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We present new NLO pQCD predictions for the inclusive photoproduction of dijets in ultra-peripheral (UPC) lead-lead collisions at 5.02 TeV with a realistic impact-parameter dependent effective photon flux obtained through the Woods-Saxon nuclear profile. For the first time in NLO inclusive UPC dijet predictions, we take into account also the modelling of the forward-neutron event class required in the experimental measurements. We show that since the dijet photoproduction at forward rapidities requires an energetic photon in the initial state, this biases the cross section to be dominated by events with relatively small impact parameters between the nuclei, of the order of a few nuclear radii. This leads to a sensitivity to the transverse-plane collision geometry, which we take properly into account by including effects from the finite extent of both the photon-emitting and the target nucleus. We also test the potential sensitivity to the spatial dependence of nuclear parton distribution functions in connection with this finding., Comment: 5 pages, 2 figures, presented at the 31st International Workshop on Deep Inelastic Scattering (DIS2024)

We investigate the effects of saturation dynamics on midrapidity flow observables by adding fluctuating hotspots into the novel Monte Carlo EKRT (MC-EKRT) event generator for high-energy nuclear collisions. We demonstrate that the intensity of the saturation effects significantly affects the ratio between the flow coefficients $v_3$ and $v_2$ at the LHC. Adding a hotspot substructure to the nucleons enhances the saturation effects and improves the agreement with the measured data. We show that the collision-energy dependence of the flow coefficients obtained using the MC-EKRT initial states with hotspots is improved in comparison with the earlier event-by-event EKRT model. In addition, we present the results for the charged hadron multiplicity distribution in Pb+Pb collisions at the LHC, and show that the minijet-multiplicity originating fluctuations of the saturation scale included in MC-EKRT, as well as the presence of hotspots, are necessary for describing the measured large-multiplicity tail in the distribution., Comment: 13 pages, 7 figures

We present a novel Monte-Carlo implementation of the EKRT model, MC-EKRT, for computing partonic initial states in high-energy nuclear collisions. Our new MC-EKRT event generator is based on collinearly factorized, dynamically fluctuating pQCD minijet production, supplemented with a saturation conjecture that controls the low-$p_T$ particle production. Previously, the EKRT model has been very successful in describing low-$p_T$ observables at mid-rapidity in heavy-ion collisions at the LHC and RHIC energies. As novel features, our new MC implementation gives a full 3-dimensional initial state event-by-event, includes dynamical minijet-multiplicity fluctuations in the saturation and particle production, introduces a new type of spatially dependent nuclear parton distribution functions, and accounts for the conservation of energy/momentum and valence-quark number. In this proof-of-principle study, we average a large set of event-by-event MC-EKRT initial conditions and compute the rapidity and centrality dependence of the charged hadron multiplicities and elliptic flow for the LHC Pb+Pb and RHIC Au+Au collisions using 3+1 D viscous fluid-dynamical evolution. Also event-by-event fluctuations and decorrelations of initial eccentricities are studied. The good agreement with the rapidity-dependent data suggests that the same saturation mechanism that has been very successful in explaining the mid-rapidity observables, works well also at larger rapidities., Comment: 31 pages, 18 figures

We present a comprehensive NLO pQCD study on inclusive dijet photoproduction in ultraperipheral nucleus-nucleus collisions (UPCs). Our analysis takes into account the finite size of both the photon-emitting and the target nucleus, estimated using the Wood-Saxon nuclear density profile. We show that a significant part of the measured dijets at large $z_\gamma$ in UPC Pb+Pb collisions at 5.02 TeV come from events with relatively small impact parameters of the order of a few nuclear radii, and the cross section predictions thus become sensitive to the modelling of the collision geometry and photon flux near the source nucleus. In addition, we include the modelling of electromagnetic breakup survival factor needed for a direct comparison with the experimental data and study the resolution power of this process in terms of the impact-parameter dependent nuclear parton distribution functions., Comment: 8 pages, 5 figures, 1st International Workshop on the physics of Ultra Peripheral Collisions (UPC 2023)

