Energy dependence of coherent photonuclear production of J/ψ mesons in ultra-peripheral Pb-Pb collisions at √sNN = 5.02 TeV

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Energy dependence of coherent photonuclear production of J/ψ mesons in ultraperipheral Pb-Pb collisions at √sNN = 5.02 TeV © 2023 CERN Published version ALICE Collaboration ALICE Collaboration. (2023). Energy dependence of coherent photonuclear production of J/ψ mesons in ultra-peripheral Pb-Pb collisions at √sNN = 5.02 TeV. Journal of High Energy Physics, 2023(10), Article 119. https://doi.org/10.1007/JHEP10(2023)119 2023 JHEP10(2023)119 Published for SISSA by Springer Received:June 7, 2023 Revised:August 8, 2023 Accepted:October 4, 2023 Published:October 20, 2023 Energy dependence of coherent photonuclear production of J/ψ mesons in ultra-peripheral Pb-Pb collisions at √sNN = 5.02 TeV The ALICE collaboration E-mail: [email protected] Abstract: The cross section for coherent photonuclear production of J/ψ is presented as a function of the electromagnetic dissociation (EMD) of Pb. The measurement is performed with the ALICE detector in ultra-peripheral Pb-Pb collisions at a centre-of-mass energy per nucleon pair of √sNN = 5.02 TeV. Cross sections are presented in five different J/ψ rapidity ranges within |y|<4, with the J/ψ reconstructed via its dilepton decay channels. In some events the J/ψ is not accompanied by EMD, while other events do produce neutrons from EMD at beam rapidities either in one or the other beam direction, or in both. The cross sections in a given rapidity range and for different configurations of neutrons from EMD allow for the extraction of the energy dependence of this process in the range 17 < WγPb,n<920 GeV, where WγPb,nis the centre-of-mass energy per nucleon of the γPb system. This range corresponds to a Bjorken-xinterval spanning about three orders of magnitude: 1.1×10−5<x<3.3×10−2. In addition to the ultra-peripheral and photonuclear cross sections, the nuclear suppression factor is obtained. These measurements point to a strong depletion of the gluon distribution in Pb nuclei over a broad, previously unexplored, energy range. These results, together with previous ALICE measurements, provide unprecedented information to probe quantum chromodynamics at high energies. Keywords: Heavy Ion Experiments, Quarkonium, Forward Physics ArXiv ePrint: 2305.19060 Open Access, Copyright CERN, for the benefit of the ALICE Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP10(2023)119 JHEP10(2023)119 Contents 1 Introduction 1 2 Theoretical models 4 2.1 The photon flux 4 2.2 The photonuclear cross section 4 3 Experimental set-up 6 3.1 Central barrel detectors 6 3.2 The muon spectrometer 7 3.3 Forward detectors 8 3.4 Triggers and luminosity 8 4 Data samples 9 4.1 Event selection with the central barrel detectors 9 4.2 Event selection with the muon spectrometer 10 4.3 Event classification using ZNA and ZNC 10 4.4 Monte Carlo samples 11 5 Analysis procedure 11 5.1 Yield extraction 11 5.2 Corrections 13 5.3 Systematic uncertainties 15 6 Results 18 6.1 Cross section in UPC 18 6.2 Extraction of the photonuclear cross section 20 6.3 Nuclear suppression factor 23 7 Summary and outlook 24 The ALICE collaboration 33 1 Introduction One of the main research topics in quantum chromodynamics (QCD) today is the study of the hadronic structure when probed at high energies, corresponding to low values of the fraction of the hadron momentum carried by the colliding parton (Bjorken-x). The gluon distribution inside the proton has been observed to increase steeply at low values of x[1]. At some point, this growth must stop to preserve unitarity. In QCD this is achieved by a dynamic equilibrium of gluon splitting and annihilation processes. This – 1 – JHEP10(2023)119 regime of the gluon distribution is known as saturation, see ref. [2] for a recent review. In a nucleus with Anucleons, the parton distributions would naively be Atimes those in a single nucleon, but modifications, known as nuclear shadowing, are observed at small x[3]. Similar considerations to those for a single nucleon regarding unitarity imply that saturation is expected to set in for large nuclei at lower energies (higher xvalues) than in protons, with this behaviour scaling roughly as A1/3[4]. Diffractive production of J/ψ vector mesons off nuclear targets is a powerful tool to study the energy evolution of the structure of heavy nuclei. The interaction can involve the full nucleus or only one nucleon; these cases are called coherent and incoherent production, respectively. The coherent process has a large experimental cross section, it is very sensitive to the gluon structure of hadrons, and it can be described within perturbative QCD owing to the large J/ψ mass, which provides a hard scale to justify the use of perturbative techniques. At the LHC, the coherent production of J/ψ can be measured in ultra-peripheral collisions (UPCs) where the incoming Pb nuclei pass each other at impact parameters larger than the sum of their radii, such that the interaction involves photons from the strong electromagnetic field of the incoming ions [5–8]. Previous measurements of this process at the LHC were performed at different centreof-mass energies per nucleon pair (√sNN) and different rapidities of the J/ψ. Using data from LHC Run 1, where the Pb nuclei collided at √sNN = 2.76 TeV, the ALICE Collaboration measured the coherent photoproduction of J/ψs in UPCs at forward rapidity [9] and midrapidity [10], while the CMS Collaboration provided a cross section for this process at an intermediate rapidity range [11]. For LHC Run 2, the energy of Pb-Pb collisions was raised to √sNN = 5.02 TeV and new measurements of this process were performed by the ALICE Collaboration at mid [12,13] and forward rapidity [14] as well as by the LHCb Collaboration at forward rapidity [15]. The importance of a wide experimental rapidity coverage is that the rapidity of the J/ψ in this process is related to the centre-of-mass energy per nucleon in the γPb system by (WγPb,n)2=m√sNN exp(−y), where mis the mass of the J/ψ and yits rapidity in the laboratory frame measured with respect to the direction of the incoming Pb nucleus. (Natural units are used in all equations.) At the LHC, either of the two incoming Pb ions can be the source of the photon and, in this circumstance, the cross section for the coherent photoproduction of J/ψ in UPCs as a function of rapidity has two components [16] dσPbPb dy=nγ(y, {b})σγPb(y) + nγ(−y, {b})σγPb(−y),(1.1) where σγPb(y)is the photonuclear cross section for the coherent production of a J/ψ at rapidity y, and nγ(y)is the photon flux which, in the equivalent photon approximation [5], quantifies the number of photons with energy k= (m/2) exp(−y). The notation {b} signifies that the flux is obtained by integrating over a range on impact parameter b. A study of the rapidity dependence of σγPb was performed in ref. [17] using ALICE Run 1 data at √sNN = 2.76 TeV. The analysis is based on two facts: (1) at y= 0 both contributions in eq. (1.1) are equal, so that knowledge of the photon flux nγ(y= 0) yields σγPb at the corresponding WγPb,n= 92 GeV; (2) at the largest rapidities accessible to – 2 – JHEP10(2023)119 ALICE, the first term in the right-hand side of eq. (1.1) contributes only about 5% so that the UPC cross section is dominated by the second term in eq. (1.1) corresponding to interactions with low-energy photons at WγPb,n= 20 GeV for the ALICE data used in the analysis. The extracted cross sections are discussed in section 6.2. In order to extract the full energy dependence of σγPb from the UPC cross section, at least two measurements at the same rapidity but with different photon fluxes are needed. Up to now, there are two proposals on how to