Study of $J/\psi$ production and cold nuclear matter effects in $p$Pb collisions at $\sqrt{s_{NN}}=5 \mathrm{TeV}$

The production of $J/\psi$ mesons with rapidity $1.5<y<4.0$ or $-5.0<y<-2.5$ and transverse momentum $p_\mathrm{T}<14 \mathrm{GeV}/c$ is studied with the LHCb detector in proton-lead collisions at a nucleon-nucleon centre-of-mass energy $\sqrt{s_{NN}}=5 \mathrm{TeV}$. The analysis is based on a data sample corresponding to an integrated luminosity of about $1.6 \mathrm{nb}^{-1}$. For the first time the nuclear modification factor and forward-backward production ratio are determined separately for prompt $J/\psi$ mesons and $J/\psi$ from $b$-hadron decays. Clear suppression of prompt $J/\psi$ production with respect to proton-proton collisions at large rapidity is observed, while the production of $J/\psi$ from $b$-hadron decays is less suppressed. These results show good agreement with available theoretical predictions. The measurement shows that cold nuclear matter effects are important for interpretations of the related quark-gluon plasma signatures in heavy-ion collisions.


Introduction
The suppression of heavy quarkonia production with respect to proton-proton (pp) collisions [1] is one of the most distinctive signatures of the formation of quark-gluon plasma, a hot nuclear medium created in ultrarelativistic heavy-ion collisions. However, the suppression of heavy quarkonia and light hadron production with respect to pp collisions can also take place in proton-nucleus (pA) collisions, where a quark-gluon plasma is not expected to be created and only cold nuclear matter effects, such as nuclear absorption, parton shadowing and parton energy loss in initial and final states occur [2][3][4][5][6][7][8]. The study of pA collisions is important to disentangle the effects of quark-gluon plasma from cold nuclear matter, and to provide essential input to the understanding of nucleus-nucleus collisions. Nuclear effects are usually characterised by the nuclear modification factor, defined as the production cross-section of a given particle in pA collisions divided by that in pp collisions and the number of colliding nucleons in the nucleus (given by the atomic number A), where y is the rapidity of the particle in the nucleon-nucleon centre-of-mass frame, p T is the transverse momentum of the particle, and √ s NN is the nucleon-nucleon centre-of-mass energy. The suppression of heavy quarkonia and light hadron production with respect to pp collisions at large rapidity has been observed in pA collisions [9,10] and in deuteron-gold collisions [11][12][13], but has not been studied in proton-lead (pPb) collisions at the TeV scale. Previous experiments [9][10][11][12][13] have also shown evidence that the production crosssection of J/ψ mesons or light hadrons in the forward region (positive rapidity) of pA or deuteron-gold collisions differs from that in the backward region (negative rapidity), where "forward" and "backward" are defined relative to the direction of the proton or deuteron beam. Measurements of the nuclear modification factor R pPb and the forward-backward production ratio are sensitive to cold nuclear matter effects. The advantage of measuring the ratio R FB is that it does not rely on the knowledge of the J/ψ production cross-section in pp collisions. Another advantage is that part of experimental systematic uncertainties and of the theoretical scale uncertainties cancel out in the ratio. The asymmetric layout of the LHCb experiment [14], covering the pseudorapidity range 2 < η < 5, allows for a measurement of R pPb for both the forward and backward regions, taking advantage of the inversion of the proton and lead beams during the pPb data-taking period in 2013. The energy of the proton beam is 4 TeV, while that of the lead beam is 1.58 TeV per nucleon, resulting in a centre-of-mass energy of the nucleon-nucleon system of 5.02 TeV, approximated as √ s NN = 5 TeV due to the uncertainty of the beam energy. Since the energy per nucleon in the proton beam is significantly larger than that in the lead beam, the nucleon-nucleon centre-of-mass system has a rapidity in the laboratory frame of +0.465 (−0.465) for pPb forward (backward) collisions. This results in a shift of the rapidity coverage in the nucleon-nucleon centre-of-mass system, ranging from about 1.5 to 4.0 for forward pPb collisions and from −5.0 to −2.5 for backward pPb collisions. The excellent vertexing capability of LHCb allows a separation of prompt J/ψ mesons and J/ψ mesons from b-hadron decays (abbreviated as "J/ψ from b" in the following). The sum of these two components is referred to as inclusive J/ψ mesons.
In this paper, the differential production cross-sections of prompt J/ψ mesons and J/ψ from b, as functions of y and p T , are measured for the first time in pPb collisions at √ s NN = 5 TeV. Measurements of R pPb and R FB , for both prompt J/ψ mesons and J/ψ from b, are presented. For the ease of the comparison with other experiments, results for inclusive J/ψ mesons are also given.

