Measurement of J/ψ production cross-sections in pp collisions at s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s} $$\end{document} = 5 TeV

The production cross-sections of J/ψ mesons in proton-proton collisions at a centre-of-mass energy of s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s} $$\end{document} = 5 TeV are measured using a data sample corresponding to an integrated luminosity of 9.13 ± 0.18 pb−1, collected by the LHCb experiment. The cross-sections are measured differentially as a function of transverse momentum, pT, and rapidity, y, and separately for J/ψ mesons produced promptly and from beauty hadron decays (nonprompt). With the assumption of unpolarised J/ψ mesons, the production cross-sections integrated over the kinematic range 0 < pT< 20 GeV/c and 2.0 < y < 4.5 areσpromptJ/ψ=8.154±0.010±0.283μb,σnonpromptJ/ψ=0.820±0.003±0.034μb,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\displaystyle \begin{array}{c}{\sigma}_{\mathrm{prompt}}\ J/\psi =8.154\pm 0.010\pm 0.283\ \upmu \mathrm{b},\\ {}{\sigma}_{\mathrm{nonprompt}}\ J/\psi =0.820\pm 0.003\pm 0.034\ \upmu \mathrm{b},\end{array}} $$\end{document} where the first uncertainties are statistical and the second systematic. These cross-sections are compared with those at s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s} $$\end{document} = 8 TeV and 13 TeV, and are used to update the measurement of the nuclear modification factor in proton-lead collisions for J/ψ mesons at a centre-of-mass energy per nucleon pair of sNN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s_{\mathrm{NN}}} $$\end{document} = 5 TeV. The results are compared with theoretical predictions.


Introduction
Quantum chromodynamics (QCD) is the fundamental theory that describes the strong interaction between quarks and gluons. One of the most important properties of QCD is that the coupling constant increases at small momentum transfers. Non-perturbative corrections, which are challenging to control theoretically, are required to describe many observables. The study of heavy quarkonium production in proton-proton (pp) collisions can provide important information to improve QCD predictions in the non-perturbative regime. The process involves the production of a QQ system, where Q denotes a beauty or charm quark, followed by its hadronisation into the heavy quarkonium state. Predictions based on the assumption of factorisation have been found to agree well with experimental data so far. The QQ production step can be calculated with perturbative QCD but the hadronisation step, being of non-perturbative nature, needs to be described by models with inputs from experiments. The colour singlet model [1][2][3][4][5][6][7] assumes that the intermediate QQ state is colourless and has the same spin-parity quantum numbers as the quarkonium state. In the nonrelativistic QCD (NRQCD) approach [8][9][10] intermediate QQ states with all possible colour and spin-parity quantum numbers may evolve into a quarkonium state. The transition probabilities are described by long-distance matrix elements (LDME) that cannot be calculated perturbatively and are therefore determined from experimental data.

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In pp collisions J/ψ mesons can be produced either directly from hard collisions of partons, through the feed-down of excited charmonium states, or via decays of beauty hadrons. The J/ψ mesons from the first two sources originate from the primary pp collision vertex (PV) and are called prompt J/ψ mesons, while those from the last source originate from decay vertices of beauty hadrons, which are typically separated from the PV, and are called nonprompt J/ψ mesons. The differential cross-sections for prompt and nonprompt J/ψ mesons in pp collisions were measured in the rapidity range 2.0 < y < 4.5 by the LHCb collaboration at centre-of-mass energies of √ s = 2.76 TeV [11] . This paper reports a J/ψ cross-section measurement in pp collisions at √ s = 5 TeV using a data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 9.13 ± 0.18 pb −1 [33]. This data sample was taken with special runs for cross-section measurements. The measurement includes the production cross-sections of prompt and nonprompt J/ψ mesons with transverse momentum p T < 20 GeV/c and rapidity 2.0 < y < 4.5, assuming unpolarised J/ψ mesons, and the cross-section ratios between 8 TeV and 5 TeV and between 13 TeV and 5 TeV. The nuclear modification factor for J/ψ mesons in pPb collisions at √ s NN = 5 TeV, which was originally published in ref. [34], is updated using the pp cross-sections reported in here.