achieve this. Both utilise the fact that the photon flux also depends on the impact-parameter range where the γPb interaction takes place. One proposal, presented in ref. [18], makes use of the coherent production of J/ψ measured in peripheral collisions originally reported by the ALICE Collaboration [19] and later on confirmed by the STAR [20], ALICE [21], and LHCb [22] Collaborations. Applying this approach to ALICE data at √sNN = 2.76 TeV for the coherent photonuclear production of J/ψ measured in peripheral collisions and in UPCs, in ref. [18] the cross sections for σγPb at three values of WγPb,n: 18GeV, 92 GeV, and 470 GeV are obtained. The extracted cross sections are discussed in section 6.2. The other proposal, presented in refs. [23,24], utilises the fact that the electromagnetic fields of the incoming nuclei are so strong that there is a sizeable probability of a second photon exchange between the colliding nuclei, which may result in the electromagnetic dissociation (EMD) of at least one of the interacting nuclei [25]. The presence of neutrons from EMD of one or both nuclei, which can be determined using zero-degree calorimeters, can be used to tag specific ranges of the impact parameter. This is so because high energy photons are emitted at smaller impact parameters than low energy photons and in order to induce the dissociation of a nucleus a photon needs a minimum energy of the order of 10 MeV. This means that events where EMD has occurred select a photon flux with {b}covering smaller impact parameters than events without EMD. In this way, the measurement of coherent J/ψ photoproduction in UPCs with no, single, or mutual EMD can be used to disentangle the two different σγPb contributions in eq. (1.1) [24]. The tagging of single and mutual EMD has been successfully tested; first, in the measurement of coherent ρ0photoproduction at midrapidity by the ALICE Collaboration [26–28], and later in the measurement of γγ →µ+µ−and γγ →e+e−in UPCs by the CMS and ATLAS Collaborations [29–31]. These ATLAS and CMS measurements have been successfully described by the newest version of the SuperChic Monte Carlo generator [32]. More recently, the CMS Collaboration submitted results on the coherent photoproduction of J/ψ accompanied by EMD in a rapidity range complementary to the one explored in this analysis [33]. In this article, the cross section for the coherent photoproduction of J/ψ accompanied by nuclear EMD is presented (section 6.1). The measurement is carried out in five rapidity regions covering the intervals |y|<0.8and 2.5<|y|<4.0. These measurements are used to extract the photonuclear cross section σγPb in the range 17 < WγPb,n<920 GeV, which corresponds to a Bjorken-xin the range 1.1×10−5<x<3.3×10−2, where x=m2/W 2 γPb,n (section 6.2). In addition, the nuclear suppression factor is obtained in this kinematic region (section 6.3). The measurements are compared to theoretical models covering a wide spectrum of approaches going from models assuming no nuclear dynamics, to stateof-the-art computations based on perturbative QCD. – 3 – JHEP10(2023)119 2 Theoretical models Many different models provide predictions for the coherent photoproduction of J/ψ in UPCs; for example, those presented in refs. [16,34–40]. Predictions for this process when accompanied by EMD of the incoming nuclei exist for only a few of the models, which are discussed in section 2.2. All the models are based on the computation of the two elements shown in eq. (1.1): the photon flux nγ(y)and the photonuclear cross section σγPb(y). There is also an interference term [41], but its effect, when the cross section is integrated over the transverse momentum of the J/ψ as for the results presented here, can be neglected. 2.1 The photon flux The predictions and the experimental results discussed below utilise photon fluxes based on the approach of the STARlight [16,42] and nO Onmodels [43]. There are two steps to compute the photon fluxes: obtaining the total flux, and computing the fractions of the flux that are assigned to the different EMD classes presented in section 4.3. The total flux as implemented in both STARlight and nO Onis computed in the semiclassical approximation (for details see, e.g. ref. [5]). In this approach, the form factor of the Pb ion is modelled with a Woods-Saxon distribution, while the coherence condition is supplemented by the requirement of no hadronic interactions, as obtained with a Poissonian model based on the nuclear overlap function and the total nucleon-nucleon cross section. Both STARlight [23] and nO On[43] compute the fractions of the total fluxes for each EMD scenario based on photoproduction data measured at lower energies and extrapolations to LHC energies. There are two relevant differences between STARlight and nO On. First, STARlight uses the Lorentz-line parameterisation of the giant-dipole resonance data described in ref. [44], while nO Onuses the data directly; the numerical difference between them is negligible. Second, nO Onuses photonuclear Pb data in the nucleon resonance region [45], while STARlight uses data from photon-nucleon interactions [46,47] in this region. Both models provide similar fluxes apart from the most forward rapidity region. In this kinematic range, the fluxes differ by up to 20%. As nO Onuses experimental data on γPb collisions, the fluxes from this model are used in section 6.2 to extract the photonuclear cross section. 2.2 The photonuclear cross section The photonuclear cross section can be computed using various theoretical approaches. The impulse approximation (IA) assumes that the nuclear scattering is given by the superposition of the scattering on the individual nucleons [48]. In the context of the coherent production of J/ψ, a nuclear suppression factor can be defined using IA, and the associated cross section σIA γPb. This factor quantifies the difference between the nucleus being a set of independent nucleons and a real nucleus: SPb(WγPb,n) = sσγPb σIA γPb .(2.1) – 4 – JHEP10(2023)119 The square root in eq. (2.1) is motivated by the fact that the diffractive photoproduction of J/ψ is proportional to the square of the gluon distribution of the target within the leading log approximation of QCD [49]. The model for the photonuclear cross section by Klein and Nystrand [16], implemented in STARlight, is based on the following steps. A parameterisation of HERA data on the exclusive forward production of J/ψ is converted, using the vector dominance model (VDM) [50], into the forward cross section for J/ψ+p →J/ψ+p; using the optical theorem, this cross section yields the total J/ψ + p cross section, which is introduced into a classical Glauber prescription to produce the total cross section for J/ψ + Pb. Finally, the optical theorem and VDM are used again to obtain the forward σγPb. The nuclear form factor is used to obtain the total σγPb. The model by Guzey, Kryshen, and Zhalov [34] is based on the leading logarithmic approximation of perturbative QCD [49] for the exclusive production of J/ψ at zero momentum transfer for γpcollisions. This cross section is scaled to the nuclear case using the square of the ratio of the gluon distribution in the Pb nucleus to the gluon distribution in the proton scaled by the Pb mass number. The computation is performed for two cases. The first one is based on the EPS09-LO parameterisation of nuclear parton density functions [51]. The second one relies on the leading twist approximation (LTA) of gluon shadowing [52]. This model includes the nuclear form factor computed with a Woods-Saxon prescription. The photon fluxes needed to compute the UPC cross section are obtained from the flux fractions given by STARlight. The theoretical uncertainties explored in this model originate in the spread of predictions from