Exclusive and dissociative J / ψ photoproduction, and exclusive dimuon production, in p–Pb collisions at √ s NN = 8 . 16 TeV

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Introduction
The strong electromagnetic fields present in ultra-peripheral collisions (UPCs) offer a unique opportunity to study a variety of phenomena, such as photonuclear and two-photon processes [1][2][3].These interactions are mediated by quasireal photons and characterised by an impact parameter larger than the sum of the radii of the colliding nuclei.Two-photon interactions can give rise to exclusive non-resonant dimuon production.Precise measurements of this process can be used to test quantum electrodynamics (QED) calculations, such as lightby-light scattering [4,5] recently measured by ATLAS [6][7][8] and CMS [9], and higher-order QED effects [10].The latter are expected to be sizeable, since the photon couples to nuclei with a large coupling Zα where Z is the charge number and α is the fine structure constant [10].Various theoretical calculations predict a different strength of higher-order effects in heavy-ion collisions [10][11][12].The use of asymmetric p-Pb collisions may provide additional insight on higher-order corrections from multiphoton exchange with a single ion [1].
Measurements of cross sections of dilepton production using UPC samples, performed by ALICE in Pb-Pb [13] and p-Pb [14], CMS [15] and ATLAS [16] in Pb-Pb, and PHENIX [17] and STAR [18][19][20] in Au-Au, are consistent with leading-order (LO) QED calculations.However, latest precision measurements by ATLAS [21] revealed a significant discrepancy with LO QED predictions from the STARlight event generator [22], up to 20% at large rapidities.This discrepancy is discussed by the authors of the SuperChic event generator in Ref. [23].They argue that STARlight does not take into account contributions from dilepton-nucleus impact parameters smaller than the nuclear radii, expected to be significant at high photon energies.Accounting for photons emitted at such impact parameters is also discussed in Refs.[10,24,25].However, this effect alone does not allow the SuperChic authors to resolve the discrepancy with the ATLAS data [24].The inclusion of higher-order corrections to the LO QED calculation could explain the ATLAS results, as suggested in Ref. [10].Dilepton measurements were also performed in pp collisions by ATLAS [26,27] and CMS [28], and in pp collisions by CDF [29,30].These measurements did not explore the low invariant mass region at forward rapidities.
Dimuons can also be produced in photonuclear reactions, from the decay of a vector meson.In particular, dimuons can be produced from the decay of a J/ψ meson in the elastic process γ + p → J/ψ + p, or with proton dissociation in the reaction γ + p → J/ψ + p ( * ) .The use of p-Pb collisions offers the possibility of assigning the photon to its source: the lead ion is in most of the cases the photon emitter due to its large charge number.The γ p centre-of-mass energy W γ p is a function of the J/ψ rapidity: W 2 γ p = 2E p M J/ψ exp(−y), where M J/ψ is the J/ψ mass, y is the J/ψ rapidity measured in the laboratory frame with respect to the proton beam direction, and E p = 6.5 TeV is the proton beam energy, corresponding to a centre-of-mass energy in the p-Pb system of √ s NN = 8. 16 TeV.The energy range studied is 27 < W γ p < 57 GeV, which corresponds to a longitudinal momentum fraction of the participating partons, Bjorken-x scale, in the range 5 × 10 −3 < x < 2 × 10 −2 , where the conversion is performed as x = (M J/ψ /W γ p ) 2 .This is a similar kinematic domain as studied at HERA [31].
Exclusive J/ψ photoproduction is sensitive to the gluon distribution in protons, since its cross section scales with the square of the gluon parton density function in the target proton, according to LO QCD calculations [32].This picture may change at next-to-leading order (NLO) according to the recent studies in Ref. [33].At high W γ p , a reduction in the growth rate of the exclusive J/ψ photoproduction cross section would indicate that non-linear QCD dynamics are present.These non-linearities may arise from gluon recombination, which tame the growth of the gluon distribution, leading in the high energy limit to the gluon saturation phenomenon [34].
On the other hand, J/ψ photoproduction off protons with proton dissociation is a scattering event that produces a J/ψ vector meson and, accompanied by a large rapidity gap, remnants of the dissociated proton.This process might serve as an experimental signature of subnucleonic fluctuations of initial state configurations in the proton target [35][36][37].At high energies, the ratio of dissociative to exclusive cross sections is predicted to vanish, owing to the onset of gluon saturation at sufficiently small x [36,37].
In this article, the measurement of exclusive dimuon continuum production in two-photon interactions in p-Pb UPCs at √ s NN = 8.16 TeV is presented.It is performed in three intervals of dimuon invariant mass, in the range 1.0 < M µ µ < 2.5 GeV/c 2 , and two intervals of rapidity, in the range 2.5 < y < 4.0.The measurement of exclusive J/ψ photoproduction off protons is also presented along with the measurement of J/ψ photoproduction with proton dissociation.These three measurements are carried out in the forward rapidity region with respect to the proton beam direction, namely 2.5 < y < 4.0, and at low dimuon transverse momentum, p T < 3 GeV/c.This corresponds to a range in the square of the momentum transferred at the proton vertex |t| 9 GeV 2 , where t ≈ −p 2 T .

