$J/\psi$ photo-production in Pb-Pb peripheral collisions at $\sqrt{s_{\rm NN}}$ = 5 TeV

The photo-production of $J/\psi$ mesons at low transverse momentum is studied in peripheral lead-lead collisions collected by the LHCb experiment at a centre-of-mass energy per nucleon pair of 5 TeV, corresponding to an integrated luminosity of 210 $\rm{\mu b}^{-1}$. The $J/\psi$ candidates are reconstructed through the prompt decay into two muons of opposite charge in the rapidity region of $2.0<y<4.5$. The results significantly improve previous measurements and are compared to the latest theoretical prediction.

One of the main open subjects in ultra-relativistic heavy-ion physics is the study of the quark-gluon plasma (QGP), an exotic state of hadronic matter predicted by quantum chromodynamics (QCD). Quantitative predictions of QGP properties are obtained from lattice computations [1]. Experimentally, one of the signatures of the QGP formation inside heavy-nuclei collisions is the suppression of heavy quarkonia production, such as the J/ψ particle [2]. The suppression is expected to depend on both the temperature of the medium and the binding energy of the state [3]. Cold nuclear matter effects [4] seem to influence the measurements in nuclei collisions. These effects must be understood prior to providing a sound interpretation in the QGP framework of the hadronically produced (through the interaction of two partons) quarkonia suppression observed at RHIC and the LHC [5-10].
The ALICE [11] and STAR [12] collaborations measured an excess with respect to expectations from purely hadronic production of J/ψ mesons at very low p T (below 300 MeV/c), where p T is the component of the J/ψ momentum transverse to the beam, in hadronic lead-lead (PbPb) collisions at the center-of-mass energy per nucleon pair √ s NN = 2.76 TeV and gold-gold (uranium-uranium) collisions at √ s NN = 200 GeV (193 GeV). It was posited that this excess is due to photo-produced J/ψ mesons, caused by the coherent interaction of the large electromagnetic fields generated by the projectile with the target nucleus [13]. These types of interactions were primarily expected to only occur in ultraperipheral collisions (UPCs) [14], in which the impact parameter, b, is larger than the sum of the radii R a and R b of the two colliding nuclei, hence without nuclear break-up of the target or the projectile. In hadronic collisions, the nucleus breaks up, so no coherent production was expected. A precise measurement of the postulated coherent J/ψ production in hadronic collisions would shed light on the coherence of the interaction and on the profile of the photon flux in peripheral PbPb collisions [15][16][17].
In this Letter, a measurement of prompt J/ψ production at very-low p T in PbPb collisions at a centre-of-mass energy per nucleon pair √ s NN = 5 TeV is reported. For the first time at the LHC, the production yield is measured versus p T and rapidity, y. The data were recorded by the LHCb detector in 2018 and correspond to an integrated luminosity of about 210 µb −1 . The LHCb detector [18,19] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector includes a high-precision tracking system consisting of a siliconstrip vertex detector surrounding the PbPb interaction region [20], 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 [21] placed downstream of the magnet. The tracking system provides a measurement of the momentum of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV/c. The minimum distance of a track to a primary PbPb collision vertex (PV), the impact parameter (IP), is measured with a resolution of (15 + 29/p T ) µm, where p T is the component of the momentum transverse to the beam, in GeV/c. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors [22]. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [23].
The trigger consists of a hardware stage, using information from the calorimeter and muon systems, followed by a software stage, which applies selections on the fully reconstructed event.
At the hardware trigger stage, events are required to have a muon with high p T or a hadron, photon or electron with high transverse energy in the calorimeters. Two samples are selected for this analysis, a signal sample and a sample of minimum bias events used to normalise through the total number of inelastic events. They have different trigger strategies. Signal events are selected if the number of clusters in the VELO N c , is 6000 < N c < 10000 or if N c < 6000 and two muons with p T > 400 MeV/c are reconstructed.
The hardware trigger for the minimum bias (MB) events requires a minimum energy deposit in one of the sub detectors (VELO, calorimeters, muon chambers), and only events with N c < 10000 are kept. To improve the signal purity, events passing the software trigger are selected if the muon candidates have a p T > 700 MeV/c, the particles are consistent with originating from a primary PbPb collision vertex (PV) and are identified as muons. The prompt J/ψ candidates, which include feed-down from excited charmonium states originating from b-hadron decays, are separated from the non-prompt candidates using the requirement t z < 0.3 ps, where t z is the pseudo decay-time defined as (z J/ψ − z PV )m J/ψ /p z . Here, (z J/ψ − z PV ) and p z are the distance between the J/ψ candidate decay vertex and the PV, and the candidate momentum along the beam axis, respectively, and m J/ψ is the known J/ψ mass [24].