the nuclear parton distribution functions (PDFs) for the EPS09-LO case, and in the uncertainty on the parameters of LTA obtained by fits to HERA diffractive data. For the LTA case, the uncertainty on the predicted cross sections reaches up to 30%, while for EPS09-LO it can be as large as a factor of 2. The authors of the LTA computations provided the upper and lower limits of their predictions. The average of these numbers is depicted in the figures shown in section 6. These figures also show the predictions for the EPS09-based model, using the central value of the EPS09 parameterisation. The model by Bendova et al. [38] is based on the solution of the impact-parameter dependent Balitsky-Kovchegov (b-BK) equation, as discussed in ref. [53] and references therein. There are two models presented in ref. [38]. One uses the b-BK equation to evolve the amplitude for the interaction of a colour dipole with a proton towards higher energies, and then uses this amplitude to compute the γpcross section at the given energy followed by the application of the Glauber-Gribov approach [54], in order to obtain the photonuclear cross section. The second model, shown in the figures below with the notation b-BK-A, starts with a nuclear initial condition for the b-BK equation whose solutions at higher energies can then be directly used to obtain the photonuclear cross section without the need of a Glauber-Gribov prescription. The photon fluxes needed to compute the UPC cross section are given by the nO Onmodel. There are some theoretical uncertainties associated with this type of model [55]. The main two uncertainties are related to the use of the Glauber-Gribov approach instead of a nuclear initial condition, and to the approach used to compute the J/ψ wave function. The first uncertainty changes the cross section – 5 – JHEP10(2023)119 for coherent production of J/ψ up to 30% [38], while the J/ψ wave function produces an uncertainty up to about 20% [37,56]. This model is valid only at small Bjorken-x, so the cross section in UPCs for |y|larger than about three cannot be predicted as these rapidities are dominated by contributions with Bjorken-xlarger than 0.01. The model by Cepila et al. [36] is based on the colour-dipole approach to QCD, including gluon saturation effects, framed within the Good-Walker formalism for diffraction [57–59]. In this model, hadrons are constituted by hot spots with the hadronic structure fluctuating event by event. For a recent review, see ref. [60]. This type of model describes HERA data [61,62]. In the model by Cepila et al. the number of hot spots increases as Bjorken-xdecreases and the transition from proton to nuclear targets is based on the Glauber-Gribov prescription. The theoretical uncertainties coming from the wave function of the J/ψ are the same as described above. Other uncertainties related to the fluctuation of the colour fields were explored in ref. [61] and found to be small with respect to the current precision of the experimental data. The uncertainty on the modelling of the nuclear case was explored in ref. [36] by comparing the Glauber-Gribov prescription with results based on a geometric-scaling approach. Differences of up to 30% were found, with recent data [12] clearly preferring the Glauber-Gribov prescription, which is shown in the figures below with the notation GG-HS. Also in this case, the photon fluxes needed to compute the UPC cross section are given by the nO Onmodel. 3 Experimental set-up The results presented here are based on a data sample collected with the ALICE detector in 2018, when the LHC provided collisions of Pb nuclei at √sNN = 5.02 TeV. The experimental signature of the events of interest for this analysis consists of a pair of leptons, from the J/ψ decay, the potential presence of neutrons emitted at beam rapidities by EMD, and no other signal above the noise threshold recorded in the detector. The two tracks produced by the leptons are measured with the central barrel detectors (dimuon and dielectron decay channels of the J/ψ) to obtain the results for |y|<0.8, discussed in section 3.1, or with the muon spectrometer (dimuon channel only) to obtain the results for 2.5< |y|<4.0, described in section 3.2. Forward detectors located in the A and C sides of the experiment1are used to record the neutrons and to veto other activity; they are introduced in section 3.3. The triggers used in this analysis, and the associated luminosity, are presented in section 3.4. The full description of the ALICE detector and its performance can be found in refs. [63,64]. 3.1 Central barrel detectors Three central barrel detectors, the Inner Tracking System (ITS), the Time Projection Chamber (TPC), and the Time-of-Flight (TOF) were used to record data for this analysis. These detectors are surrounded by a large solenoid magnet producing a magnetic field of B= 0.5T. Their common pseudorapidity acceptance is |η|<0.9. 1The A and C nomenclature is used LHC wide and refers to the direction of flight of the beams in the accelerator as being antior clockwise when the LHC is seen from the top. – 6 – JHEP10(2023)119 The ITS [65] consists of six cylindrical layers of silicon detectors. The innermost layer is at a radius of 3.9 cm with respect to the beam axis, while the outermost layer is at 43 cm. The two layers closest to the beam form the Silicon Pixel Detector (SPD) and cover the range in pseudorapidity |η|<1.4. The SPD is a fine granularity detector with about 10 million pixels. It serves as a tracking device and can also be used to issue triggers. Surrounding the SPD there are two layers of silicon drift chambers and then two layers of silicon microstrips. These four outer layers of the ITS are used in this analysis exclusively for tracking. The TPC [66] is a five metre long cylindrical chamber separated into two drift volumes by a 100 kV central electrode. The two end-plates are 250 cm away from the central electrode along the beam direction; they are instrumented with multi-wire proportional chambers that are readout by about 560 000 pads allowing for high precision tracking in the transverse plane. The longitudinal coordinate is given by the drift time of ionisation electrons in the TPC electric field. For each individual track, the TPC provides up to 159 track points, which also provide energy-loss measurements that are used for particle identification (PID). In the momentum range of the tracks considered in this analysis (from 1 to 2 GeV/c) the PID from the TPC allows for a clean separation of electrons from muons. The TPC covers the range |η|<0.9. The TOF detector consists of a barrel of multi-gap resistive plate chambers that provide a high precision timing for tracks traversing TOF [67]. It surrounds the TPC and has a pseudorapidity coverage of |η|<0.9. The TOF readout channels are arranged into 18 azimuth sectors that can provide topological trigger decisions [68]. 