Experimental setup and trigger
The ALICE detector is described in Ref. [46] and its performance is detailed in Ref. [47].The main ALICE tracking detector used in this analysis is the single-arm muon spectrometer, covering the pseudorapidity interval −4.0 < η < −2.5. 1 .The analysis also uses other detector systems, namely the Silicon Pixel Detector (SPD), VZERO (V0), Zero Degree Calorimeters (ZDCs) and ALICE Diffractive (AD) detectors.
The muon spectrometer consists of a ten hadronic interaction length absorber, followed by five tracking stations, each made of two planes of cathode pad chambers.The third station is placed inside a dipole magnet with a 3 T×m integrated magnetic field.Muon tracks are reconstructed by the tracking algorithm described in Ref. [48] using the five tracking stations.The muon trigger system, downstream of the tracking chambers, consists of four planes of resistive plate chambers placed behind a 7.2 interaction length iron wall.The muon tracks detected in these planes are used in the trigger and matched offline to the muon tracks reconstructed in the five tracking stations.
The central region |η| < 1.4 is covered by the SPD consisting of two cylindrical layers of silicon pixels, from which tracklets are reconstructed.Tracklets are track fragments created from the primary vertex and two reconstructed points in the SPD, one in each layer.
The V0 detector is composed of two arrays of scintillator counters, namely the V0C and V0A detectors.Each array consists of 32 cells forming four concentric rings with eight sectors each.V0C, placed at the longitudinal coordinate z = −90 cm, covers the interval −3.7 < η < −1.7, while V0A, z = 330 cm, covers the pseudorapidity interval 2.8 < η < 5.1.The AD detector [49,50] is composed of two scintillator tile arrays, the ADC and ADA subdetectors, located at z = −19.5 m and z = +16.9m and covering the pseudorapidity ranges −7.0 < η < −4.9 and 4.7 < η < 6.3, respectively.The time resolution of V0 and AD detectors is better than 1 ns, which makes it possible to discriminate between beam-beam and beam-gas events, in which beam particles interact with residual gas inside the beam pipe.The raw signals of the V0 and AD detectors are used in the trigger.Offline, these detectors are used to differentiate beam-beam and beam-gas interactions.
The two ZDCs are located at 112.5 m from the nominal interaction point along the beam axis on either side of the ALICE detector.They are used to detect neutrons emitted in the very forward region and measure timing information of signals, thus making possible the discrimination of background signals such as beam-satellite events described in Ref. [51].
Exclusive dimuon production from the decay of a J/ψ or from two-photon interactions has a clear experimental signature: the µ + µ − pair in an otherwise empty detector.On the other hand, the study of J/ψ photoproduction with a dissociative proton implies that the detector might not be empty on the proton side.The trigger used in these analyses is required to have at least one track with a low transverse momentum threshold (p T ∼ 0.5 GeV/c) in the muon spectrometer trigger system, and vetoes on V0A and ADA which are located in the flight direction of the outgoing Pb ion.
The measurements presented here use a sample of events collected during the 2016 p-Pb data taking period, at √ s NN = 8. 16 TeV, corresponding to an integrated luminosity of L = 7.90 ± 0.14 nb −1 [52].In these collisions the incoming proton beam travelled towards the muon spectrometer.
3 Data sample

Event selection
Besides the trigger selection, events have to fulfill additional criteria.First, there must be exactly two tracks with opposite electric charge reconstructed in the muon spectrometer.Both tracks are required to match muon trigger tracks with a p T threshold above 0.5 GeV/c.Each track pseudorapidity is required to be within the acceptance of the muon spectrometer −4.0 < η < −2.5.To reject tracks crossing the highdensity section of the front absorber, where multiple scattering and energy loss effects are large, the muon tracks are required to exit the front absorber at a radial distance from the beam axis 17.6 < R abs < 89.5 cm.The product of the total track momentum p and the distance of closest approach (DCA), defined as the distance in the transverse plane between the extrapolated position of the reconstructed track in the tracking stations and the position of the nominal interaction point, is required to be smaller than 6 times the standard deviation of the dispersion due to multiple scattering and detector resolution.This ensures that the selected muons come from the interaction vertex without rejecting signal events.The dimuon rapidity has to be in the range 2.5 < y < 4.0, and the dimuon p T must be less than 3 GeV/c.
To ensure that the Pb ion remains intact, the V0A and ADA are required to have no signal at the offline level.The neutron ZDC on the Pb side (ZNA) must have no activity within ±2 ns of the expected time of the collision.In order to suppress hadronic interactions producing particles at midrapidity, events with more than two tracklets in the SPD layers are rejected.
Finally, the number of cells with a signal over threshold in V0C must be smaller than or equal to the sum of the number of fired V0C cells matched to a muon and two additional fired cells.The matching of a muon to a fired V0C cell is performed by using the (η, ϕ) coordinates of each track, where ϕ is the azimuthal coordinate.Studies with the RAPGAP 3.3 event generator [53], a Monte Carlo program used to simulate dissociative J/ψ photoproduction in electron-proton collisions, show that the proton remnants do not leave a signal in the acceptance of the V0C detector.The requirement on the number of fired V0C cells prevents contamination from hadronic interactions at forward rapidity.
Allowing two midrapidity tracklets in the SPD layers and two additional fired V0C cells prevents detectors from vetoing events of interest due to an additional activity, such as muon bremsstrahlung or pile-up events.Pile-up events are induced mainly by independent hadronic or electromagnetic processes, e.g.dielectron production in the γγ → e + e − process, accompanying the process of interest.