We present next-to-leading order perturbative QCD predictions for inclusive dijet photoproduction in ultra-peripheral nucleus-nucleus collisions (UPCs) within the impact-parameter dependent equivalent photon approximation. Taking into account the finite size of both the photon-emitting and the target nucleus, we show that this process is sensitive to the transverse-plane geometry of the UPC events. We show that this leads to a sizeable, 20-40% effect for large values of the $z_\gamma$ variable in the dijet photoproduction cross section in lead-lead UPCs at 5.02 TeV compared to the widely-used pointlike approximation where the nuclear radius is accounted for only as a sharp cut-off in the photon flux calculation. This resolution of the spatial degrees of freedom is a result of having high-transverse-momentum jets in the final state, which at the large-$z_\gamma$ kinematics requires a highly energetic photon in the initial state, thus biasing the collisions to small impact-parameter ''near-encounter'' configurations. We further discuss the role of the forward-neutron event-class selection in isolating the photonuclear cross section in the nucleus-nucleus collisions, and employ the needed electromagnetic breakup survival factor in our predictions., Comment: 13 pages, 10 figures; accepted for publication in Physical Review C

We demonstrate how deep convolutional neural networks can be trained to predict 2+1 D hydrodynamic simulation results for flow coefficients, mean-transverse-momentum and charged particle multiplicity from the initial energy density profile. We show that this method provides results that are accurate enough, so that one can use neural networks to reliably estimate multi-particle flow correlators. Additionally, we train networks that can take any model parameter as an additional input and demonstrate with a few examples that the accuracy remains good. The usage of neural networks can reduce the computation time needed in performing Bayesian analyses with multi-particle flow correlators by many orders of magnitude., Comment: 4 pages, 4 figures. Presented at the XXXth International Conference on Ultra-relativistic Nucleus-Nucleus Collisions (Quark Matter 2023), Houston, Texas, USA

We present the first study of coherent exclusive quarkonium ($J/\psi$, $\Upsilon$) photoproduction in ultraperipheral nucleus-nucleus collisions (UPCs) at the LHC in the framework of collinear factorization and next-to-leading order (NLO) perturbative QCD (pQCD). We make NLO predictions for the $J/\psi$ and $\Upsilon$ rapidity distributions for lead (Pb) and oxygen (O) beams, and quantify their dependence on the factorization/renormalization scale, nuclear parton distribution functions (PDFs) and their uncertainties, and on differences between nuclear PDFs and generalized parton distribution functions (GPDs). We show that within the PDF-originating uncertainties our approach provides a good description of the available $J/\psi$ photoproduction data in Pb+Pb UPCs at the LHC but that the scale uncertainty is significant. We demonstrate that at NLO pQCD the quark contributions are important in the $J/\psi$ case but that gluons clearly dominate the $\Upsilon$ cross sections. We also study how the scale dependence could be tamed by considering O+O/Pb+Pb ratios of the exclusive $J/\psi$ UPC cross sections, and how HERA and p+p/Pb LHC data can help in obtaining better-controlled NLO predictions in the $\Upsilon$ case., Comment: 6 pages, 5 figures, contributed talk by K.J.E. at the 11th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions, Hard Probes 2023, 26-31 March 2023, Aschaffenburg, Germany

We make predictions for the cross section of coherent $J/\psi$ photoproduction in Pb-Pb and O-O ultraperipheral collisions (UPCs) at the LHC as a function of the $J/\psi$ rapidity $y$ in the framework of collinear factorization and next-to-leading order (NLO) perturbative QCD. We quantify the strong scale dependence and significant uncertainties due to nuclear PDFs and show that our approach provides a reasonable description of the LHC data on coherent $J/\psi$ photoproduction in Pb-Pb UPCs. We demonstrate that these uncertainties are reduced by approximately a factor of 10 in the scaled ratio of the O-O and Pb-Pb UPC cross sections. Our analysis indicates the dominance of the quark contribution to the UPC cross section at central rapidities, which affects the interpretation of the UPC data., Comment: 10 pages, 6 figures. Contribution to Proceedings of XXIX Cracow EPIPHANY Conference on Physics at the Electron-Ion Collider and Future Facilities, Cracow, Poland, January 16-19, 2023