3.2 The muon spectrometer The muon spectrometer, located in the C side of the experiment, covers the pseudorapidity interval −4< η < −2.5. The composition of the muon spectrometer, when seen from the nominal interaction point (IP), is as follows. First, there is a ten hadronic interaction-length absorber — made of carbon, concrete, and steel — with the task of filtering out hadrons produced in the collisions. The absorber is followed by five tracking stations, each made of two planes of cathode pad chambers. The third station is inside a dipole magnet producing a 3 T m integrated magnetic field. The next element is an iron wall with a thickness of 7.2 hadronic interaction lengths, which is followed by the muon trigger system consisting of two stations, each instrumented with two layers of resistive plate chambers. In addition, a conical absorber made of tungsten, lead, and steel surrounds the beam pipe at small polar angles (less than 2◦) with the mission of shielding the spectrometer from secondary particles. Muon tracks detected in the trigger stations are used by the trigger and matched offline to the tracks reconstructed in the five tracking stations. The trigger system provides single-muon and dimuon triggers for tracks above a programmable transverse-momentum threshold. For the 2018 data used in this analysis the threshold was set to 1 GeV/c. The trigger efficiency for tracks measured with both the trigger and the tracking chambers increases with transverse momentum and it is approximately 50% at 1 GeV/c. – 7 – JHEP10(2023)119 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 )c (GeV/ T p 3− 10 2− 10 1− 10 1 -1 )c (GeV/ T p/dN dN1/ = 5.02 TeV NN sPb −ALICE, Pb -1 bµ 7 ± = 233 int LUPC, 2 c < 3.20 GeV/ ll m2.90 < | < 0.8y| 0n0n ψCoherent J/ ψIncoherent J/ with nucleon dissociationψIncoherent J/ ’ decayψ from ψCoherent J/ ’ decayψ from ψIncoherent J/ ll→ γγContinuum =2.09dof/ 2 χFit: 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 )c (GeV/ T p 3− 10 2− 10 1− 10 1 -1 )c (GeV/ T p/dN dN1/ = 5.02 TeV NN sPb −ALICE, Pb -1 bµ 7 ± = 233 int LUPC, 2 c < 3.20 GeV/ ll m2.90 < | < 0.8y| XnXn ψCoherent J/ ψIncoherent J/ with nucleon dissociationψIncoherent J/ ’ decayψ from ψCoherent J/ ’ decayψ from ψIncoherent J/ ll→ γγContinuum =1.18dof/ 2 χFit: 0 0.5 1 1.5 2 2.5 3 )c (GeV/ T p 4− 10 3− 10 2− 10 1− 10 1 -1 )c (GeV/ T p/dN dN1/ = 5.02 TeV NN sPb −ALICE, Pb -1 bµ 13 ± = 533 int LUPC, 2 c < 3.35 GeV/ µµ m2.85 < | < 4y2.5 < | 0n0n ψCoherent J/ ψIncoherent J/ with nucleon dissociationψIncoherent J/ ’ decayψ from ψCoherent J/ ’ decayψ from ψIncoherent J/ µµ → γγContinuum =1.35dof/ 2 χFit: 0 0.5 1 1.5 2 2.5 3 )c (GeV/ T p 3− 10 2− 10 1− 10 1 -1 )c (GeV/ T p/dN dN1/ = 5.02 TeV NN sPb −ALICE, Pb -1 bµ 13 ± = 533 int LUPC, 2 c < 3.35 GeV/ µµ m2.85 < | < 4y2.5 < | XnXn ψCoherent J/ ψIncoherent J/ with nucleon dissociationψIncoherent J/ ’ decayψ from ψCoherent J/ ’ decayψ from ψIncoherent J/ µµ → γγContinuum =1.00dof/ 2 χFit: Figure 2. Transverse momentum distributions for events of the 0n0n (left) and XnXn (right) neutron classes measured at mid (top) and forward rapidity (bottom). The solid black markers represent data, the vertical line through each of them is the associated statistical uncertainty. The black lines depict the fit model described in the text. transverse polarisation as expected for the case of photoproduction and recently confirmed by the ALICE Collaboration [80]. Polarisation could also play a role at midrapidity due to the interference of the two possible photon sources. As the incoming photon is linearly polarised, the interference causes an azimuthal anisotropy that can be observed in the final state [81,82]. Interference effects appear at low values of transverse momenta and at midrapidity where both amplitudes are similar [41]. As the measurements presented here are integrated over transverse momentum, the potential impact of the interference is suppressed. Furthermore, the interference contributes mainly at small impact parameters, that is in the XnXn class, where our data sample has the largest statistical uncertainty and the contribution of interference effects is not visible. The other two terms, ϵpu, and ϵemd, take into account the effects of pile-up. The first one, ϵpu, accounts for cases where, in addition to the coherent production of J/ψ, another independent collision leaves signals in V0 or AD causing the event to be rejected at the – 14 – JHEP10(2023)119 trigger level. The pile-up probability is measured using data selected with an unbiased trigger based on the timing of bunches crossing the IP. For the midrapidity analysis ϵpu = 0.920 ±0.002, while for the forward rapidity sample ϵpu = 0.962 ±0.001; the uncertainty comes from the size of the unbiased data sample. The second pile-up factor, ϵemd, takes into account events where the dissociation of the incoming nucleus produces, in addition to neutrons, charged particles that leave a signal in AD or V0. These extra particles come from EMD events with the neutron emission accompanied by the emission of protons or pions. According to ref. [83], the corresponding cross sections are expected to be large. This factor is determined with a data sample triggered by an energy deposition over the threshold in either ZNA or ZNC; this sample is populated by EMD events [79]. For the 0n0n events ϵemd = 1.0as there is no nuclear dissociation. For the analysis at midrapidity ϵemd = 0.74±0.04 and ϵemd = 0.57±0.05 for the 0nXn+Xn0n and XnXn classes, respectively. For the analysis at forward rapidity ϵemd = 0.88 ±0.01 and ϵemd = 0.84 ±0.05 for the Xn0n and XnXn classes, respectively. The uncertainty reflects the size of the data sample used to determine these factors. 5.3 Systematic uncertainties A number of studies were undertaken to estimate potential systematic uncertainties. Their effect on the measured cross sections is summarised in tables 1and 2. To study the uncertainty on the model used for the signal extraction at midrapidity, the yield according to the Crystal Ball function is compared to counting the events under the peak region after the background is subtracted using the exponential shape from the fit. The model based on the Crystal Ball function is used as the baseline and half of the difference, amounting to 1.5%, is assigned as the systematic uncertainty. Another contribution to the uncertainty on the signal extraction comes from the description of the background. This was estimated by varying the fit range which produces a 0.3% effect which is added in quadrature to the uncertainty on the modelling of the signal. For the analysis at forward rapidity the uncertainty is estimated by varying the values of the tail parameters of the Crystal Ball function in the ranges found by fits to the signal in the simulated MC samples. This uncertainty varies from 0.1% to 1.3% and is considered uncorrelated across rapidity and neutron classes. There is an uncorrelated source of uncertainty for the determination of fIthat originates in the modelling of the different templates needed for the fit to the transverse momentum distribution described in section 5.1. For the midrapidity analysis, it is estimated by using for the template of the γγ →l+l−process either the transverse momentum distribution obtained at either side of the J/ψ peak in the invariant mass distribution or the template from the STARlight MC. For the forward analysis, the shape of the incoherent distribution is obtained either from the fit described in section 5.1 or it is constrained by fitting the transverse momentum distribution of the 0nXn sample with the requirement of activity in the ADC detector; this sample is dominated by incoherent production. The uncorrelated uncertainty for fIvaries from a fraction of a percent to a few percent. There is also a correlated uncertainty related to the extraction of the incoherent contamination. It is known that the STARlight MC does not describe correctly the shape of – 15 – JHEP10(2023)119 |y|<0.2 0.2<|y|<0.8 Source Type 0n0n 0nXn+Xn0n XnXn 0n0n 0nXn+Xn0n XnXn Signal extraction U 1.5 1.5 1.5 1.5 1.5 1.5 Incoherent fraction U 0.1 1.5 1.3 0.1 1.5 1.3 Coherent shape C 0.1 0.8 0.6 0.1 0.8 0.6 Feed-down C 0.6 0.6 0.6 0.6 0.6 0.6 Branching ratio C 0.5 0.5 0.5 0.5 0.5 0.5 Luminosity C 2.5 2.5 2.5 2.5 2.5 2.5 Trigger live time C 1.5 1.5 1.5 1.5 1.5 1.5 ITS-TPC matching C 2.8 2.8 2.8 2.8 2.8 2.8 TOF trigger C 0.7 0.7 0.7 0.7 0.7 0.7 SPD trigger C 1 1 1 1 1 1 ϵpu C 3 3 3 3 3 3 ϵemd C 0 3.2 3.5 0 3.2 3.5 Migrations A −3.93.4 0.9 −3.63.1 1.1 Table 1. Summary of the systematic uncertainties, given in percent, related to the measurements performed with the central barrel detectors. The minus sign in the entry for migrations in the 0n0n class signifies that this uncertainty is anti-correlated with those from migrations in the 0nXn+Xn0n and XnXn classes. The second column identifies the type of uncertainty (U=uncorrelated, C=correlated, A=anticorrelated) as used in eq. (6.1). 