Event selection with exclusivity in the proton side
The exclusive-dominated sample is obtained by applying the following additional criteria on the proton side.The ADC is required to have no signal and the neutron ZDC on the proton side must have no activity within ±6 ns of the expected time of the collision.This selection is more restrictive than on  the Pb side, due to an observed asymmetry of time distributions between both sides.Furthermore, since exclusive events are expected to be dominant at low p T , dimuons are required to have p T < 1.2 GeV/c.

Monte Carlo samples
The STARlight 2.2.0 Monte Carlo generator [22,54] is used to generate the following processes: exclusive J/ψ production in γ p interactions, production of J/ψ in γ Pb interactions, production of J/ψ events from decays of ψ(2S) in γ p interactions, and exclusive dimuon continuum production.The decay muons are propagated through a model of the apparatus implemented in GEANT 3.21 [55], and events pass through a simulation of the detector matching the data taking conditions.For exclusive J/ψ production, the t distribution is modelled in STARlight by a function of the form exp(−bt), where b is set to 3.75 GeV −2 to better describe the J/ψ p T distribution in data.

Signal extraction for the two-photon process at low masses
The yields of dimuons from exclusive two-photon interactions, N γγ , are measured by performing an unbinned log-likelihood fit of the p T distribution up to p T = 3 GeV/c of the selected dimuons in the invariant mass range 1.0 < M µ µ < 2.5 GeV/c 2 , where no contamination is expected from the J/ψ peak.The measurements are performed as a function of the dimuon invariant mass, in the three intervals 1.0 < M µ µ < 1.5 GeV/c 2 , 1.5 < M µ µ < 2.0 GeV/c 2 , and 2.0 < M µ µ < 2.5 GeV/c 2 .They are presented in the rapidity interval 2.5 < y < 4.0, and for 2.5 < y < 3.25 and 3.25 < y < 4.0, where the rapidity is measured in the laboratory frame with respect to the proton beam direction.
Figure 1 shows the p T distribution of the dimuon candidates that satisfy the selections for 1.5 < M µ µ < 2.0 GeV/c 2 .The data contain a mixture of exclusive and non-exclusive two-photon interactions, which are distinguished by their characteristic p T distribution.While exclusive events dominate in the data at low p T , the tail extending up to higher p T is mostly due to non-exclusive interactions.
Exclusive γγ → µ + µ − events are described with a Landau distribution, which is found to describe well the Monte Carlo data up to p T = 0.38 GeV/c.A single-component fit of a Landau distribution is performed to the data requiring exclusivity on the proton side, as described in Sec.3.2, up to p T = 0.38 GeV/c.In this selection, non-exclusive events are expected to be negligible.The location and scale parameters of the Landau distribution are extracted.The obtained location parameter ranges between 0.054 and 0.092 for the different bins.The scale parameter ranges between 0.23 and 0.39.They are then used when fitting the data that passed the standard selection, which includes both exclusive and nonexclusive components.Changing the maximum p T value of the fitting interval or using a two-component model to account for exclusive and non-exclusive events instead of a single-component description might impact the location and scale parameters obtained from the fit of the exclusive-dominated sample.This is taken into account in the "signal extraction" systematic uncertainty (see Sec 5.3.2).
Non-exclusive events are modelled according to a parameterisation by H1 for dissociative events [40] with a function of the form dN/dp T ∝ p T × 1 + p 2 T × (b dis /n dis ) −n dis , where b dis and n dis are free parameters.Non-exclusive dimuons represent 37% of events in the analysed mass range and for p T < 3 GeV/c.
The N γγ yields extracted from the fit are then corrected for the acceptance and reconstruction efficiency (A × ε) γγ .The yields, the correction factors, and the cross sections are presented in Table 1 for the different mass and rapidity intervals.The correction factors are evaluated by means of the Monte Carlo simulations introduced in Sec. 4.
Additional activity in the V0A, ADA, ZNA, or SPD detectors results in event rejection and a corresponding correction needs to be applied.Such events mainly originate from independent hadronic and electromagnetic pile-up processes.The probability of event rejection due to pile-up of each veto is defined as the probability of detecting activity using events selected with an unbiased trigger based only on the timing of bunches crossing the interaction region.It is found to scale linearly with the expected number of collisions per bunch crossing.By varying the event selection in the analysis, the average pile-up probability varied from 3.7% to 4.1%.Therefore, the pile-up probability is estimated as p pu = (3.9± 0.2)% where most of the pile-up rejection (3.7%) is from V0A.The average pile-up correction factor is calculated using ε veto = exp(−p pu ), and is found to be ε veto = (96.2± 0.2)%.

