nuclear modification factor [31] is also shown. Statistical and systematic uncertainties are represented with error bars and boxes, respectively. The fully correlated global uncertainty of 4.2% (that affects both charmonia) is displayed as a box around R pPb = 1.
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]. In the ranges 4 < p T < 6.5 and 6.5 < p T < 10 GeV/c the value R pPb for prompt ψ(2S) production remains below unity independent of rapidity, while in the highest p T bin (10 < p T < 30 GeV/c) it is consistent with unity (although systematically smaller). The R pPb values of prompt J/ψ lie systematically above those of prompt ψ(2S) mesons, indicating different nuclear effects in the production of the two states. 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 produced in pPb collisions.

Acknowledgments
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. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Aus   [9] CMS Collaboration, "Observation of sequential Υ suppression in PbPb collisions", Phys. Rev [15] E. G. Ferreiro, F. Fleuret, J. P. Lansberg, and A. Rakotozafindrabe, "Impact of the nuclear modification of the gluon densities on J/ψ production in pPb collisions at √ s NN = 5 TeV", Phys. Rev. C 88 (2013) 047901, doi:10.1103/PhysRevC.88.047901, arXiv:1305.