2.5<|y|<3.0 3.0<|y|<3.5 3.5<|y|<4.0 Source Type 0n0n Xn0n XnXn 0n0n Xn0n XnXn 0n0n Xn0n XnXn Signal extraction U 0.2 1.3 0.8 0.1 0.6 0.7 0.5 0.5 0.9 Incoherent fraction U 0.4 0.6 1.6 0.4 0.9 3.3 0.4 0.5 2.2 Coherent shape C 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 Feed-down C 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 Branching ratio C 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 Luminosity C 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 Tracking C 3 3 3 3 3 3 3 3 3 Trigger C 6.2 6.2 6.2 6.2 6.2 6.2 6.2 6.2 6.2 Matching C 1 1 1 1 1 1 1 1 1 ϵpu C 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 ϵemd C 0 1.1 6 0 1.1 6 0 1.1 6 Migrations A −0.33.8 3.3 −0.23.6 3.6 −0.23.3 3.6 Table 2. Summary of the systematic uncertainties, given in percent, related to the measurements performed with the muon spectrometer. The minus sign in the entry for migrations in the 0n0n class signifies that this uncertainty is anti-correlated with those from migrations in the 0nXn+Xn0n and XnXn classes. The second column identifies the type of uncertainty (U=uncorrelated, C=correlated, A=anticorrelated) as used in eq. (6.1). the transverse momentum distribution for the coherent production of J/ψ [13]. A different shape for the transverse momentum dependence of coherent production was used in the fit and half the difference in the results is assigned as an uncertainty. The effect is below 1% and it is larger for the midrapidity analysis since the resolution of the muon spectrometer is not as good as for the central barrel detectors, so it is not so sensitive to this effect. – 16 – JHEP10(2023)119 The uncertainty on feed-down is estimated by varying fDwithin its uncertainty. As the determination of feed-down is independently done using the central barrel detectors and the muon spectrometer, this uncertainty is correlated only across the corresponding measurements and it is uncorrelated between the results obtained at mid and forward rapidities. It amounts to 0.6% and 0.7%, respectively. Two other sources of uncertainties are also considered as correlated: the uncertainty on the branching ratios is obtained from ref. [77]; the uncertainty on the determination of the luminosity, coming from the measurement of the reference cross sections and from the stability of the calibration over time, is taken from ref. [74] and amounts to 2.5%. For CBtrig there is another source of uncertainty related to the luminosity of the data sample, namely the precision to which the live time of the trigger is known, which is 1.5%. The live time of MStrig is known with a very good precision and produces a negligible uncertainty. For the central barrel analysis there are four uncertainty sources that are correlated across the corresponding measurements. A systematic uncertainty on the tracking efficiency of 2% per track is estimated by comparing, in data and in MC, the matching efficiency for track segments reconstructed in the TPC and in the ITS. This leads to a 2.8% systematic uncertainty for two tracks. The uncertainty of the TOF trigger efficiency due to the spread of the arrival times of various particle species to TOF is evaluated as 0.5% per track (1% in total). The uncertainty associated with the determination of the trigger efficiency of the SPD is obtained directly from data by varying the requirements to select the tracks used to measure this efficiency. This uncertainty amounts to 1%. There are three correlated uncertainties associated with the muon spectrometer. The uncertainty on the tracking efficiency amounts to 3%. It is estimated by comparing the single-muon tracking efficiency values obtained in MC and data, with a procedure that exploits the redundancy of the information from the tracking chambers [84]. The systematic uncertainty on the dimuon trigger efficiency has two contributions. The uncertainty on the intrinsic efficiencies of the muon trigger chambers is determined by varying them in the MC by an amount equal to the statistical uncertainty on their measurement with a data-driven method and amounts to 1.5%. The uncertainty on the response of the trigger algorithm is obtained by comparing the trigger response function between data and MC; it amounts to 6.0%. These two contributions are added in quadrature. There is also a 1% uncertainty on the matching efficiency of tracks reconstructed with the tracking and the trigger chambers. The uncertainty on ϵpu for the forward rapidity analysis is obtained by varying this factor within its uncertainty. It amounts to 0.2%. As there are more detector systems contributing to ϵpu in the CBtrig case, the uncertainty for the midrapidity measurements is estimated by repeating the analysis without the offline veto from AD and V0, which increases both the yield and ϵpu. These increases do not compensate exactly and the ensuing difference of 3% is assigned as a systematic uncertainty. The uncertainty on ϵemd is obtained by varying it within its uncertainty. It is of the order of a few percent, differing among the neutron classes and rapidity intervals. The uncertainty on migrations across the different neutron classes is obtained by varying the pile-up in ZNA and ZNC as well as the efficiencies of these detectors within their uncertainties. At midrapidity the efficiency is the leading uncertainty for the XnXn neu- – 17 – JHEP10(2023)119 Class Nfit fI(A ×ϵ)det dσPbPb/dy(mb) |y|<0.2 0n0n 1744 ±49 0.014 ±0.002 0.053 3.130 ±0.090 ±0.047 ±0.164 ∓0.122 0nXn+Xn0n 412 ±23 0.179 ±0.011 0.053 0.730 ±0.050 ±0.015 ±0.045 ±0.025 XnXn 84 ±11 0.144 ±0.021 0.053 0.250 ±0.024 ±0.005 ±0.016 ±0.002 0.2<|y|<0.8 0n0n 2179 ±54 0.014 ±0.002 0.024 2.900 ±0.070 ±0.044 ±0.152 ∓0.104 0nXn+Xn0n 597 ±28 0.179 ±0.011 0.024 0.800 ±0.040 ±0.017 ±0.050 ±0.025 XnXn 134 ±13 0.144 ±0.021 0.024 0.300 ±0.029 ±0.006 ±0.019 ±0.003 2.5<|y|<3.0 0n0n 2939 ±84 0.0140 ±0.0038 0.069 2.668 ±0.076 ±0.011 ±0.199 ∓0.009 Xn0n 318 ±28 0.070 ±0.0061 0.069 0.242 ±0.021 ±0.003 ±0.018 ±0.009 XnXn 247 ±23 0.1180 ±0.0159 0.069 0.256 ±0.024 ±0.005 ±0.024 ±0.009 3.0<|y|<3.5 0n0n 7102 ±102 0.0130 ±0.0041 0.194 2.322 ±0.033 ±0.010 ±0.173 ∓0.005 Xn0n 638 ±37 0.0480 ±0.0090 0.194 0.172 ±0.010 ±0.002 ±0.013 ±0.006 XnXn 450 ±32 0.1590 ±0.0332 0.194 0.161 ±0.011 ±0.005 ±0.015 ±0.006 3.5<|y|<4.0 0n0n 2403 ±74 0.0070 ±0.0037 0.097 1.590 ±0.049 ±0.010 ±0.119 ∓0.003 Xn0n 189 ±16 0.0270 ±0.0053 0.097 0.101 ±0.009 ±0.001 ±0.008 ±0.003 XnXn 111 ±16 0.1650 ±0.0223 0.097 0.079 ±0.011 ±0.002 ±0.008 ±0.003 Table 3. Values for the number of J/ψ candidates (Nfit), the incoherent fraction (fI), correction for the detector acceptance and efficiency ((A ×ϵ)det) and the measured cross section (dσPbPb/dy) for the different neutron classes and rapidity ranges. The first uncertainty in the last column is statistical, the rest are systematic. The second uncertainty is uncorrelated, the third correlated, and the fourth originates from migrations across neutron classes. Note that for each rapidity range the 0n0n uncertainty related to migrations is preceded by a ∓, while the other neutron classes have a±; this means that these uncertainties are anti-correlated. tron class, while pile-up dominates the other two neutron classes. At forward rapidities the efficiency is the leading uncertainty. The largest difference, with respect to the nominal measurement, from all variations is taken as the uncertainty. As mentioned above, these uncertainties are anti-correlated across the neutron classes within one rapidity range. 