Signal extraction for J/ψ photoproduction candidates
The yields of exclusive and dissociative J/ψ are obtained by performing an unbinned log-likelihood fit to dimuon invariant mass M µ µ and transverse momentum p T distributions simultaneously.Events are selected in 2.5 < M µ µ < 3.5 GeV/c 2 and p T < 3 GeV/c intervals.The dimuon invariant mass and p T spectra after these selections are shown in Fig. 2. For the invariant mass distribution, the J/ψ peak is well described by a double-sided Crystal Ball parameterisation, which has a non-Gaussian tail at both sides of the resonance peak [56,57].The J/ψ mass and its width at the pole position are free parameters of the fit, while the tail parameters in the Crystal Ball function are fixed to values obtained from fits to the Monte Carlo sample corresponding to the exclusive J/ψ photoproduction.The invariant mass distribution of the dimuon continuum is described by dN/dM µ µ ∝ exp(−aM µ µ ), where a is a free parameter.J/ψ events can be divided into three categories: exclusive photoproduction off protons, dissociative photoproduction off protons, and exclusive photoproduction off Pb nuclei.Dissociative photoproduction off Pb nuclei is vetoed by the ZDC selection, as described in Sec.3.1.The events contained in the dimuon continuum below the J/ψ peak can either be exclusive or non-exclusive two-photon interactions.The various physics processes in the J/ψ peak and in the dimuon continuum can be distinguished by their different p T distributions.
The p T distribution for γγ → µ + µ − events below the J/ψ peak is modelled with a Landau distribution for which the location and scale parameters are fixed, similarly as in Sec.5.1.Their values are obtained using the sample described in Sec.3.2.In order to factorise the p T distribution of J/ψ and continuum dimuon events, the numerical tool sPlot is used [58].Based on an extended maximum likelihood fit to  the mass distribution of the sample (left panel of Fig. 3), the sPlot procedure assigns weights denoted as sw n on an event-by-event basis.Assuming these weights can be computed as a linear combination of conditional probabilities, they are given by the following formula for the category n = 1, 2 of events in the sample (J/ψ signal or γγ → µ + µ − ) where f is the probability density function of the fit, M µ µ denotes the mass used as the discriminating variable for each event, i and j are the indices indicating a sum over the N s = 2 categories, and V is the covariance matrix of the yields N j which is evaluated in a separate fit, in which all shape-related parameters are fixed.The p T distribution for two-photon interactions extracted with the sPlot technique is shown in the right panel of Fig. 3 and is fitted up to p T = 0.38 GeV/c with a single-component fit parametrised with a Landau distribution, from which the location and scale parameters are extracted.The small correlation between the mass and p T of dimuons produced in two-photon interactions was found to have a negligible impact on the sPlot procedure.In addition, the extracted number of γγ → µ + µ − events in the J/ψ peak range (2.5 < M µ µ < 3.5 GeV/c 2 ) is compared with STARlight and an agreement within 1σ is found (accounting for the statistical uncertainties only).This number is also in good agreement with the number of continuum dimuon events extracted from the final two-dimensional fit.
The shape of the p T distribution for the exclusive J/ψ events in γ p interactions is given by the H1 parameterisation , where b exc is a fixed parameter.J/ψ mesons coming from ψ(2S) decays are also included in this contribution.The b exc value is determined using the sample described in Sec.3.2, by fitting simultaneously the dimuon invariant mass and p T without the contribution of dissociative J/ψ events.The dimuon invariant mass and p T projections of this fit are shown in Fig. 4. Studies conducted with the RAPGAP Monte Carlo program [53] in the kinematic range of the present measurement show that more than 99% of dissociative J/ψ events are removed by the selection requiring exclusivity on the proton side.The values obtained are b exc = 3.62 ± 0.14 [GeV/c ] −2 for 2.5 < y µ µ < 4.0, b exc = 3.38 ± 0.17 [GeV/c ] −2 for 3.25 < y µ µ < 4.0 (27 < W γ p < 39 GeV), and b exc = 3.86 ± 0.20 [GeV/c ] −2 for 2.5 < y µ µ < 3.25 (39 < W γ p < 57 GeV).The p T resolution of the muon spectrometer is the main limitation in unfolding these values and comparing them with the H1 measurement of the t-slope, b exc = (4.3±0.2) [GeV ] −2 for 25 < W γ p < 80 GeV [40].As an alternative method to extract the b exc value, the J/ψ p T distribution obtained with sPlot was fitted with a two-component model including J/ψ events from γ p interactions and from γ Pb interactions.The bias induced by the method used to extract b exc is accounted for in the "signal extraction" systematic uncertainty (see Sec. 5.3.3).The p T distribution for coherent J/ψ photoproduction in γ Pb interactions is obtained using the corresponding reconstructed Monte Carlo sample within the specified mass and p T ranges.The p T distributions for dissociative J/ψ events and non-exclusive two-photon interactions are modelled by functions of the form dN/dp T ∝ p T × 1 + p 2 T × (b dis /n dis ) −n dis where b dis and n dis are free parameters.
Five parameterisations for exclusive J/ψ photoproduction off protons, dissociative J/ψ photoproduction off protons, J/ψ photoproduction off Pb nuclei, exclusive, and non-exclusive γγ → µ + µ − , are defined as products of each corresponding mass and p T distributions.The normalisation for the component corresponding to J/ψ produced in γ Pb interactions is fixed to the expected number according to a computation based on the measurement from Ref. [59] under the assumption that the fraction of low-and high-energy photon contributions to the forward rapidity measurement is the same as predicted by STARlight.The normalisation for all other components are free parameters of the fit.
The extracted yields of exclusive and dissociative J/ψ from γ p interactions are corrected for acceptance and reconstruction efficiency (A × ε) J/ψ , which are obtained from the Monte Carlo simulation samples described in Sec. 4, having values ranging from 18% to 21%.