Detector and data set
The LHCb detector [14] is a single-arm forward spectrometer designed for the study of particles containing b or c quarks. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector (VELO) surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream. The VELO has the unique feature of being located very close to the beam line (about 8 mm). This allows excellent resolutions in reconstructing the position of the collision point, i.e., the primary vertex, and the vertex of the hadron decay, i.e., the secondary vertex. For primary (secondary) vertices, the resolution in the plane transverse to the beam is σ x,y ≈ 10 (20) µm, and that along the beam is σ z ≈ 50 (200) µm. The combined tracking system has a momentum resolution ∆p/p that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c, and an impact parameter resolution of 20 µm for tracks with large transverse momentum. Charged hadrons are identified using two ring-imaging Cherenkov detectors [15]. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [16]. The trigger [17] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage which applies a full event reconstruction. This analysis is based on a data sample acquired during the pPb run in early 2013, corresponding to an integrated luminosity of 1.1 nb −1 (0.5 nb −1 ) for forward (backward) collisions. The instantaneous luminosity was around 5 × 10 27 cm −2 s −1 , five orders of magnitude below the typical LHCb luminosity for pp collisions.
The hardware trigger during this period was simply an interaction trigger, which rejects empty events. The software trigger requires one well-reconstructed track with hits in the muon system and a p T greater than 600 MeV/c.
Simulated samples based on pp collisions at 8 TeV are reweighted to reproduce the experimental data at 5 TeV, and are used to determine acceptance and reconstruction efficiencies, where the effect of the asymmetric beam energies in pPb collisions has been properly taken into account. In the simulation, pp collisions are generated using Pythia 6.4 [18] with a specific LHCb configuration [19]. Hadron decays are described by EvtGen [20], where final state radiation is generated using Photos [21]. The interactions of the generated particles with the detector and its response are implemented using the Geant4 toolkit [22] as described in Ref. [23].