6 Results 6.1 Cross section in UPC Using the analysis strategy described in section 5, the cross section for the coherent production of J/ψ vector mesons in UPCs of Pb nuclei at √sNN = 5.02 TeV is obtained. The measurements are reported in table 3along with other numerical values needed in eq. (5.1) and (5.2). The results are compared to the predictions from different models in figure 3. The theoretical uncertainties associated to each model are discussed in section 2. In all cases the IA calculation is well above the data signalling important shadowing effects that have a similar magnitude in each of the different neutron emission classes. The STARlight model – 18 – JHEP10(2023)119 4−3−2−1−0 1 y 0 1 2 3 4 5 6 7 8 (mb)y/dσd ALICE 0n0n Impulse approximation STARlight EPS09 LO LTA GG-HS b-BK-A = 5.02 TeV NN sPb −ALICE Pb 4−3−2−1−0 1 y 0.0 0.5 1.0 1.5 2.0 2.5 (mb)y/dσd ALICE 0nXn+Xn0n Impulse approximation STARlight EPS09 LO LTA GG-HS b-BK-A = 5.02 TeV NN sPb −ALICE Pb 4−3−2−1−0 1 y 0.0 0.2 0.4 0.6 0.8 1.0 1.2 (mb)y/dσd ALICE Xn0n Impulse approximation STARlight EPS09 LO LTA GG-HS b-BK-A = 5.02 TeV NN sPb −ALICE Pb 4−3−2−1−0 1 y 0.0 0.2 0.4 0.6 0.8 1.0 (mb)y/dσd ALICE XnXn Impulse approximation STARlight EPS09 LO LTA GG-HS b-BK-A = 5.02 TeV NN sPb −ALICE Pb Figure 3. Measured cross section for the coherent production of J/ψ in UPCs at √sNN = 5.02 TeV. The solid markers represent the measured cross section (the measurement at 0.2<|y|<0.8is shown at negative rapidities and reflected into positive rapidities with an open marker). The vertical line across a marker is the sum in quadrature of the statistical and uncorrelated systematic uncertainty. The width of the boxes depicts the range in rapidity covered by each measurement, while the height of a box is the sum in quadrature of the correlated systematic uncertainties and the effect of migrations across neutron classes. Note that the uncertainties from migrations are anti-correlated between the 0n0n and the other two neutron classes in each rapidity interval. The lines depict the prediction of the different models discussed in section 2. describes well the data at forward rapidity in the 0n0n class, while overestimating the data in all the other classes. At midrapidity, this model does not describe the data in any of the neutron classes. The predictions of the other four models — EPS09-LO, LTA, b-BK-A, and GG-HS — are qualitatively similar, while quantitatively they differ with the maximum spread given by the GG-HS and b-BK-A models, whose predictions differ by up to about 20%. These four models describe the data reasonably well, except for the rapidity range 3.5<|y|<2.5in the 0n0n class, where the data are clearly above the predictions. For the XnXn neutron class the data at forward rapidity are systematically slightly above the predictions. The IA and STARlight models do not include gluon shadowing or saturation effects. The EPS09-LO and LTA models do not include explicitly gluon saturation, while the b-BKA and GG-HS predictions do not include explicitly shadowing effects beyond saturation. The data indicate that the IA and STARlight predictions are disfavoured, implying the need of some QCD dynamic effect, beyond what is included in these models, to describe the – 19 – JHEP10(2023)119 y nγ(0n0n) nγ(0nXn+Xn0n) nγ(XnXn) σIA γPb (µb) 3.5< y < 4178.51 18.18 6.34 10 3< y < 3.5162.99 18.19 6.34 14 2.5< y < 3147.46 18.19 6.34 19 0.2< y < 0.877.88 17.88 6.33 48 −0.2< y < 0.262.86 17.47 6.27 58 −0.8< y < −0.248.31 16.75 6.18 71 −3< y < −2.53.91 4.97 2.78 176 −3.5< y < −31.22 2.15 1.42 215 −4< y < −3.50.26 0.61 0.48 262 Table 4. Theoretical input needed to obtain the photonuclear cross section and the nuclear suppression factor. Photon fluxes, see eq. (1.1), computed with nO Onfor the different neutron classes and rapidity ranges. The last column shows the value of σIA γPb as computed in ref. [17]. measurements. Within the experimental precision and the large theoretical uncertainties mentioned in section 2, models that include either shadowing or gluon saturation give an equally good description of the data. 6.2 Extraction of the photonuclear cross section Having several independent UPC measurements allows for the extraction of the two photonuclear cross sections in each rapidity interval. A χ2minimisation is applied to the three measurements in each yrange. The used χ2approach incorporates the correlated uncertainties through nuisance parameters and the uncorrelated and statistical ones utilising relative uncertainties. This method has already been used by the ALICE Collaboration to extract the energy dependence of exclusive photoproduction of J/ψ in p-Pb collisions [85,86] and it was originally used by the H1 Collaboration for the measurement of the inclusive deeply inelastic cross section at HERA [87]. The χ2definition is given by χ2 exp m, b=X imi−Pjγi jmibj−µi2 δ2 i,statµimi−Pjγi jmibj+δi,uncor mi2+X j b2 j.(6.1) Here, µiis the measured central value at a point i,miare given by the right-hand side of eq. (1.1) with the fluxes computed with the nO Onprogram [43] (see section 2.1 and table 4 for the flux values), and σγPb(±y)the two parameters to be extracted from the fit. Note that for the rapidity range |y|<0.2there is only one photonuclear cross section. The relative statistical and uncorrelated systematic uncertainties for each rapidity range (see tables 1and 2) are given by δi,stat = ∆i,stat/µiand δi,uncor = ∆i,uncor/µi, respectively. Finally, γi jis the matrix of the correlated systematic uncertainty for the source of type j at the point i, where bjis the associated set of nuisance parameters. The uncertainties for the measurement of σγPb(y)are obtained as follows. A fit including the statistical as well as the correlated and uncorrelated systematic uncertainties is performed. Another fit including only the statistical and uncorrelated systematic uncertainties is performed. The uncertainty from this second fit is quoted as the uncorrelated – 20 – JHEP10(2023)119 y WγPb,n(GeV) σγPb (µb) unc. (µb) corr. (µb) mig. (µb) flux frac. (µb) 3.5< y < 419.12 8.84 0.30 0.68 0.02 0.04 −4< y < −3.5813.05 57.32 20.77 7.57 6.41 6.56 3< y < 3.524.55 13.89 0.23 1.08 0.05 0.08 −3.5< y < −3633.21 46.58 6.61 5.73 3.77 3.63 2.5< y < 331.53 16.89 0.59 1.32 0.11 0.18 −3< y < −2.5493.14 44.68 6.38 5.15 2.73 2.97 0.2< y < 0.897.11 21.73 5.12 3.12 4.32 2.73 −0.8< y < −0.2160.10 25.00 7.33 4.88 5.43 3.91 −0.2< y < 0.2124.69 24.15 0.69 1.37 0.50 0.06 Table 5. Photonuclear cross sections extracted from the UPC measurements using the procedure described in the text. The quoted uncertainties are uncorrelated (unc.), correlated (corr.), caused by migrations across neutron classes (mig.) and by variations of the flux fractions in the different classes (flux frac.). The lines separate the different ranges in |y|. Note that two photonuclear cross sections in each rapidity interval are anti-correlated. uncertainty. The difference between the uncertainties from the first and second fit, taken in quadrature, are quoted. There are two contributions to the uncertainty associated to the photon fluxes. One is related to the total flux and the other to the fractions of the total flux in each neutron class. The first contribution is obtained by varying the parameter of the nuclear radius in the Woods-Saxon distribution according to neutron-skin measurements [88]; this uncertainty amounts to 2% correlated over all rapidity intervals and neutron classes. This factor is already taken into account in the correlated uncertainties mentioned in the previous paragraph. The second contribution is estimated by varying by ±5% all cross sections used as input in nO Onfor the computation of the photon flux fractions (see also ref. [89]). The relative change in the photon fluxes goes from 1% to 8% depending on rapidity and neutron