Systematic uncertainties
The experimental systematic uncertainties for the exclusive dimuon production from two-photon interactions and for the photoproduced J/ψ are listed in Table 2.The systematic sources can be divided into three types: those common to both measurements and those affecting one or the other.

Systematic uncertainties common to both measurements
The uncertainty on the integrated luminosity is discussed in Sec. 2, and amounts to 1.8%.The systematic uncertainties on muon trigger efficiency, tracking efficiency, and muon matching efficiency were obtained as described in Ref. [63].The single-muon trigger response functions evaluated in data and Monte Carlo simulations are incorporated in the acceptance and efficiency (A × ε) calculations for the reconstruction of the dimuons.The differences between (A × ε) calculations when incorporating the response functions either from data or Monte Carlo range from 0.1% to 4.9% depending on the studied process and rapidity interval.The total uncertainty is obtained by combining this contribution in quadrature with the uncertainty on the intrinsic efficiency of muon trigger detectors, which amounts to 1%.
The uncertainty on the tracking efficiency was calculated by comparing the efficiencies evaluated in data and Monte Carlo simulations.These efficiencies are calculated according to the tracking algorithm by combining the efficiency of each tracking plane measured using the redundancy of the system.The estimated value of the systematic uncertainty related to the tracking efficiency is 1% in this data sample.The muon matching efficiency is the efficiency of associating a muon track candidate to a trigger track above the 0.5 GeV/c p T threshold in the trigger chambers of the muon spectrometer.Its uncertainty is estimated by varying the χ 2 cutoff applied to the pairing of the reconstructed tracks in the muon tracking and triggering systems, and it is found to be 1%.The pile-up correction factor, discussed in Sec.5.1, has a relative uncertainty of 0.2%.
The uncertainty on the veto efficiency of the V0C is calculated by varying the number of allowed cells with a signal over the threshold in the offline selection.When increasing this number, the numbers of exclusive J/ψ and γγ → µ + µ − events are found to be stable, while the number of dissociative J/ψ events increases, as the sample is more sensitive to contamination from inclusive photoproduction or hadronic production of J/ψ mesons which have a similar behaviour in p T .The expected number of dissociative J/ψ events is computed as the number of exclusive J/ψ events multiplied by the ratio of dissociativeto-exclusive J/ψ events when all the fired cells in V0C are required to be matched to a muon.The systematic uncertainty on the number of dissociative J/ψ events is computed as the relative difference between the expected and extracted numbers of dissociative J/ψ events and is found to be 12.7%, while the systematic uncertainty on the number of exclusive J/ψ events is obtained by varying the condition on V0C and the obtained value is 2.6%.Similarly, the uncertainty on the number of exclusive γγ → µ + µ − events is obtained by varying the condition on V0C (see line "V0C veto" in Table 2) and the obtained values vary between 0.5% and 1.7%.

Uncertainties associated with the dimuon continuum production
The main source of systematic uncertainty on the γγ → µ + µ − signal extraction is obtained by varying both parameters of the Landau distribution within their statistical uncertainties obtained from fitting the purely exclusive sample described in Sec.3.2 and taking into account their correlation (see line "signal extraction" in Table 2).
In the lowest invariant mass interval studied, 1.0 < M µ µ < 1.5 GeV/c 2 , the production of φ mesons decaying to dimuons might contaminate the sample.The expected number of φ → µ + µ − events in the sample at low mass, N φ , is computed.The calculation is based on the cross section ratio of φ photoproduction with respect to J/ψ production based on STARlight and their branching ratios provided by the PDG [60], detector acceptance and efficiency factors, and the number of J/ψ mesons measured in the muon spectrometer.The uncertainty induced by this contamination is estimated by comparing N φ to the number of γγ → µ + µ − events.It is found to be 1.5%.

Uncertainties associated with the J/ψ photoproduction only
The main source of systematic uncertainty on the J/ψ signal extraction is obtained by varying the b exc parameter within its statistical uncertainty determined from fitting the purely exclusive sample described in Sec.3.2 (see line "signal extraction" in Table 2).It ranges between 2.9% and 5.5%.Changing the p T model for the exclusive γγ → µ + µ − component and varying the number of J/ψ events produced in γ Pb interactions were found to have a negligible impact on signal extraction.
The photon flux, which enters in the computation of the cross section presented in Sec.6.2, is computed using STARlight.Its uncertainty is obtained by varying the nuclear radii and the nuclear density ρ 0 of the Pb nucleus, assuming that the latter has a cubic dependence on the radius.The radius of the lead nucleus is changed by ±0.5 fm, which corresponds to the nuclear skin thickness.This uncertainty is evaluated to be 2%.The branching ratio of J/ψ decaying into dimuons and its uncertainty (0.55%) are given by the Particle Data Group [60].
For the measured ratio of dissociative-to-exclusive cross sections, σ diss /σ exc , most of the systematic un- certainties cancel out.The remaining sources of uncertainty are due to the variation of the b exc parameter, and the variation on the number of allowed fired V0C cells.The systematic uncertainties on the ratio given in Table 2 are then computed as the quadratic sum of these two components only.