Detector and simulation
The LHCb detector [35,36] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet. The tracking system provides a measurement of the momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV/c. The minimum distance of a track to a primary pp collision vertex, the impact parameter (IP), is measured with a resolution of (15 + 29/p T ) µm, where p T is in GeV/c. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov -2 -

Cross-section determination
The double-differential cross-section of J/ψ production in a given (p T ,y) interval is defined as where N (J/ψ → µ + µ − ) is the signal yield, ε tot is the detection efficiency, L is the integrated luminosity, B = (5.961 ± 0.033)% [47] is the branching fraction of the J/ψ →µ + µ − decay, and ∆p T and ∆y are the interval widths. Details on the interval scheme are provided in section 6.
The yields of prompt and nonprompt J/ψ mesons are simultaneously extracted from an unbinned extended maximum-likelihood fit to the two-dimensional distribution of m µ + µ − and t z independently in each (p T ,y) interval. The total J/ψ signal yield is about 1.4 (0.14) million for prompt (nonprompt) J/ψ mesons. Figure 1 shows the projections of the twodimensional distribution, together with the fit, on m µ + µ − and t z for one (p T ,y) interval. There are four components: prompt J/ψ signal, nonprompt J/ψ signal, J/ψ signal with incorrect PV association, and non-J/ψ background from random tracks. The first three J/ψ signals have the same mass shape but their t z distributions are different.
In each interval the mass shape of J/ψ signals is described by the sum of two Crystal Ball (CB) functions [48] with a common mean value and independent widths. The simulation is used to determine the values of the two power-law tail parameters, which are shared between the two CB functions and fixed in the fit. Only the mean and widths of the CB functions and the ratio between the two functions are left as free shape parameters in the fit. The mass distribution of the non-J/ψ background is modelled with an exponential function.
The true t z values for prompt J/ψ mesons are assumed to be zero while those for nonprompt J/ψ mesons are assumed to follow an exponential function. These distributions are convolved with the sum of two Gaussian functions to model the t z resolution. The two Gaussian functions share the same mean value and their widths are proportional to the t z uncertainty σ tz . The J/ψ signal with incorrect PV association contributes to the long tail present in the t z distribution. This component can be modelled from data using event mixing, i.e., calculating t z with the J/ψ candidate associated to the closest PV in the next event of the sample. The yield of this component is divided into two parts, N tail p and N tail np , according to the ratio between prompt and nonprompt yields, and then N tail p and N tail np are added to the prompt and nonprompt yields respectively. The t z distribution of the -4 -

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non-J/ψ background is described by an empirical function composed of a delta function and five exponential functions that are convolved with the sum of two Gaussian resolution functions sharing the same mean value. All parameters of the empirical function are fixed to the values obtained from a fit to the t z distribution of the J/ψ mass sidebands, defined by the region The detection efficiency is determined in each (p T ,y) interval using simulated samples. The distribution of the number of SPD hits in simulation is weighted to match that in data to correct the effect of the detector occupancy in simulation. The efficiency ε tot is factorised into the product of four efficiencies: the acceptance, ε acc , the reconstructionand-selection efficiency, ε rec&sel , the particle identification (PID) efficiency, ε PID , and the trigger efficiency, ε tri . The efficiencies ε acc and ε rec&sel are evaluated separately for prompt and nonprompt J/ψ mesons. The efficiencies ε PID and ε tri are calculated combining the simulated samples of prompt and nonprompt J/ψ mesons, as the differences between the two production processes are observed to be negligible. The efficiency ε tri is validated using data, and the efficiencies of track reconstruction and PID obtained from simulation are corrected using control channels in data, as detailed in section 5.