We train a deep convolutional neural network to predict hydrodynamic results for flow coefficients, average transverse momenta and charged particle multiplicities in ultrarelativistic heavy-ion collisions from the initial energy density profiles. We show that the neural network can be trained accurately enough so that it can reliably predict the hydrodynamic results for the flow coefficients and, remarkably, also their correlations like normalized symmetric cumulants, mixed harmonic cumulants and flow-transverse-momentum correlations. At the same time the required computational time decreases by several orders of magnitude. To demonstrate the advantage of the significantly reduced computation time, we generate 10M initial energy density profiles from which we predict the flow observables using the neural network, which is trained using 5k, and validated using 90k events per collision energy. We then show that increasing the number of collision events from 90k to 10M can have significant effects on certain statistics-expensive flow correlations, which should be taken into account when using these correlators as constraints in the determination of the QCD matter properties., Comment: 11 pages, 10 figures

We present predictions for the rapidity-differential cross sections of exclusive $\Upsilon$ photoproduction in ultraperipheral collisions (UPCs) of lead ions at the Large Hadron Collider (LHC). We work in the framework of collinear factorization at next-to-leading order (NLO) in perturbative QCD, modeling the generalized parton distributions (GPDs) through the Shuvaev transform of nuclear parton distribution functions (nPDFs). While the effects due to the GPD modeling turn out to be small, the direct NLO predictions still carry significant nPDF-originating uncertainties and depend strongly on the choices of the factorization and renormalization scales. To tame the scale dependence and to account for the fact that the NLO calculations generally underpredict the photoproduction measurements on protons, we also present alternative, data-driven predictions. In this approach the underlying photoproduction cross sections on lead are found by combining their nuclear modifications calculated at NLO with the measured photoproduction cross sections on protons. The data-driven strategy reduces the uncertainties associated with the scale choices, and essentially eliminates the effects of GPD modeling thereby leaving the cross sections sensitive mainly to the input nPDFs. Our estimates indicate that the process is measurable in ${\rm Pb}+{\rm Pb}$ collisions at the LHC., Comment: 14 pages

We present predictions for the cross sections of coherent $J/\psi$ photoproduction in lead-lead and oxygen-oxygen ultraperipheral collisions (UPCs) as a function of the $J/\psi$ rapidity at the LHC in the framework of collinear factorization at next-to-leading order (NLO) in perturbative QCD. Taking generalized parton distribution functions in their forward limit and using the EPPS21, nNNPDF3.0, and nCTEQ15WZSIH nuclear parton distribution functions, we update our recent results for Pb-Pb collisions, make detailed predictions for O-O collisions for several beam energy configurations, and examine the ratio of O-O and Pb-Pb UPC cross sections. We show that the latter observable allows one to significantly reduce the scale uncertainty of NLO predictions for this process., Comment: 21 pages, 18 figures. Revised version with corrected error bands for nNNPDF3.0 results in Figs. 4 and 15-18. Matches the published Erratum, Phys. Rev. C 108, 069901 (2023)

We present the first NLO pQCD study of coherent exclusive $J/\psi$ photoproduction in ultraperipheral heavy-ion collisions (UPCs) at the LHC. Taking the generalized parton distributions (GPDs) in their forward limit, as parton distribution functions (PDFs), we quantify the NLO contributions in the rapidity-differential cross section, show that the real part of the amplitude must not be neglected, study the gluon and quark contributions, chart the scale-choice and PDF uncertainties, and compare the NLO results with LHC and HERA data. We show that the scale dependence is significant but a scale choice can be found with which we reproduce the 2.76 and 5.02 TeV UPC data. In particular, we show that the process is clearly more sensitive to the nuclear quark PDFs than thought before., Comment: 5 pages, 5 figures, contributed talk by T.L. at the XXIX International Conference on Ultra-relativistic Nucleus-Nucleus Collisions, Quark Matter 2022, 4-10 April, 2022, Krakow, Poland