Cross sections for the dimuon continuum in two-photon interactions
The cross section corresponding to the exclusive γγ → µ + µ − process is measured using where N γγ is the number of reconstructed γγ → µ + µ − events, (A × ε) γγ is the corresponding factor which takes into account acceptance and reconstruction efficiency in the mass and rapidity interval studied, ε veto is the pile-up correction factor and ∆M µ µ is the width of the invariant mass interval.
The rapidity range of the experimental results corresponds to a high-energy photon emitted from the proton (corresponding to small impact parameters with respect to the proton) and a low-energy photon emitted from the nucleus (corresponding to large impact parameters with respect to the nucleus).The differential cross sections, dσ γγ /dM µ µ , are presented in Table 1 in two rapidity intervals and integrated over rapidity along with the predictions from STARlight 2.2.0 and SuperChic 4.15 [64] for comparison.
The STARlight generator simulates UPCs at colliders based on the equivalent photon approximation.SuperChic was designed for exclusive production in proton-proton collisions and has been extended to collisions involving nuclei starting from Ref. [65].For γγ-induced dilepton production, SuperChic provides calculations on amplitude level to treat the probability of no hadronic interaction within the same collision.Both generators implement LO QED calculations, neglecting final-state radiation.
The measured cross sections and predictions from STARlight and SuperChic are shown in Fig. 5.Both predictions agree within 3 standard deviations, depending on the mass and rapidity intervals.In the two lowest mass intervals, the central values of the measured cross sections are larger compared with STARlight and SuperChic, while the opposite behaviour is seen in the highest mass interval.For the kinematic intervals studied, SuperChic predicts larger cross sections than STARlight.The difference between STARlight and SuperChic discussed in Ref. [23], related to the sharp cut-off on the impact parameter between the produced dilepton and the nucleus, is found not to be the primary source of discrepancy observed here.
The relative uncertainties on the measurements vary from 7% to 17%.This is significantly larger than the 2% uncertainty for the photon flux used in the calculation of the photoproduction cross section presented in Sec.6.2.Thus, with the current experimental precision, it is not possible to constrain the photon fluxes via the γγ → µ + µ − measurement.

Cross sections for J/ψ photoproduction off protons
The cross sections corresponding to exclusive and dissociative J/ψ photoproduction off protons are measured using where N J/ψ is the number of reconstructed exclusive or dissociative J/ψ in the dimuon decay channel, (A × ε) J/ψ is the corresponding factor of acceptance times reconstruction efficiency in the rapidity interval studied, and BR = (5.961± 0.033)% is the branching ratio for the decay into a muon pair [60].
The photon flux is calculated using STARlight in impact parameter space and convoluted with the probability of no hadronic interaction.The average photon flux values for the different rapidity intervals are listed in Table 3, together with the extracted cross sections σ (γ +p → J/ψ +p) and σ (γ +p → J/ψ +p ( * ) )   [22,54] and from SuperChic [64].
Table 3: Rapidity differential cross sections dσ exc J/ψ /dy and dσ diss J/ψ /dy and the corresponding cross sections σ (γ + p → J/ψ + p) and σ (γ + p → J/ψ + p ( * ) ) for exclusive and dissociative J/ψ photoproduction off protons in p-Pb UPCs at √ s NN = 8.16 TeV for each rapidity range.The first uncertainty is the statistical one and the second uncertainty is the systematic one.The numbers of events obtained from signal extraction with their statistical uncertainties, N exc J/ψ and N diss J/ψ , the photon flux, and the range and the mean of W γ p are also presented.and the corresponding W γ p .The latter is computed as the average of W γ p weighted by the cross section σ (γ p) from STARlight.