Systematic uncertainties
A summary of systematic uncertainties is presented in table 1. Uncertainties arising from signal extraction and efficiency determination are mostly evaluated in each (p T ,y) interval, while those due to branching fraction and luminosity measurement are common to all intervals. The details of the evaluation are discussed in the following.
An uncertainty is attributed to the choice of the probability density function used to model the dimuon invariant-mass distribution of the signal components. As an alternative to the sum of two CB functions, the signal invariant-mass distribution is described by a model derived from simulation using the approach of kernel density estimation [49]. To account for the resolution difference between data and simulation, the alternative model is convolved with a Gaussian function with zero mean and width varied freely. The default and alternative model are compared in each (p T ,y) interval and the relative difference, which is up to 2.0%, is taken as a systematic uncertainty.
The exponential function describing the background is replaced by a linear function and the relative difference, varying up to 0.7%, is taken as a systematic uncertainty. The resulting uncertainty is considered as fully correlated between intervals. The t z model used for the description of the non-J/ψ background is replaced by the use of the sPlot method [50] using the m µ + µ − as the discriminating variable. The relative difference between the two methods varies up to 1.2% for prompt and 4.0% for nonprompt J/ψ mesons in different intervals.
An uncertainty is attributed to the method that is used to separate prompt and nonprompt J/ψ mesons, i.e., two-dimensional fits to m µ + µ − and t z distributions. To evaluate this uncertainty in each (p T ,y) interval, the same t z probability density function is used to fit the simulation. While the relative differences between the fitted and the true yields are small for most intervals, they are significant for nonprompt J/ψ mesons in a few small--5 -JHEP11(2021)181 p T intervals. These differences, varying up to 0.8% for prompt and 14.7% for nonprompt J/ψ mesons, are taken as systematic uncertainties, and are assumed to be fully correlated between p T intervals and uncorrelated between y intervals as indicated by simulation.
A systematic uncertainty related to the tracking efficiency is evaluated as follows. The efficiency correction factors are obtained from dedicated data and simulation samples of J/ψ →µ + µ − decays in which one muon track is fully reconstructed and the other track is reconstructed using a subset of tracking systems [51]. These correction factors are found to depend on different event multiplicity variables. This introduces a systematic uncertainty of 0.8% per track. The statistical uncertainties on these factors are propagated to the systematic uncertainties of the cross-sections, which vary up to 3.7% depending on the (p T ,y) interval.
The PID efficiency is evaluated using a dedicated sample of J/ψ →µ + µ − candidates in which only one track is required to be identified as a muon. The uncertainties of the muon identification efficiencies due to the finite size of the calibration data sample are propagated to the systematic uncertainties of the cross-sections, which are up to 2.2% in different intervals. Another uncertainty comes from the choice of interval scheme of the calibration sample. The resulting uncertainties vary up to 1.5% depending on the (p T ,y) interval.
The trigger efficiency in simulation is validated with data. One muon is requested to pass the hardware-trigger requirement such that the other muon can be regarded as an unbiased probe of the efficiency of one muon. The hardware-trigger efficiency of the J/ψ candidate is the probability that at least one muon track passes the trigger requirement. The relative difference between data and simulation, varying up to 1.9% across intervals, is taken as a systematic uncertainty on the hardware-trigger efficiency. The software-trigger efficiency is determined using a subset of events that would pass the trigger requirement if the J/ψ signals were excluded [52]. The fraction of J/ψ candidates for which two tracks pass the software-trigger requirement is taken as the efficiency both for data and simulation. The overall relative difference between data and simulation is 1.0%, and is taken as a systematic uncertainty on the software-trigger efficiency common to all intervals.
The statistical uncertainties of the efficiencies due to the finite size of the simulated sample result in uncertainties on the cross-sections. The values range up to 3.7% for prompt and 7.7% for nonprompt J/ψ mesons depending on the (p T ,y) interval.
The uncertainty on the J/ψ →µ + µ − branching fraction [47] results in an uncertainty on the measured cross-sections of 0.6%. The luminosity is determined using methods similar to those described in ref. [33] and the relative uncertainty is 2.0%. The tail shape on the left side of the CB function is used to describe the effect of QED radiation, which leads to energy loss in some J/ψ candidates. A small fraction of the J/ψ signal lies outside the mass range of the fit. This signal loss is taken into account in the efficiency ε rec&sel estimated with the simulated sample. The imperfect modelling of the radiative decay is considered as a source of systematic uncertainty. Based on a detailed comparison between the radiative tails in simulation and data a systematic uncertainty of 1.0% is assigned.