We present the first study of rapidity-differential cross sections of coherent exclusive $J/\psi$ photoproduction in heavy-ion ultraperipheral collisions (UPCs) at the LHC, $\text{d}\sigma(\text{Pb}+\text{Pb}\rightarrow \text{Pb}+J/\psi+\text{Pb})/\text{d}y$, to NLO in collinear factorisation. Taking the generalised parton distributions as their forward limit counterparts, the NLO contributions in the cross sections are quantified and we show that the real part of the amplitude and quark-PDF contributions must not be neglected. We further evaluate the uncertainties arising from the scale-choice at both LO and NLO, and compare our results with exclusive $J/\psi$ photoproduction data in Pb+Pb UPCs from LHC. The scale dependence in $\text{d}\sigma(\text{Pb}+\text{Pb}\rightarrow \text{Pb}+J/\psi+\text{Pb})/\text{d}y$ is sizable, but we can find a scale-choice at NLO that reproduces the Pb+Pb UPC data at both Run 1 and Run 2 collision energies. This process has traditionally been suggested to be a direct probe of nuclear gluon distributions. We show that the situation changes rather dramatically from LO to NLO, where the interplay of both gluon and quark contributions, and in particular their relative signs, play a significant role. We end with some concluding remarks about the outlook of this observable within a tamed collinear factorisation., Comment: 5 pages, 4 figures. Proceedings of the XXIX International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2022)

We extend the applicability of the hydrodynamics, perturbative QCD and saturation -based EKRT (Eskola-Kajantie-Ruuskanen-Tuominen) framework for ultrarelativistic heavy-ion collisions to peripheral collisions by introducing dynamical freeze-out conditions. As a new ingredient compared to the previous EKRT computations we also introduce a non-zero bulk viscosity. We compute various hadronic observables and flow correlations, including normalized symmetric cumulants, mixed harmonic cumulants and flow-transverse momentum correlations, and compare them against measurements from the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC). We demonstrate that the inclusion of the dynamical freeze-out and bulk viscosity allows a better description of the measured flow coefficients in peripheral collisions and enables the use of an extended centrality range when constraining the properties of QCD matter in the future., Comment: 22 pages, 17 figures

We present the first next-to-leading-order (NLO) perturbative QCD (pQCD) study of rapidity-differential cross sections of coherent exclusive photoproduction of $J/\psi$ mesons in heavy-ion ultraperipheral collisions (UPCs) at the LHC, $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$. For this, we account for the photon-nucleon NLO cross sections at the forward limit, the $t$ dependence using a standard nuclear form factor, and the photon fluxes of the colliding nuclei. Approximating the generalized parton distributions with their forward-limit parton distribution functions (PDFs), we quantify the NLO contributions in the cross sections, show that the real part of the amplitude and quark-PDF contributions must not be neglected, quantify the uncertainties arising from the scale-choice and PDFs, and compare our results with ALICE, CMS and LHCb $J/\psi$ photoproduction data in Pb+Pb UPCs, exclusive $J/\psi$ photoproduction data from HERA, and LHCb data in p+p. The scale dependence in $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$ is significant, but we can find a scale-choice that reproduces the Pb+Pb UPC data both at 2.76 and 5.02 TeV collision energies. This process has traditionally been suggested to be a direct probe of nuclear gluon distributions. We show that the situation changes rather dramatically from LO to NLO: the NLO cross sections reflect the nuclear effects of both gluons and quarks in a complicated manner where the relative signs of the LO and NLO terms in the amplitude play a significant role., Comment: 22 pages, 13 figures

We discuss the recent CMS Collaboration measurement of $W^\pm$ boson production in p+Pb collisions at 8.16 TeV in terms of the constraining power on nuclear parton distribution functions (PDFs). The impact of the free-proton PDF uncertainties on the nuclear PDF extraction is quantified by using a theoretical covariance-matrix method and Hessian PDF reweighting. We discuss different ways to mitigate these theoretical uncertainties, including self-normalization, forward-to-backward ratios and nuclear-modification ratios. It is found that none of these methods offer perfect cancellation of the free-proton PDFs but, with the present data uncertainties, the residual free-proton-PDF dependence has, conveniently for the global analyses, little effect on the extraction of the nuclear modifications. Based on a simple estimate of obtainable statistics at the LHC Run 3, we argue that this will change in the near future and it becomes more important to propagate the proton-PDF uncertainties accordingly. Using the obtained information on the correlations of the free-proton uncertainties, we also identify a new charge asymmetry ratio, where the cancellation of the proton-PDF uncertainties is found to be extremely good., Comment: 15 pages, 17 figures