class. These changes are anti-correlated in neutron classes for each rapidity interval. To compute the associated uncertainties, fits — including the statistical, correlated and uncorrelated systematic uncertainties — are performed using the modified fluxes. The largest difference, divided by √2, between these fits and the fit with the default photon-flux values from nO Onis taken as the uncertainty originating from the photon flux. If the fluxes of STARlight were used, instead of those from nO On, then the results would vary by less than one percent, except for the two largest energies, where the cross sections would be larger by 2.6% and 7.7% at WγPb,n= 633 GeV and WγPb,n= 813 GeV, respectively. This is well within the uncorrelated uncertainties of the measurement. Uncertainties caused by the migrations across neutron classes are treated in a similar way to those associated with the photon flux. The input UPC cross sections are modified by the migration uncertainties, new fits are performed and the largest difference, divided by √2, with respect to the fit that uses the unmodified UPC cross sections is taken as the systematic uncertainty due to migration effects. The results obtained by following this procedure are listed in table 5and shown in figure 4, where they are compared to the predictions of the different models. Note that – 21 – JHEP10(2023)119 20 30 40 50 2 10 2 10×23 10 (GeV) Pb,nγ W 10 2 10 3 10 b)µ Pb) (γ(σ 5− 10 4− 10 3− 10 2− 10 x Bjorken- = 5.02 TeV NN sPb −PbALICE, (PLB 726 (2013) 290-295) = 2.76 TeV NN sPb −using ALICE PbGuzey et al., (PRC 96 (2017) 015203) = 2.76 TeV NN sPb −using ALICE PbContreras, Impulse approximation STARlight EPS09 LO LTA GG-HS b-BK-A Figure 4. Photonuclear cross section for the γ+ Pb →J/ψ + Pb process as a function of WγPb,n (lower axis) or Bjorken-x(upper axis). The solid markers represent the measured cross section. The vertical line across a marker is the uncorrelated uncertainty. The height of an empty box is the sum in quadrature of the correlated systematic uncertainties and the effect of migrations across neutron classes. The gray box represents the theoretical uncertainty coming from the computation of the photon flux. The lines depict the prediction of the different models discussed in section 2. The open triangular and square markers show the cross sections extracted in refs. [17,18] using ALICE Run 1 data. according to eq. (1.1) the results for the cross section at low and high WγPb,nin one rapidity interval are anti-correlated. Note that the uncertainties for the high WγPb,nregion are large, reaching about 30% at WγPb,n= 813 GeV. The predictions obtained with IA [17] are consistent with the data for the energy region below 40 GeV, although systematically above the data; at all other energies the predictions from IA are well above the measurements with the difference increasing with energy. STARlight predictions describe the data for energies below 40 GeV, but overestimate the measurements at all other energies. None of the EPS09-LO, LTA, b-BK-A, and GG-HS models describe the data in the WγPb,n range from about 25 to 35GeV. The EPS09-LO model describes the measurements at the lowest energy and at intermediate energies, but overestimates the measurements at the highest energies. The GG-HS model does not include the reduction of phase space at low WγPb,n, but it describes the data, except for the mentioned energy range, for all other measurements, with the predictions systematically on the higher side of the measurements. The predictions of the LTA and b-BK-A models are very similar and describe the data fairly well at all energies, except for the energy range from about 25 to 35 GeV. – 22 – JHEP10(2023)119 The photonuclear cross sections extracted in refs. [17,18] using ALICE Run 1 data are also shown in figure 4. The cross sections at the two highest WγPb,n, namely 92 GeV and 470GeV, agree with the new measurements presented here, while the two cross sections at low WγPb,nare below the new measurements by around 1.5 standard deviations. The fact that the cross sections extracted using the peripheral and ultra-peripheral results from Run 1 and the new measurements presented here agree reasonably well is remarkable, because they involve a different set of systematic uncertainties. It is also worth noting that the new measurements extend the range in WγPb,nby about 350 GeV, up to WγPb,n= 813 GeV, with respect to the maximum energy reached by ALICE Run 1 data. As mentioned above, the CMS Collaboration submitted results on this process [33]. The CMS data cover the ranges around 40 GeV to 50 GeV and 300 to 400GeV in WγPb,n. These ranges lie in between the ranges covered by the ALICE forward and midrapidity analyses. The results of the CMS Collaboration smoothly follow the same trend as the cross sections measured by ALICE. At low energies the measurements are compatible with the STARlight predictions and at high energies with the LTA and b-BK-A predictions. 6.3 Nuclear suppression factor The nuclear suppression factor is defined in eq. (2.1). To obtain it, the measured photonuclear cross sections are divided by the IA values, where we use the implementation from ref. [17]. The corresponding values of IA are listed in table 4. According to ref. [17] the computation of IA has an uncertainty of about 5%, which reflects the uncertainties related to the experimental input data and its parameterisation. This uncertainty is taken into account in the results shown below. The nuclear suppression factor is important because it provides a quantitative measure of shadowing in this process and several theoretical uncertainties, e.g. that associated to the J/ψ wave function, should largely cancel in the ratio. Not all uncertainties cancel out completely; for example, in ref. [17] it is argued that the interpretation of the nuclear suppression factor in terms of the gluon shadowing factor has a theoretical uncertainty due to corrections, amounting to about 10%, that account for the skewedness and the real part of the amplitude. The nuclear suppression factor is shown in figure 5, where the measurement is compared with the predictions of the different models. The nuclear suppression factor at low energies is about 0.94, decreases to values slightly above 0.64 at intermediate energies, and decreases further down to about 0.47 at the highest measured energies. The STARlight model describes only the WγPb,nrange from about 25 to 35 GeV. The other four models do not describe this energy range, but provide a fair description at higher energies, except for the EPS09-LO model, which predicts a nuclear suppression factor that remains constant with increasing WγPb,n, while the data and the other models exhibit a decreasing trend. 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Sharma 54,108, M. Sharma 92, S. Sharma 77, S. Sharma 92, U. Sharma 92, A. Shatat 73, O. Sheibani115, K. Shigaki 93, M. Shimomura78, J. Shin12, S. Shirinkin 141, Q. Shou 40, Y. Sibiriak 141, S. Siddhanta 52, T. Siemiarczuk 80, T.F. Silva 111, D. Silvermyr 76, T. Simantathammakul106, R. Simeonov 37, B. Singh92, B. Singh 96, K. Singh 48, R. Singh 81, R. Singh 92, R. Singh 48, S. Singh 16, V.K. Singh 133, V. Singhal 133, T. Sinha 100, B. Sitar 13, M. Sitta 131,56, T.B. Skaali20, G. Skorodumovs 95, M. Slupecki 44, N. Smirnov 138, R.J.M. Snellings 59, E.H. Solheim 20, J. Song 115, A. Songmoolnak106, C. Sonnabend 33,98, F. Soramel 28, A.B. Soto-hernandez 89, R. Spijkers 85, I. Sputowska 108, J. Staa 76, J. Stachel 95, I. Stan 63, P.J. Steffanic 121, – 36 – JHEP10(2023)119 S.F. Stiefelmaier 95, D. Stocco 104, I. Storehaug 20, P. Stratmann 136, S. Strazzi 26, A. Sturniolo 31,53, C.P. Stylianidis85, A.A.P. Suaide 111, C. Suire 73, M. Sukhanov 141, M. Suljic 33, R. Sultanov 141, V. Sumberia 92, S. Sumowidagdo 83, S. Swain61, I. Szarka 13, M. Szymkowski 134, S.F. Taghavi 96, G. Taillepied 98, J. Takahashi 112, G.J. Tambave 81, S. Tang 6, Z. Tang 119, J.D. Tapia Takaki 117, N. Tapus125, L.A. Tarasovicova 136, M.G. Tarzila 46, G.F. Tassielli 32, A. Tauro 33, G. Tejeda Muñoz 45, A. Telesca 33, L. Terlizzi 25, C. Terrevoli 115, S. Thakur 4, D. Thomas 109, A. Tikhonov 141, A.R. Timmins 115, M. Tkacik107, T. Tkacik 107, A. Toia 64, R. Tokumoto93, K. Tomohiro93, N. Topilskaya 141, M. Toppi 49, T. Tork 73, V.V. Torres 104, A.G. Torres Ramos 32, A. Trifiró 31,53, A.S. Triolo 33,31,53, S. Tripathy 51, T. Tripathy 47, S. Trogolo 33, V. Trubnikov 3, W.H. Trzaska 116, T.P. Trzcinski 134, A. Tumkin 141, R. Turrisi 54, T.S. Tveter 20, K. Ullaland 21, B. Ulukutlu 96, A. Uras 127, G.L. Usai 23, M. Vala38, N. Valle 22, L.V.R. van Doremalen59, M. van Leeuwen 85, C.A. van Veen 95, R.J.G. van Weelden 85, P. Vande Vyvre 33, D. Varga 137, Z. Varga 137, M. Vasileiou 79, A. 