Correlated between intervals
Software-trigger efficiency 1.0% Correlated between intervals

Production cross-sections results
The measured double-differential cross-sections for prompt and nonprompt J/ψ mesons are shown in figure 2 and listed in tables 2 and 3 in appendix A, for the range 0 < p T < 14 GeV/c and 2.0 < y < 4.5 with ∆p T between 1 and 4 GeV/c and ∆y = 0.5. By integrating the double-differential results over p T or y, the single-differential cross-sections dσ/dp T and dσ/dy are obtained, and are listed in tables 4, 5, 6 and 7 in appendix A. The dσ/dp T results include a further p T interval in the range 14 < p T < 20 GeV/c, which is not divided into y intervals due to the limited size of the data sample. The integrated cross-sections for prompt and nonprompt J/ψ mesons in the range 0 < p T < 20 GeV/c and 2.0 < y < 4.5 are where the first uncertainties are statistical and the second systematic. These results are obtained under the assumption that the polarisation of the J/ψ mesons is negligible. The J/ψ polarisation measurement at √ s = 7 TeV [53] indicates that the polarisation parameters λ θ , λ θφ and λ φ are consistent with zero while the central value of λ θ is around −0.2 in the helicity frame. The polarisation affects the detection efficiency and the dependence of the cross-sections on the polarisation is reported in appendix B. When the polarisation parameter λ θ is assumed to be −0.2 [53], the total cross-section decreases by 2.8% (2.9%) for prompt (nonprompt) J/ψ mesons. The single-differential cross-sections for prompt J/ψ mesons are compared with NRQCD calculations and colour glass condensate (CGC) effective theory results, as shown in figure 3. Theoretical calculations in the high p T region are obtained from the NLO NRQCD model with LDMEs fixed from the Tevatron data [54], and those in the low-p T region are obtained by combining the NRQCD model with CGC effective theory [55], in which nonperturbative parameters are fixed by fits to the Tevatron [56] and HERA [57] data. Uncertainties due to LDMEs determination, renormalisation scales, and factorisation scales are considered for the NRQCD and CGC calculations.
A comparison between single-differential cross-sections for nonprompt J/ψ mesons and fixed order plus next-to-leading logarithms (FONLL) calculations [58,59] is shown in figure 4. The FONLL approach provides cross-sections for b-quark production, and the branching fraction of the decay b → J/ψX, (1.16 ± 0.10)% [47], is taken from measurements performed in e + e − collisions at LEP. The FONLL calculations take into account the uncertainties of parton distribution functions (PDFs), the uncertainty due to the b-quark mass, and that due to the scales of renormalisation and factorisation. The total uncertainty of FONLL is dominated by the latter source.
The fraction of nonprompt J/ψ mesons is defined as the ratio between the nonprompt cross-section and the sum of prompt and nonprompt cross-sections, and the results in (p T ,y) intervals are shown in figure 5 and table 8 in appendix A. Most systematic uncertainties cancel in the ratio. Only the uncertainties due to the t z fit and the size of simulated sample are included. The fraction increases as a function of p T . For a given p T , the fraction decreases with increasing y.
The production cross-sections of J/ψ mesons at 5 TeV are compared with those previously measured at 8 TeV [13] and 13 TeV [14] in the range 0 < p T < 14 GeV/c and 2.0 < y < 4.5. The ratios of differential cross-sections for prompt J/ψ mesons between 8 TeV and 5 TeV measurements are shown in figure 6, and those between 13 TeV and 5 TeV in figure 7, both compared with NRQCD and CGC calculations. For nonprompt J/ψ mesons, the ratios of differential cross-sections between 8 TeV and 5 TeV measurements are shown in figure 8, and those between 13 TeV and 5 TeV in figure 9, compared with FONLL  Figure 3. Differential cross-sections (left) dσ/dp T and (right) dσ/dy for prompt J/ψ mesons compared with NRQCD and CGC calculations [54,55]. Uncertainties due to LDMEs determination, renormalisation scales, and factorisation scales are included in the NRQCD and CGC predictions.   