Event selection and cross-section determination
The J/ψ production cross-section measurement follows the approach described in Refs. [24][25][26]. The J/ψ candidates are reconstructed and selected using dimuon final states in the events with at least one primary vertex, which consists of no less than five tracks. Reconstructed J/ψ → µ + µ − candidates are selected from pairs of oppositely charged particles with transverse momentum p T > 0.7 GeV/c, which are identified as muons by the muon detector and have a track fit χ 2 per number of degree of freedom less than 3. To suppress combinatorial background, the difference between the logarithms of the likelihoods for the muon and the pion hypotheses DLL µπ [16,27] is required to be greater than 1.0 (3.5) for the forward (backward) sample. The two muons are required to originate from a common vertex with a χ 2 -probability larger than 0.5%. Candidates are kept if the reconstructed invariant mass is in the range 2990 < m µµ < 3210 MeV/c 2 , which is within about ±110 MeV/c 2 of the known J/ψ mass [28].
The double differential cross-section for J/ψ production in a given (p T , y) bin is defined as where N cor (J/ψ → µ + µ − ) is the efficiency-corrected number of observed J/ψ → µ + µ − signal candidates in the given bin, L is the integrated luminosity, B(J/ψ → µ + µ − ) = (5.93 ± 0.06)% [28] is the branching fraction of the J/ψ → µ + µ − decay, and ∆p T and ∆y the widths of the (p T , y) bin. The numbers of prompt J/ψ mesons and J/ψ from b in bins of the kinematic variables y and p T are obtained by performing combined extended maximum likelihood fits to the unbinned distributions of dimuon mass and pseudo proper time t z in each kinematic bin. The pseudo proper time of the J/ψ meson is defined as where z J/ψ is the z position of the J/ψ decay vertex, z PV that of the primary vertex, p z is the z component of the measured J/ψ momentum, and M J/ψ is the known J/ψ mass [28]. The signal dimuon invariant mass distribution in each p T and y bin is modelled with a Crystal Ball function [29], and the combinatorial background with an exponential function. The t z signal distribution is described by the sum of a δ-function at t z = 0 for prompt J/ψ production and an exponential decay function for J/ψ from b, both convolved with a double-Gaussian resolution function whose parameters are free in the fit. The t z distribution of background in each kinematic bin is independently modelled with an empirical function based on the t z distribution observed in background events obtained using the sPlot technique [30]. All the parameters of the t z background distribution are fixed in the final combined fits to the distributions of invariant mass and pseudo proper time. The total fit function is the sum of the products of the mass and t z fit functions for the signal and background components. Figure 1 shows projections of the fit to the dimuon invariant mass and t z distributions, for two representative bins of y in the forward and backward regions. Higher combinatorial background in the backward region is seen due to its larger multiplicity. The dimuon invariant mass resolution is about 15 MeV/c 2 for both the forward and backward samples, consistent with the mass resolution measured in pp collisions [24][25][26] and in simulation. The total signal yield for prompt J/ψ mesons in the forward (backward) sample is 25 280 ± 240 (8 830 ± 160), and the total signal yield for J/ψ from b in the forward (backward) sample is 3 720±80 (890±40), where the uncertainty is statistical. Based on the fit results for prompt J/ψ mesons and J/ψ from b, a signal weight factor w i for the ith candidate is obtained with the sPlot technique, using the dimuon invariant mass and t z as discriminating variables. The sum of w i /ε i over all events in a given bin leads to the efficiency-corrected signal yield N cor in that bin, where the efficiency ε i depends on p T and y and includes the geometric acceptance, reconstruction, muon identification, and trigger efficiencies.
The acceptance and reconstruction efficiencies are estimated from simulated samples, assuming production of unpolarised J/ψ mesons. The efficiency of the DLL µπ selection is obtained by a data-driven tag-and-probe approach [31]. The trigger efficiency is obtained from data using a sample of J/ψ decays unbiased by the trigger decision [17]. Figure 2 shows the background-subtracted distributions of the track multiplicity per event and the J/ψ p T , p, and the rapidity in the laboratory frame y lab in experimental pPb and simulated pp data. The differences in the distributions of p T , p, and y lab between data and simulated samples are small. Sizeable differences in the distributions of the track multiplicity are observed, particularly between the simulation and the backward sample, for which the particle production cross-section is larger [9,[11][12][13]. To take this effect into account, the simulated pp samples are reweighted to match the data with weight factors derived from the distributions in Fig. 2.

Systematic uncertainties
Acceptance and reconstruction efficiencies depend not only on the kinematic distributions of the J/ψ meson but also on its polarisation. The LHCb measurement in pp collisions [32] indicated a longitudinal polarisation consistent with zero in most of the kinematic region. Based on the expectation that the nuclear environment does not enhance the polarisation, it is assumed that the J/ψ mesons are produced with no polarisation. No systematic uncertainty is assigned to the effect of polarisation in this analysis.
Several contributions to the systematic uncertainties affecting the cross-section mea- surement are discussed in the following and summarised in Table 1. The influence of the model assumed to describe the shape of the dimuon invariant mass distribution is estimated by adding a second Crystal Ball to the fit function. The relative difference of 2.3% (3.4%) in the signal yield for forward (backward) collisions is taken as a systematic uncertainty. Due to the muon bremsstrahlung, a small fraction of signal candidates with low reconstructed invariant mass are excluded from the signal mass region. This effect is included in the reconstruction efficiency, and an uncertainty of 1.0% is assigned based on the comparison between the observed radiative tail in data and simulation.
The systematic uncertainties due to the muon identification efficiency and the track reconstruction efficiency are estimated using a data-driven tag-and-probe method [31] based on partially reconstructed J/ψ decays. To estimate the uncertainty due to the muon identification efficiency, J/ψ candidates are reconstructed with one muon identified by the  muon system ("tag") and the other ("probe") identified by selecting a track depositing the energy of a minimum-ionising particle in the calorimeters. The resulting uncertainty is 1.3%. Taking into account the effect of the track-multiplicity difference between pPb and pp data, an uncertainty of 1.5% is assigned due to the track reconstruction efficiency.
From the counting rate of visible interactions in the VELO, the luminosity is determined with an uncertainty of 1.9% (2.1%) for the pPb forward (backward) sample. For both configurations the relation between visible interaction rate and instantaneous luminosity was calibrated using the van der Meer method [33,34]. Details of the procedure are described in Ref. [35]. The statistical uncertainties are negligible, the beam intensities are determined with a precision of better than 0.4%. The dominant contributions to the systematic uncertainties are 0.6% (1.3%) for the pPb forward (backward) sample due to the reproducibility of the van der Meer scans and uncontrolled beam drifts, 1.0% from the absolute length scale calibration of the beam displacements, 0.4% due to longitudinal movements of the luminous region, and between 0.6% and 1.0% from beam-beam induced Table 1: Relative systematic uncertainties on the differential production cross-sections. The uncertainty due to the radiative tail and branching fraction cancels in both R pPb and R FB . The uncertainty due to the tracking efficiency and the luminosity partially cancels for R FB .