We present an updated global analysis of collinearly factorized nuclear parton distribution functions (PDFs) at next-to-leading order in perturbative QCD. In comparison to our previous fit, EPPS16, the present analysis includes more data from proton-lead collisions at the Large Hadron Collider: 5TeV double-differential CMS dijet and LHCb D-meson data, as well as 8TeV CMS W$^\pm$ data. These new data lead to significantly better-constrained gluon distributions at small and intermediate values of the momentum fraction $x$, confirming the presence of shadowing and antishadowing for gluons in large nuclei. In addition, we include Jefferson Lab measurements of deeply inelastic scattering which probe nuclear PDFs at large $x$ and low virtualities. For the first time within the Hessian framework, we now also explore the uncertainties of nuclear PDFs due to the errors in the baseline proton PDFs. We release the results of our analysis as a new public parametrization of nuclear PDFs called EPPS21., Comment: Minor changes to match the published version

We report on the progress in updating our global analysis of nuclear PDFs. In particular, we will discuss the inclusion of double differential 5.02 TeV dijet and D-meson measurements, as well as 8.16 TeV W-production data from p-Pb collisions at the LHC. The new EPPS21 analysis will also involve recent JLab data for deep-inelastic scattering. As a novel aspect within our approach, we now also quantify the impact of free-proton PDF uncertainties on our extraction of nuclear PDFs., Comment: v2: Resubmission to SciPost, 8 pages, 4 figures, Proceedings for the XXVIII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2021)

The Glauber modeling plays a key role in centrality-dependent measurements of heavy-ion collisions. A central input parameter in Glauber models is the inelastic nucleon-nucleon cross section $\sigma_{\text{nn}}^{\text{inel}}$ which is nearly always taken from proton-proton measurements. At the LHC energies $\sigma_{\text{nn}}^{\text{inel}}$ depends on the QCD dynamics at small $x$ and low interaction scales where the shadowing/saturation phenomena are expected to become relatively more important for larger nuclei than for the proton. Thus, $\sigma_{\text{nn}}^{\text{inel}}$ e.g. in Pb+Pb collisions may well be lower than what is seen in proton-proton collisions. In this talk, we demonstrate how to use the recent $W^\pm$ and $Z$ measurements as a "standard candle" to extract $\sigma_{\text{nn}}^{\text{inel}}$ in Pb+Pb collisions. Our analysis -- built on the ATLAS data, state-of-the-art NNLO QCD calculations and nuclear PDFs -- indicate that at the LHC energies $\sigma_{\text{nn}}^{\text{inel}}$ in Pb+Pb collisions is suppressed relative to the proton-proton measurements by tens of percents. We demonstrate that this is in line with expectations from nuclear PDFs., Comment: 5 pages, 4 figures, to appear in the proceedings of the 10th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions, 1 - 5 June 2020, Austin, Texas, USA

The Large Hadron electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High Luminosity--Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron-proton and proton-proton operation. This report represents an update of the Conceptual Design Report (CDR) of the LHeC, published in 2012. It comprises new results on parton structure of the proton and heavier nuclei, QCD dynamics, electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics in extending the accessible kinematic range in lepton-nucleus scattering by several orders of magnitude. Due to enhanced luminosity, large energy and the cleanliness of the hadronic final states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, the report represents a detailed updated design of the energy recovery electron linac (ERL) including new lattice, magnet, superconducting radio frequency technology and further components. Challenges of energy recovery are described and the lower energy, high current, 3-turn ERL facility, PERLE at Orsay, is presented which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution and calibration goals which arise from the Higgs and parton density function physics programmes. The paper also presents novel results on the Future Circular Collider in electron-hadron mode, FCC-eh, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies., Comment: 373 pages, many figures, to be published by J. Phys. G