Figure 6. Ratios of differential cross-sections between 8 TeV and 5 TeV measurements as a function of (left) p T and (right) y for prompt J/ψ mesons compared with NRQCD and CGC calculations [54,55]. Uncertainties due to the LDMEs determination, renormalisation scales, and factorisation scales are included in the NRQCD and CGC calculations.  Figure 7. Ratios of differential cross-sections between 13 TeV and 5 TeV measurements as a function of (left) p T and (right) y for prompt J/ψ mesons compared with NRQCD and CGC calculations [54,55]. Uncertainties due to the LDMEs determination, renormalisation scales, and factorisation scales are included in the NRQCD and CGC calculations.
calculations. Some of the systematic uncertainties are considered to fully cancel in the ratio, such as those due to branching fraction and the radiative tail. The uncertainties due to the t z fit and simulation sample size are taken as uncorrelated between the two measurements, and therefore remain. All other systematic uncertainties are assumed to cancel only partially. For example, the systematic uncertainty due to the luminosity measurement is estimated to be correlated at 50%. The overall uncertainty on the measured ratio is dominated by the luminosity measurement for prompt J/ψ mesons, and by the t z fit and the luminosity measurement for nonprompt J/ψ mesons. For the NRQCD and CGC estimates of the cross-section ratios, the uncertainties due to LDMEs determination, renormalisation scales, and factorisation scales between different energies mostly cancel. For the FONLL calculations, the uncertainty on the ratio is dominated by the uncertainties of PDFs for the low-p T and large-y regions and by the uncertainty due to the scales of the renormalisation and factorisation for the high-p T and small-y regions.  Figure 8. Ratios of differential cross-sections between 8 TeV and 5 TeV measurements as a function of (left) p T and (right) y for nonprompt J/ψ mesons compared with FONLL calculations [58,59]. The orange band shows the total FONLL calculation uncertainty; the violet band shows the uncertainties on PDFs and that due to b-quark mass added in quadrature; the red band shows only the uncertainty due to the b-quark mass.  Figure 9. Ratios of differential cross-sections between 13 TeV and 5 TeV measurements as a function of (left) p T and (right) y for nonprompt J/ψ mesons compared with FONLL calculations [58,59]. The orange band shows the total FONLL calculation uncertainty; the violet band shows the uncertainties on PDFs and that due to b-quark mass added in quadrature; the red band shows only the uncertainty due to b-quark mass.
show good agreement between NLO NRQCD calculations and the measurement results in the high-p T region. The inclusion of CGC effects achieves a reasonable agreement between data and theory in the low-p T region but a small discrepancy is still observed, which indicates that a pure fixed-order calculation may be insufficient and Sudakov resummation [60] may be required. A comparison of figures 6 and 7 suggests that the energy dependence of the cross-sections may differ between the theoretical calculation and the experimental measurements. Figures 8 and 9 show that the FONLL calculations agree with the experimental results for nonprompt J/ψ mesons.   Figure 10. Nuclear modification factor R pPb as a function of y for (left) prompt and (right) nonprompt J/ψ mesons, together with the theoretical predictions from (yellow dashed line and brown band) ref. [61], (blue band) ref. [62], and (violet solid line with band) refs. [63,64]. In the data points the full error bars represent the statistical and systematic uncertainties added in quadrature, while the smaller ones represent the statistical uncertainties.