During data taking, neon (Ne) gas was injected into the beam pipe near the interaction point using LHCb's SMOG system [25] to record fixed-target collisions simultaneously with the PbPb collisions. These fixed-target PbNe collisions are rejected by placing requirements on the position of the PV. In order to remove potential contamination from UPCs, which may bias the measurement especially for very low event activity, a minimal energy deposit in the electromagnetic calorimeter (ECAL) is also required (E tot > 585 GeV).
The PbPb sample is divided into intervals of N c which correspond to different numbers of participating nucleons, N part . This quantity is related to the centrality, defined as the percentile of the total inelastic hadronic PbPb cross-section as a function of the released collision energy, which can be approximated by the total energy deposit in ECAL (E tot ). The more central is the collision, the larger E tot is and the larger N part is. The percentiles are determined using the Glauber Monte Carlo (GMC) model [26,27]. The model is used to perform a binned fit to the E tot distribution of the MB data sample, collected with the same detector conditions as the signal sample. The quantity N part is estimated for each collision and the mean value, N part , is derived from events within a given N c range. Results for each N c interval are summarized in Table 1. The distribution of N part in the three N c intervals is shown in Fig. 1. More details on the centrality determination in LHCb can be found in Ref. [28] and in the supplemental material [29].
In this Letter, the J/ψ photo-production differential yield is measured, defined as    Table 1.
where i indicates the N c range, N i J/ψ is the number of photo-produced J/ψ meson candidates reconstructed through the J/ψ → µ + µ − decay channel in the (p T , y) interval of width (∆p T , ∆y), B = (5.961 ± 0.033)% [24] is the branching fraction of the decay J/ψ → µ + µ − , N i MB is the total number of MB events, and ε i tot is the efficiency to reconstruct and select the J/ψ candidates. The dimuon invariant mass, m(µ + µ − ), of the selected candidates is shown in Fig. 2 for a representative centrality interval for J/ψ candidates with p T <15.0 GeV/c and 2.0 < y < 4.5. An unbinned fit of these candidates is performed using a Crystal-Ball (CB) function for the signal and a first order polynomial for the background.
Photo-produced J/ψ mesons and hadronically produced J/ψ mesons are then disentangled through an unbinned maximum likelihood fit to the dimuon p T spectrum. The fit is performed after subtracting correlated background, i.e. arising from γγ → µ + µ − or the Drell-Yan process, and combinatorial background from uncorrelated muon pairs which is the dominant source, using the sPlot method [30] with m(µ + µ − ) as discriminating variable. To cross check the validity of the sPlot method, the kinematic distributions (p T y, N c ) of the estimated background are compared to the same (normalised) distributions in two invariant mass ranges below and above the resonance peak. A very good agreement is found. The empirical fit model comprises a double-sided Crystal-Ball function [31] expressed in ln(p 2 T ) for the photo-production contribution and a function for the hadronic component that typically has a larger p T where n 1 , n 2 , n 3 and p 0 are parameters free to vary in the fit. The projections of the fits in the centrality interval N part =10.6 ± 2.9 are shown in Fig. 2, overlaid to the data distributions. A good description of the data is observed in all centrality intervals. The photo-produced J/ψ candidates are visible in the range 0 < p T < 250 MeV/c. The p T distribution of the photo-produced J/ψ candidates does not rise towards vanishing p T due to the interference caused by the negative parity of the photon as explained in Ref. [17].
Simulation is required to model the effects of the detector acceptance and of the selection requirements on the signal. The PbPb collisions are generated using EPOS [32] and the hard process is generated with Pythia [33] with a specific LHCb configuration [34].
An additional signal sample where the J/ψ is transversely polarised was produced using the STARlight [35] generator to study the acceptance assuming the coherent photoproduction scenario. The interactions of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [36] as described in Ref. [37]. The total efficiency is determined independently in each interval of centrality, and it includes the effects of the geometrical acceptance ( acc ), the trigger efficiency ( trigger ), the reconstruction and selection efficiency ( rec&sel ), and the efficiency of the particle identification (PID) criteria ( PID ). The acceptance is determined using the STARlight sample in the kinematic range of the analysis. The efficiency rec&sel is estimated using simulation and data calibration techniques. The main component of the reconstruction inefficiency is due to the tracking algorithms, as the performance is affected by the high occupancy in PbPb collisions. The relative reconstruction efficiency between data and simulation is evaluated using two D 0 meson decay channels (D 0 → K − π + and D 0 → K − π + π − π + ). The yields are evaluated in PbPb data and simulation and the difference of their ratio to unity is encoded in a factor k(N c ). This factor depends on the event multiplicity with k ranging from 0.97 to 0.91 with increasing N c , assuming k(N c ) is the same for the π and µ tracks. The latter factor is used to correct the reconstructed J/ψ candidates in simulation. An additional correction is applied to correct discrepancies between reconstructed J/ψ kinematic distributions by weighting the variables N c , p T , and y of the J/ψ in simulation to match the data. The PID efficiency PID is evaluated using a tag-and-probe approach with J/ψ → µµ decays reconstructed in proton-proton collisions that provides PID efficiency tables for single muons. Those efficiencies are used to perform a two-dimensional (p T , N c ) extrapolation, using first-and second-order polynomial functions, to estimate the decrease of the efficiencies for higher multiplicities seen in PbPb collisions. No extrapolation is performed based on the rapidity as no correlation is seen between N c and y.