Exclusive J/ψ photoproduction
Figure 6 shows the exclusive J/ψ photoproduction cross section σ (γ + p → J/ψ + p) reported in Table 3 as a function of W γ p , covering the range 27 < W γ p < 57 GeV.Comparisons with previous measurements and with several theoretical models are also shown.
Measurements at low W γ p were performed by fixed target experiments, such as those reported by the E401 [66], E516 [67] and E687 [68] Collaborations.Recently, measurements were performed near threshold by the GlueX Collaboration [69] and by the E12-16-007 experiment [70] which are not shown in Fig. 6 since they fall outside of the power-law applicability discussed below.
The cross sections are also compared with previous ALICE results in p-Pb at √ s NN = 5.02 TeV [14,71], at forward, mid, and backward rapidity, covering the energy range 21 < W γ p < 952 GeV.
In this analysis, a χ 2 fit of a power-law function, N(W γ p /W 0 ) δ , is performed to the two ALICE data sets at √ s NN = 8.16 TeV and √ s NN = 5.02 TeV together, with W 0 = 90.0GeV, as done in HERA  Exclusive J/ψ photoproduction cross section off protons measured as a function of the centre-of-mass energy of the photon-proton system W γ p by ALICE in p-Pb UPCs and compared with previous measurements [14, 38-40, 43-45, 66-68, 71] and with next-to-leading-order JMRT [73,74] and CCT [37] models.The power-law fit to the ALICE data is also shown.The uncertainties of the data points are the quadratic sum of the statistical and systematic uncertainties.
analyses [38][39][40] and for previous ALICE measurements [14].The technique follows what was done by the H1 Collaboration [72] and the fit takes into account the statistical and systematic uncertainties.The parameters obtained from the fit are N = 71.6 ± 3.7 nb and δ = 0.70 ± 0.04 with a correlation of +0.16 between the two parameters.The quality of the fit is χ 2 /ndf = 1.62 for 9 degrees of freedom.The value of the exponent is the same as in previous ALICE measurements [14].The H1 and ZEUS measurements, performed over an energy range W γ p that encompasses the new ALICE measurements, are also shown in the same figure.They, respectively, found δ = 0.69 ± 0.02 (stat.)± 0.03 (syst.), and δ = 0.67 ± 0.03 (tot.)[38][39][40].Thus the measurements by ALICE are compatible with the values measured by HERA experiments, and no deviation from a power law is observed up to about 700 GeV.
LHCb measured the exclusive J/ψ photoproduction cross sections in pp collisions, at √ s NN = 7 TeV [43,44] and 13 TeV [45].The LHCb analyses use data from a symmetric system and thus suffer from the ambiguity in identifying the photon emitter and the photon target.Since the non-exclusive J/ψ photoproduction depends on W γ p , these processes are difficult to subtract and make the extraction of the underlying σ (W γ p ) strongly model dependent.Moreover, the uncertainty in the hadronic survival probability in pp collisions is much larger than in p-Pb collisions, and samples of pp collisions can contain a contamination of J/ψ production through Odderon-Pomeron fusion [30,75].For each dσ /dy measurement, LHCb reported two solutions, one for low W γ p and one for high W γ p .Despite these ambiguities and assumptions, the LHCb solutions are found to be compatible with ALICE measurements within the current uncertainties.
ALICE measurements are also compared with the Jones-Martin-Ryskin-Teubner (JMRT) calculation.Two calculations are available from the JMRT group [73,74].The first one, referred to as LO, is based on a power-law description of the process from the result in Ref. [32], while the second one, labeled as NLO, includes contributions which mimic effects expected from the dominant NLO corrections.At high W γ p , they deviate from a simple power-law shape.Both models are fitted to the same data and their energy dependence is rather similar, so only the NLO version is shown.2 × 10 −5 .A more recent NLO computation of this process suggests a stronger sensitivity to quark contributions than previously considered [33].
Figure 6 also shows predictions from the Cepila-Contreras-Takaki (CCT) model [37] based on the colour dipole approach.This model incorporates a fluctuating hot spot structure of the proton in the impact parameter plane, with the number of hot spots growing with decreasing x.It is compatible with ALICE measurements at √ s NN = 5.02 TeV and √ s NN = 8.16 TeV.Future UPC measurements by ALICE will explore the high W range, particularly with future detector upgrades such as FoCal [76].

Dissociative J/ψ photoproduction
Figure 7 shows the ALICE measurement of the dissociative J/ψ photoproduction cross section σ (γ + p → J/ψ + p ( * ) ) as a function of W γ p , covering the range 27 < W γ p < 57 GeV.The cross sections are also reported in Table 3.A previous measurement at similar energies by H1 [40] is also shown and is in good agreement with the ALICE measurement.In addition, the experimental results are compared with the CCT model [37] discussed in the previous section.In the framework of this model, the exclusive cross section is sensitive to the average interaction of the colour dipole qq with the proton, and the dissociative cross section is sensitive to the fluctuations in the qq-proton interaction between the different colour field configurations of the proton.The model describes correctly the energy evolution of the dissociative cross section both for H1 and ALICE measurements and predicts that the cross section will reach a maximum at W γ p ≃ 500 GeV, then decrease at higher energies.This behaviour is expected due to the hot spots saturating the proton area.
6.2.3 Ratio of dissociative-to-exclusive J/ψ photoproduction ALICE measurements for the ratio of dissociative-to-exclusive J/ψ photoproduction cross sections, σ (γ + p → J/ψ + p ( * ) )/σ (γ + p → J/ψ + p), are given in Table 4.These measurements are also shown in Fig. 8 as a function of W γ p , together with the measurements by H1 [40] at similar energies.Two models are compared with the measurements: the CCT model [37], and a model calculation by Mäntysaari-  .The uncertainties of the data points are the quadratic sum of the statistical and systematic uncertainties.The experimental uncertainties for the H1 data are computed assuming completely independent uncertainties for the exclusive and dissociative cross sections.The measurements are compared with the CCT model [37] and a model by Mäntysaari-Schenke (MS) [77].The uncertainty band of the MS model corresponds to the statistical uncertainty of the calculation.Schenke (MS) [77].The MS model is based on the perturbative JIMWLK (Jalilian-Iancu-McLerran-Weigert-Leonidov-Kovner) evolution [78,79], with initial parameters constrained from fits to H1 data starting from x ∼ 10 −3 .At high W γ p , where the gluon saturation regime is expected, the models predict that the ratio of dissociative-to-exclusive cross sections vanishes.