We investigate the temperature dependence of the shear viscosity to entropy density ratio $\eta/s$ using a piecewise linear parametrization. To determine the optimal values of the parameters and the associated uncertainties, we perform a global Bayesian model-to-data comparison on Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and Pb+Pb collisions at $2.76$ TeV and $5.02$ TeV, using a 2+1D hydrodynamical model with the EKRT initial state. We provide three new parametrizations of the equation of state (EoS) based on contemporary lattice results and hadron resonance gas, and use them and the widely used $s95p$ parametrization to explore the uncertainty in the analysis due to the choice of the equation of state. We found that $\eta/s$ is most constrained in the temperature range $T\approx 150$--$220$ MeV, where, for all EoSs, $0.08 < \eta/s < 0.23$ when taking into account the 90% credible intervals. In this temperature range the EoS parametrization has only a small $\approx 10\%$ effect on the favored $\eta/s$ value, which is less than the $\approx 30\%$ uncertainty of the analysis using a single EoS parametrization. Our parametrization of $(\eta/s)(T)$ leads to a slightly larger minimum value of $\eta/s$ than the previously used parametrizations. When we constrain our parametrization to mimic the previously used parametrizations, our favored value is reduced, and the difference becomes statistically insignificant., Comment: 19 pages, 12 figures. Published in Phys. Rev. C

Experimental results of inclusive hard-process cross sections in heavy-ion collisions conventionally lean on a normalization computed from Glauber models where the inelastic nucleon-nucleon cross section $\sigma_{\rm nn}^{\rm inel}$ -- a crucial input parameter -- is simply taken from proton-proton measurements. In this letter, using the computed electro-weak boson production cross sections in lead-lead collisions as a benchmark, we determine $\sigma_{\rm nn}^{\rm inel}$ from the recent ATLAS data. We find a significantly suppressed $\sigma_{\rm nn}^{\rm inel}$ relative to what is usually assumed, show the consequences for the centrality dependence of the cross sections, and address the phenomenon in an eikonal minijet model with nuclear shadowing., Comment: 6 pages, 4 figures

We discuss the new constraints on gluon parton distribution function (PDF) in lead nucleus, derivable with the Hessian PDF reweighting method from the 5.02 TeV p+Pb measurements of dijet (CMS) and $D^0$-meson (LHCb) nuclear modification ratios. The impact is found to be significant, placing stringent constraints in the mid- and previously unconstrained small-$x$ regions. The CMS dijet data confirm the existence of gluon anti-shadowing and the onset of small-$x$ shadowing, as well as reduce the gluon PDF uncertainties in the larger-$x$ region. The gluon constraints from the LHCb $D^0$ data, reaching down to $x \sim 10^{-5}$ and derived in a NLO perturbative QCD approach, provide a remarkable reduction of the small-$x$ uncertainties with a strong direct evidence of gluon shadowing. Furthermore, we find a good description of the data even down to zero $D^0$-meson transverse momentum within a purely DGLAP-based approach without a need for imposing any non-linear effects. Importantly, the constraints obtained from the dijet and $D^0$ data are mutually fully consistent, supporting the universality of nuclear PDFs in hard-scattering processes., Comment: 4 pages, 4 figures, presented at the XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2019), Wuhan, China

We quantify the impact of LHCb D-meson measurements at $\sqrt{s}=5 \, {\rm TeV}$ on the EPPS16 and nCTEQ15 nuclear PDFs. In our study, the theoretical description of D-meson production is based on the recently developed SACOT-$m_{\rm T}$ variant of the general-mass variable-flavour-number formalism, and the impact on PDFs is estimated via reweighting methods. We pay special attention on the theoretical uncertainties known to us, and are led to exclude the $p_{\rm T}<3 \, {\rm GeV}$ region from our main analysis. The LHCb data can be accommodated well within EPPS16 and nCTEQ15, and the data provide stringent constraints on the gluons in the shadowing/antishadowing regions. No evidence of non-linear effects beyond standard DGLAP evolution is found even if the full kinematic region down to zero $p_{\rm T}$ is considered., Comment: To appear in proceedings of the DIS'19 conference