Several sources of systematic uncertainties are considered. The uncertainty associated with the fit model used to evaluate the signal yields is determined by testing alternative fit functions. The p T of the hadronically produced J/ψ candidates is modelled by a Tsallis function [38]. The background shape is also modified to account for incoherent photo-produced J/ψ , defined as the interaction between one photon and a single nucleon implying the destruction of the nucleus. This contribution typically produces J/ψ mesons at higher p T than the coherent photo-production source. Therefore, another double CB function is added to model this potential contribution. The incoherent contribution shares the shape parameters of the coherent contribution with the mean p T and width shifted according to the differences obtained in the STARlight simulations. By computing the difference to the reference fit, a total uncertainty of about 1.3% averaged over all centrality intervals is obtained.
The systematic uncertainty associated with the evaluation of the efficiencies is divided into uncertainties due to the rec&sel , PID , and trigger efficiencies. Three systematic effects are considered for the measurement of rec&sel : the uncertainty on the weighting procedure, the uncertainty associated with the evaluation of the factor k, and the correlation between the variables p T and y. The uncertainty on the weighting procedure is estimated by comparing p T , y, and N c of the weighted distributions of the J/ψ mesons in simulation with those in data after background subtraction. The difference between the two leads to a global uncertainty of 2%. The uncertainty on the factor k is evaluated by varying its value within its uncertainty and propagating it to the tracking efficiency. An uncertainty from 2.9% to 7.4% is found depending on the considered multiplicity interval. The uncertainty on the correlation between the variables p T and y is estimated to be 1% using calibration samples from proton-proton collisions.
The uncertainty coming from the muon PID efficiency tables is evaluated with a smearing technique. The J/ψ PID efficiency is computed using efficiency PID tables with the values in each interval varied within their uncertainty. This procedure is repeated several times and the largest difference is taken as systematic uncertainty; the effect is smaller than 1% and considered negligible compared to the uncertainty given by the difference of the two functions used for the extrapolation.
The uncertainty on trigger is estimated by comparing the trigger efficiency measurement with another method based on data. The method consists of evaluating the efficiency using a sample selected by the same trigger algorithms but independent from those used in the selection of the signal. The difference of 3% between the two methods is taken as systematic uncertainty on the trigger efficiency. The total systematic uncertainties are obtained by summing in quadrature the different sources of uncertainties.
The differential J/ψ photo-production yields, Eq. (1), as a function of the rapidity for N part =19.7 ± 9.2 and as a function of N part are shown in Fig. 3 (top). The doubledifferential J/ψ photo-production yields, Eq. (2), as a function of the transverse momentum are as well shown in Fig. 3 (bottom). The mean p T of the coherent J/ψ is found to be p T = 64.9 ± 2.4 MeV/c. The results are compared to the theoretical prediction [17,39] and detailed results are presented in the supplemental material [29]. The model assumes  [17,39] that take (black) or not take (green) into account the effect from the overlap region of the collision. two scenarios in which the coherence of the J/ψ production is (overlap effect) or is not (no overlap effect) affected by interactions with the overlap region of the two colliding nuclei. Little difference is observed between the two theory scenarios. The divergence is important in more central collisions due to the increase of the photon flux with a decrease of the impact parameter. In the overlapping scenario, this effect is balanced by excluding the overlapping region from the interaction.
The measured yield of the coherent J/ψ production is higher at low rapidity than at high rapidity and it is consistent with being constant with respect to N part for the region considered in the analysis.
In summary, the yield of coherently photo-produced prompt J/ψ mesons at very low p T in peripheral PbPb collisions collected at √ s NN = 5 TeV is measured with the LHCb experiment. The yields are studied as a function of rapidity and transverse momentum of the J/ψ meson in intervals of the number of participant nucleons N part . These results are the most precise to date, and support the hypothesis of coherent J/ψ photo-production in peripheral hadronic collisions suggested by the other experiments [11,12]. The shape of the results is qualitatively described by the theoretical prediction [17,39], although a normalization discrepancy is observed which could hide a possible additional contribution.