Nuclear modification factor
The production cross-sections in pp collisions are essential inputs for the study of nuclear effects in collisions involving heavy ions. Nuclear effects are usually characterized by the nuclear modification factor. In proton-lead (pPb) collisions, this factor, R pPb , is defined as the production cross-section of a given particle per nucleon pair in pPb collisions divided by that in pp collisions. The previous R pPb measurement performed by the LHCb collaboration at a centre-of-mass energy per nucleon pair of √ s NN = 5 TeV [34] made use of J/ψ production cross-sections in pp collisions at 5 TeV derived from an interpolation of LHCb measurements at 2.76, 7 and 8 TeV [11-13] using a power-law fit. Based on the direct measurement presented in this paper, the nuclear modification factor R pPb is updated. In the data taking of pPb collisions, two distinct beam configurations are used, pPb and Pbp. In the pPb configuration particles produced in the direction of the proton beam are analysed, while in the Pbp configuration particles are analysed in the Pb beam direction. Rapidity y is defined in the nucleon-nucleon rest frame, and the coverage at LHCb is 1.5 < y < 4.0 (−5.0 < y < −2.5) in the pPb (Pbp) configuration.
The R pPb values, as a function of y in the range p T < 14 GeV/c, for prompt and nonprompt J/ψ mesons, are shown in figure 10 along with several theoretical predictions. The values are also listed in table 9 in appendix A. The predictions are obtained with the nDSg LO nuclear parton distribution function (nPDF) parameterisation [61], the EPS09 LO nPDF parameterisation [61], and the EPS09 NLO nPDF parameterisation [62], and from the fully coherent energy loss (FCEL) model [63]. Conservatively, the systematic uncertainties are assumed to be uncorrelated between the results obtained in pPb and pp collisions. For prompt J/ψ mesons, the measurement agrees with most theoretical calculations, while the calculation with the EPS09 NLO nPDF parameterisation [62] gives a poorer description. The comparison for nonprompt J/ψ mesons shows good agreement.

Conclusion
The J/ψ production cross-sections in proton-proton collisions at a centre-of-mass energy √ s = 5 TeV are studied using a data sample corresponding to an integrated luminosity of 9.18 ± 0.35 pb −1 collected by the LHCb detector. The J/ψ differential cross-sections, as a function of p T and y, are measured separately for prompt and nonprompt J/ψ mesons in the range 0 < p T < 20 GeV/c and 2.0 < y < 4.5. The J/ψ production cross-section ratios between 8 TeV and 5 TeV, and between 13 TeV and 5 TeV are also determined and compared with the theory models. The measured prompt J/ψ results are in good agreement with NLO NRQCD calculations in the high-p T region. A small tension is observed between data for prompt J/ψ in the low-p T region and NRQCD and CGC calculations, which may indicate the need for further corrections in the theory model. The FONLL calculations describe the measured results for nonprompt J/ψ mesons well. The nuclear modification factor in proton-lead collisions for J/ψ mesons at a centre-of-mass energy per nucleon pair of √ s NN = 5 TeV is updated and supersedes that in the previous publication [34].  Table 2. Double-differential production cross-sections d 2 σ dp T dy [nb/(GeV/c) per unit rapidity] for prompt J/ψ mesons in (p T ,y) intervals. The first uncertainties are statistical, the second are correlated systematic uncertainties shared between intervals, the third are uncorrelated systematic uncertainties, and the last are correlated between p T intervals and uncorrelated between y intervals.   Table 3. Double-differential production cross-sections d 2 σ dp T dy [nb/(GeV/c) per unit rapidity] for nonprompt J/ψ mesons in (p T ,y) intervals. The first uncertainties are statistical, the second are correlated systematic uncertainties shared between intervals, the third are uncorrelated systematic uncertainties, and the last are correlated between p T intervals and uncorrelated between y intervals.  Table 4. Single-differential production cross-sections dσ dp T [nb/(GeV/c)] for prompt J/ψ mesons in the rapidity range 2−4.5. The first uncertainties are statistical, the second are correlated systematic uncertainties shared between intervals, and the last are uncorrelated systematic uncertainties.  Table 5. Single-differential production cross-sections dσ dp T [nb/(GeV/c)] for nonprompt J/ψ mesons in the rapidity range 2−4.5. The first uncertainties are statistical, the second are correlated systematic uncertainties shared between intervals, and the last are uncorrelated systematic uncertainties. 3.5 − 4.0 2833.3 ± 6.2 ± 92.6 ± 5.9 2812.6 ± 6.2 ± 91.8 ± 5.9