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Zarochentsev 141, P. Závada 62, N. Zaviyalov141, M. Zhalov 141, B. Zhang 6, C. Zhang 129, L. Zhang 40, S. Zhang 40, X. Zhang 6, Y. Zhang119, Z. Zhang 6, M. Zhao 10, V. Zherebchevskii 141, Y. Zhi10, D. Zhou 6, Y. Zhou 84, J. Zhu 98,6, Y. Zhu6, S.C. Zugravel 56, N. Zurlo 132,55 1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2AGH University of Science and Technology, Cracow, Poland 3Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine 4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India 5California Polytechnic State University, San Luis Obispo, California, United States 6Central China Normal University, Wuhan, China 7Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 8Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico 9Chicago State University, Chicago, Illinois, United States 10 China Institute of Atomic Energy, Beijing, China 11 China University of Geosciences, Wuhan, China 12 Chungbuk National University, Cheongju, Republic of Korea 13 Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovak Republic – 37 – JHEP10(2023)119 14 COMSATS University Islamabad, Islamabad, Pakistan 15 Creighton University, Omaha, Nebraska, United States 16 Department of Physics, Aligarh Muslim University, Aligarh, India 17 Department of Physics, Pusan National University, Pusan, Republic of Korea 18 Department of Physics, Sejong University, Seoul, Republic of Korea 19 Department of Physics, University of California, Berkeley, California, United States 20 Department of Physics, University of Oslo, Oslo, Norway 21 Department of Physics and Technology, University of Bergen, Bergen, Norway 22 Dipartimento di Fisica, Università di Pavia, Pavia, Italy 23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy 24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy 25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy 26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy 27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy 28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy 29 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy 30 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy 31 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy 32 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy 33 European Organization for Nuclear Research (CERN), Geneva, Switzerland 34 Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia 35 Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway 36 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 37 Faculty of Physics, Sofia University, Sofia, Bulgaria 38 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic 39 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 40 Fudan University, Shanghai, China 41 Gangneung-Wonju National University, Gangneung, Republic of Korea 42 Gauhati University, Department of Physics, Guwahati, India 43 Helmholtz-Institut für Strahlenund Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany 44 Helsinki Institute of Physics (HIP), Helsinki, Finland 45 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico 46 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 47 Indian Institute of Technology Bombay (IIT), Mumbai, India 48 Indian Institute of Technology Indore, Indore, India 49 INFN, Laboratori Nazionali di Frascati, Frascati, Italy 50 INFN, Sezione di Bari, Bari, Italy 51 INFN, Sezione di Bologna, Bologna, Italy 52 INFN, Sezione di Cagliari, Cagliari, Italy 53 INFN, Sezione di Catania, Catania, Italy 54 INFN, Sezione di Padova, Padova, Italy 55 INFN, Sezione di Pavia, Pavia, Italy 56 INFN, Sezione di Torino, Turin, Italy 57 INFN, Sezione di Trieste, Trieste, Italy 58 Inha University, Incheon, Republic of Korea 59 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands 60 Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic – 38 – JHEP10(2023)119 61 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India 62 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 63 Institute of Space Science (ISS), Bucharest, Romania 64 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 65 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico 66 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil 67 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico 68 iThemba LABS, National Research Foundation, Somerset West, South Africa 69 Jeonbuk National University, Jeonju, Republic of Korea 70 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany 71 Korea Institute of Science and Technology Information, Daejeon, Republic of Korea 72 KTO Karatay University, Konya, Turkey 73 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France 74 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 75 Lawrence Berkeley National Laboratory, Berkeley, California, United States 76 Lund University Department of Physics, Division of Particle Physics, Lund, Sweden 77 Nagasaki Institute of Applied Science, Nagasaki, Japan 78 Nara Women’s University (NWU), Nara, Japan 79 National and Kapodistrian University of Athens, School of Science, Department of Physics , Athens, Greece 80 National Centre for Nuclear Research, Warsaw, Poland 81 National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India 82 National Nuclear Research Center, Baku, Azerbaijan 83 National Research and Innovation Agency - BRIN, Jakarta, Indonesia 84 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 85 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands 86 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom 87 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež, Czech Republic 88 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States 89 Ohio State University, Columbus, Ohio, United States 90 Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia 91 Physics Department, Panjab University, Chandigarh, India 92 Physics Department, University of Jammu, Jammu, India 93 Physics Program and International Institute for Sustainability with Knotted Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan 94 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany 95 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 96 Physik Department, Technische Universität München, Munich, Germany 97 Politecnico di Bari and Sezione INFN, Bari, Italy 98 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 99 Saga University, Saga, Japan 100 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India 101 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 102 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 103 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 104 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France 105 Sungkyunkwan University, Suwon City, Republic of Korea 106 Suranaree University of Technology, Nakhon Ratchasima, Thailand 107 Technical University of Košice, Košice, Slovak Republic – 39 –