Summary
This article presents three different measurements carried out by the ALICE Collaboration in ultraperipheral p-Pb collisions at √ s NN = 8.16 TeV.The exclusive dimuon continuum production from two-photon interactions in the invariant mass range from 1 to 2.5 GeV/c 2 is presented.It is compared with STARlight and SuperChic and found to be compatible within three standard deviations.Since these models are based on LO QED calculations, this measurement can be used to provide a limit on higherorder corrections for this process.Furthermore, the exclusive and dissociative J/ψ photoproductions off protons were measured.The measurement of exclusive J/ψ photoproduction cross section is compared with those previously performed by ALICE, LHCb, H1, and ZEUS Collaborations.The ALICE measurements are consistent with a power-law dependence on W γ p of σ (γ p → J/ψp), with the power found to be δ = 0.70 ± 0.04.The measurement of the cross section of dissociative photoproduction of J/ψ mesons is the first of its kind at the LHC and a first measurement of this type at a hadron collider.It is in good agreement with H1 measurements.This is the first step to probe the fluctuation of the subnucleonic structure in protons in ultra-peripheral collisions at high energies.

Figure 1 :
Figure 1: Transverse momentum distribution of opposite-sign dimuons with 1.5 < M µ µ < 2.0 GeV/c 2 and 2.5 < y < 4.0.The data are represented by full circles with vertical bars for the statistical uncertainties and horizontal bars for the interval width.The solid line represents the fit to the data, and the dashed and dot-dashed lines represent the fit components.

Figure 2 :
Figure 2: Projections of the two-dimensional fit on the dimuon invariant mass (left) and p T (right).

Figure 3 :
Figure3: Left: dimuon invariant mass distribution using the selection given in Sec.3.2, fitted with a twocomponent model to separate J/ψ events from two-photon interactions in the continuum.Right: p T distribution of the exclusive γγ → µ + µ − continuum extracted using the sPlot technique.The distribution is fitted with a Landau distribution.

Figure 4 :
Figure4: Projections of the two-dimensional fit on the dimuon invariant mass (left) and p T (right) with the selection described in Sec.3.2 to extract the shape of the p T distribution for the exclusive J/ψ events in γ p interactions.

Figure 5 :
Figure 5: Differential cross sections for exclusive γγ → µ + µ − production measured by ALICE in p-Pb UPCs at √ s NN = 8.16 TeV, as a function of M µ µ , for 2.5 < y < 3.25 (left) and 3.25 < y < 4 (right).The vertical error bars represent the statistical and systematic uncertainties summed in quadrature.The results are compared with the prediction from STARlight[22,54] and from SuperChic[64].
fit to ALICE data

Figure 6 :
Figure6: Exclusive J/ψ photoproduction cross section off protons measured as a function of the centre-of-mass energy of the photon-proton system W γ p by ALICE in p-Pb UPCs and compared with previous measurements[14,  38-40, 43-45, 66-68, 71]  and with next-to-leading-order JMRT[73,74] and CCT[37] models.The power-law fit to the ALICE data is also shown.The uncertainties of the data points are the quadratic sum of the statistical and systematic uncertainties.

Figure 7 :
Figure 7: Dissociative J/ψ photoproduction cross section off protons measured by ALICE in p-Pb UPCs at √ s NN = 8.16 TeV and compared with H1 data [40].A comparison with the CCT model [37] is shown.The uncertainties of the data points are the quadratic sum of the statistical and systematic uncertainties.

Figure 8 :
Figure 8: Ratio of dissociative-to-exclusive J/ψ photoproduction cross sections measured by ALICE in p-Pb UPCs at √ s NN = 8.16 TeV and compared with H1 measurements [40].The uncertainties of the data points are the quadratic sum of the statistical and systematic uncertainties.The experimental uncertainties for the H1 data are computed assuming completely independent uncertainties for the exclusive and dissociative cross sections.The measurements are compared with the CCT model[37] and a model by Mäntysaari-Schenke (MS)[77].The uncertainty band of the MS model corresponds to the statistical uncertainty of the calculation.

Table 1 :
Differential cross sections dσ γγ /dM µ µ for exclusive γγ → µ + µ − production in p-Pb UPCs at √ s NN = 8.16 TeV for each mass and rapidity interval, measured by ALICE and computed with STARlight and SuperChic.The first uncertainty is the statistical one and the second uncertainty is the systematic one.The corresponding number of exclusive γγ → µ + µ − events with their statistical uncertainties and factors of acceptance times reconstruction efficiency are given.

Table 2 :
Summary of systematic uncertainties on the measured cross sections.The value ranges correspond to different rapidity intervals.Uncertainties on signal extraction, tracking, trigger, and muon matching efficiencies are considered as uncorrelated across y.All other components are taken as fully correlated across the rapidity y.The final uncertainties for γγ and J/ψ, labeled "Total", are obtained as the sum in quadrature of common uncertainties and those affecting one signal or the other.

Table 4 :
Ratio of dissociative-to-exclusive J/ψ photoproduction cross sections in p-Pb UPCs at √ s NN = 8.16 TeV.The first uncertainty is the statistical one.Its size is strongly impacted by the anti-correlation between exclusive and dissociative J/ψ components in the two-dimensional fit.The second uncertainty is the systematic one.It is computed as the quadratic sum of the signal extraction ratio uncertainty, and the uncertainty on the V0C veto.