Source
Forward (%) Backward (%) Correlated between bins Mass fits 2. background. The uncertainty of the branching fraction of the J/ψ → µ + µ − decay is 1.0% [28]. Differences of the p T and y spectra between data and simulation within a given (p T , y) bin due to the finite bin sizes can affect the result. This effect is estimated by doubling the number of bins in p T and shifting each rapidity bin by half a unit. The relative difference with respect to the default binning, which varies between 0.1% and 8.7% depending on the bin, is taken as systematic uncertainty. The uncertainties in most bins are below 2.0%, but increase in the lowest rapidity bins.
To estimate the effect of reweighting the track multiplicity in the simulation, the efficiency without reweighting is calculated. The relative difference in each bin between the two methods is taken as systematic uncertainty.
Uncertainties related to the t z fit procedure are measured by fitting directly the t z signal component, which is determined using the sPlot technique. This gives results consistent with those obtained from the combined fit; the relative difference between results in each bin is taken as systematic uncertainty.

Results
Single differential production cross-sections as functions of p T and y, for both prompt J/ψ mesons and J/ψ from b in the pPb forward and backward regions, are displayed in Fig. 3 and shown in Tables 2 and 3, respectively, assuming no J/ψ polarisation.
The J/ψ production cross-section in pp collisions at 5 TeV, used as a reference to determine the nuclear modification factor R pPb , is obtained by a power-law interpolation, σ( prompt J/ψ mesons, and p 0 = 1.1 ± 0.2 TeV and p 1 = 10.0 ± 0.8 for J/ψ from b. Alternative interpolations based on linear and exponential fits are also tried; the largest deviation from the default value is taken as a systematic uncertainty due to the interpolation, 3.1% (2.8%) for prompt (from b) J/ψ mesons. The reference production cross-section in pp collisions at 5 TeV for prompt J/ψ mesons is 4.79 ± 0.22 ± 0.15 µb, and that for J/ψ from b is 0.47 ± 0.04 ± 0.01 µb [36]. The nuclear modification factor R pPb is then determined in the rapidity ranges −4.0 < y < −2.5 and 2.5 < y < 4.0 for both prompt J/ψ mesons and J/ψ from b. Figure 5(a) shows the nuclear modification factor for prompt J/ψ production, together with several theoretical predictions [2][3][4]. Calculations in Ref. [2] are based on the Leading Order Colour Singlet Model (LO CSM) [37,38], taking into account the modification effects of the gluon distribution function in nuclei with the parameterisation EPS09 [39] or nDSg [40]. The Next-to-Leading Order Colour Evaporation Model (NLO CEM) [41] is used in Ref. [3], considering the parton shadowing with EPS09 parameterisation. Reference [4] provides theoretical predictions of a coherent parton energy loss effect both in initial and final states, with or without additional parton shadowing effects parameterised with EPS09. The single free parameter q 0 in this model is 0.055 (0.075) GeV 2 / fm when EPS09 is (not) taken into account. A suppression of about 40% at large rapidity is observed for prompt J/ψ production. The measurements agree with most predictions. However, the calculation [3] based on NLO CEM with the EPS09 parameterisation provides a less good description of the measurement in the forward region. Figure 5(b) shows the nuclear modification factor for J/ψ from b, together with the theoretical predictions [42]. The data show a modest suppression of J/ψ from b production in pPb forward region, with respect to that in pp collisions. This is the first indication of the suppression of b hadron production in pPb collisions. The theoretical predictions agree with the measurement in the forward region. In the backward region the agreement is not as good. The observed production suppression of J/ψ from b with respect to pp collisions is smaller than that of prompt J/ψ , which is consistent with theoretical predictions. The measured values of the nuclear modification factor, together with the results for inclusive Refs. [2,42], (blue band) Ref. [3], and (green solid and blue dash-dotted lines) Ref. [4]. The inner error bars (delimited by the horizontal lines) show the statistical uncertainties; the outer ones show the statistical and systematic uncertainties added in quadrature. The uncertainty due to the interpolated J/ψ cross-section in pp collisions at √ s = 5 TeV is 5.5% (8.4%) for prompt J/ψ mesosns (J/ψ from b).
J/ψ mesons, are given in Table 5. Figure 6 shows the forward-backward production ratio R FB as a function of |y|, compared with theoretical calculations [2][3][4]42]. The value of R FB for J/ψ from b is closer to unity than for prompt J/ψ mesons, indicating a smaller asymmetry in the forward-backward production. The results agree with theoretical predictions. The calculation [3] with the EPS09 NLO nPDF alone predicts a smaller forward-backward production asymmetry for prompt J/ψ mesons than observed. Figure 7 shows the forward-backward production ratio R FB as a function of p T for prompt J/ψ mesons and J/ψ from b in the range 2.5 < y < 4.0 of the nucleon-nucleon centre-of-mass frame. Theoretical predictions [3,5] are only available for prompt J/ψ mesons. The calculation [5] based on parton energy loss with the EPS09 NLO nPDF agrees with the measurement of R FB for prompt J/ψ mesons. The measured values of the forward-backward production ratio R FB are given in Tables 6 and 7, where the results for inclusive J/ψ mesons are also listed.