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4.0 − 4.5 2109.5 ± 6.7 ± 80.0 ± 7.8 2099.5 ± 6.7 ± 79.6 ± 7.8 Table 6. Single-differential production cross-sections dσ dy [nb per unit rapidity] for prompt J/ψ mesons. The first uncertainties are statistical, the second are correlated systematic uncertainties shared between intervals, and the last are uncorrelated systematic uncertainties.  Table 7. Single-differential production cross-sections dσ dy [nb per unit rapidity] for nonprompt J/ψ mesons. The first uncertainties are statistical, the second are correlated systematic uncertainties shared between intervals, and the last are uncorrelated systematic uncertainties.  Table 9. Nuclear modification factor R pPb as a function of y with p T < 14 GeV/c. The first uncertainty is statistical and the second is systematic.  Table 10. Cross-section ratios between 8 TeV and 5 TeV measurements for prompt J/ψ mesons as a function of p T with 2.0 < y < 4.5. The first uncertainty is statistical and the second is systematic.  Table 11. Cross-section ratios between 8 TeV and 5 TeV measurements for prompt J/ψ mesons as a function of y with p T < 8 GeV/c. The first uncertainty is statistical and the second is systematic.
-18 -  Table 12. Cross-section ratios between 13 TeV and 5 TeV measurements for prompt J/ψ mesons as a function of p T with 2.0 < y < 4.5. The first uncertainty is statistical and the second is systematic.  Table 13. Cross-section ratios between 13 TeV and 5 TeV measurements for prompt J/ψ mesons as a function of y with p T < 8 GeV/c. The first uncertainty is statistical and the second is systematic. .81 ± 0.14 ± 0.24 Table 16. Cross-section ratios between 13 TeV and 5 TeV measurements for nonprompt J/ψ mesons as a function of p T with 2.0 < y < 4.5. The first uncertainty is statistical and the second is systematic.  Table 17. Cross-section ratios between 13 TeV and 5 TeV measurements for nonprompt J/ψ mesons as a function of y with p T < 14 GeV/c. The first uncertainty is statistical and the second is systematic.

B Dependence of cross-sections on the polarisation
The angular distribution of the J/ψ →µ + µ − decay is described by where θ and φ are the polar and azimuthal angles between the direction of µ + and the chosen polarisation axis, and λ θ , λ θφ and λ φ are polarisation parameters. In the helicity -20 -
frame, the polarisation axis coincides with the flight direction of the J/ψ meson in the centre-of-mass frame of the colliding hadrons. The detection efficiency of the J/ψ mesons is function of the polarisation, especially of λ θ . Zero polarisation is assumed in the simulation since there is no prior knowledge of the polarisation of the J/ψ mesons in pp collisions at 5 TeV, and only small longitudinal polarisations have been found in the J/ψ polarisation analyses at the LHC [53,65,66].
To evaluate the change of results assuming a non-zero polarisation, we reweight the angular distribution of the muon tracks in rest frame of the J/ψ mesons in simulation and calculate the change in the total efficiency, which impacts the cross-sections. The relative change of the cross-section for a polarisation of λ θ = −0.2 [53] in the helicity frame compared to zero polarisation in each (p T ,y) interval is given in table 18. In addition, the relative change of the cross-section for a polarisation of λ θ = −1 (+1) in the helicity frame, which corresponds to the fully longitudinally (transversely) polarised scenario, compared to zero polarisation in each (p T ,y) interval is given in table 19 (20). [22] ALICE collaboration, Measurement of prompt J/ψ and beauty hadron production cross sections at mid-rapidity in pp collisions at √ s = 7