Conclusion
The production of prompt J/ψ mesons and of J/ψ from b-hadron decays is studied in pPb collisions with the LHCb detector at the nucleon-nucleon centre-of-mass energy √ s NN = 5 TeV. The measurement is performed as a function of the transverse momentum and rapidity of the J/ψ meson in the region p T < 14 GeV/c and 1.5 < y < 4.0 (forward) and −5.0 < y < −2.5 (backward). The nuclear modification factor R pPb and the forwardbackward production ratio R FB are determined for the first time separately for prompt J/ψ mesons and those from b-hadron decays. The measurement indicates that cold nuclear matter effects are less pronounced for J/ψ mesons from b-hadron decays, hence for b hadrons, than for prompt J/ψ mesons. These results show good agreement with the available theoretical predictions and provide useful constraints to the parameterisation of theoretical models. The measured nuclear modification factor for prompt J/ψ mesons shows that it is necessary to include cold nuclear matter effects in the interpretation of quark-gluon plasma signatures in heavy-ion collisions. The results for inclusive J/ψ mesons are in agreement with those presented by the ALICE collaboration [43]. Table 2: Single differential production cross-sections (in µb/( GeV/c)) for prompt J/ψ mesons and J/ψ from b as functions of transverse momentum. The first uncertainty is statistical, the second is the component of the systematic uncertainty that is uncorrelated between bins, and the third is the correlated component.

Appendices A Results in tables
dσ/dp T (prompt J/ψ ) dσ/dp T (J/ψ from b)  Table 3: Single differential production cross-sections (in µb) for prompt J/ψ mesons and J/ψ from b as functions of rapidity. The first uncertainty is statistical, the second is the component of the systematic uncertainty that is uncorrelated between bins, and the third is the correlated component.
|y| dσ/dy (prompt J/ψ ) dσ/dy (J/ψ from b) Forward (p T < 14 GeV/c) Table 4: Double differential production cross-sections (in µb/( GeV/c)) for prompt J/ψ mesons and J/ψ from b as functions of p T and y in pPb forward data. The first uncertainty is statistical, the second is the component of the systematic uncertainty that is uncorrelated between bins, and the third is the correlated component.  Table 5: Nuclear modification factor R pPb as a function of y with p T < 14 GeV/c. The first uncertainty is statistical, the second is the systematic, and the third is the uncertainty related to the interpolation error.