PDF reweighting in the Hessian matrix approach

We introduce the Hessian reweighting of parton distribution functions (PDFs). Similarly to the better-known Bayesian methods, its purpose is to address the compatibility of new data and the quantitative modifications they induce within an existing set of PDFs. By construction, the method discussed here applies to the PDF fits that carried out a Hessian error analysis using a non-zero tolerance $\Delta\chi^2$. The principle is validated by considering a simple, transparent example. We are also able to establish an agreement with the Bayesian technique provided that the tolerance criterion is appropriately accounted for and that a purely exponential Bayesian likelihood is assumed. As a practi…

Impact of dijet and D-meson data from 5.02 TeV p+Pb collisions on nuclear PDFs

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…

EPPS16: Nuclear parton distributions with LHC data

We introduce a global analysis of collinearly factorized nuclear parton distribution functions (PDFs) including, for the first time, data constraints from LHC proton-lead collisions. In comparison to our previous analysis, EPS09, where data only from charged-lepton-nucleus deep inelastic scattering (DIS), Drell-Yan (DY) dilepton production in proton-nucleus collisions and inclusive pion production in deuteron-nucleus collisions were the input, we now increase the variety of data constraints to cover also neutrino-nucleus DIS and low-mass DY production in pion-nucleus collisions. The new LHC data significantly extend the kinematic reach of the data constraints. We now allow much more freedom…

Can we fit nuclear PDFs with the high-x CLAS data?

AbstractNuclear parton distribution functions (nuclear PDFs) are non-perturbative objects that encode the partonic behaviour of bound nucleons. To avoid potential higher-twist contributions, the data probing the high-x end of nuclear PDFs are sometimes left out from the global extractions despite their potential to constrain the fit parameters. In the present work we focus on the kinematic corner covered by the new high-x data measured by the CLAS/JLab collaboration. By using the Hessian re-weighting technique, we are able to quantitatively test the compatibility of these data with globally analyzed nuclear PDFs and explore the expected impact on the valence-quark distributions at high x. W…

EPS09 - Global NLO analysis of nuclear PDFs

In this talk, we present our recent work on next-to-leading order (NLO) nuclear parton distribution functions (nPDFs), which we call EPS09. As an extension to earlier NLO analyses, we complement the deep inelastic scattering and Drell-Yan dilepton data by inclusive midrapidity pion production measurements from RHIC to reduce the otherwize large freedom of the nuclear gluon densities. In addition, our Hessian-type error analysis leading to a collection of nPDF error sets, is the first of its kind among the nPDF analyses.

NuTeV sin2θWanomaly and nuclear parton distributions revisited

By studying the Paschos-Wolfenstein (PW) ratio of deep inelastic νFe and Fe scattering cross sections, we show that it should be possible to explain the NuTeV sin2θW anomaly with quite conventional physics, by introducing mutually different nuclear modifications for the valence-u and valence-d quark distributions of the protons in iron. Keeping the EKS98 nuclear modifications for uV+dV as a baseline, we find that some 20-30 % nuclear modifications to the uV and dV distributions account for the change induced in the PW ratio by the NuTeV-suggested increase Δsin2θW = 0.005. We show that introduction of such nuclear modifications in uV and dV individually, does not lead into contradiction with…

LHC data challenges the contemporary parton-to-hadron fragmentation functions

We discuss the inclusive high-pT charged-particle production in proton-proton collisions at the LHC. The experimental data are compared to the NLO perturbative QCD calculations employing various sets of parton-to-hadron fragmentation functions. Most of the theoretical predictions are found to disastrously overpredict the measured cross sections, even if the scale variations and PDF errors are accounted for. The problem appears to arise from the presently too hard gluon-to-hadron fragmentation functions.

The LHC p+Pb run from the nuclear PDF perspective

The p+Pb and Pb+Pb runs at the LHC have opened a possibility to investigate the validity of collinear factorization in a clearly higher center-of-mass energy scale than earlier in nuclear collisions. Indeed, some processes that have been measured routinely in p+p($\overline {\rm p}$) collisions and utilized for years in free proton PDF fits, can now finally be reached also in the nuclear case. Such new data are expected to provide conclusive answers concerning the universality of the nuclear PDFs. In this talk, I will contrast some of the first p+Pb and Pb+Pb measurements to the predictions based on the nuclear PDFs.

Hadroproduction of open heavy flavour for PDF analyses

Due to the large masses of the charm and bottom quarks, their production cross sections are calculable within the perturbative QCD. This makes the heavy-quark mesons important observables in high-energy collisions of protons and nuclei. However, the available calculations for heavy-flavored-meson hadroproduction have been somewhat problematic in reliably describing the cross sections across the full kinematic range from zero to very high $p_{\rm T}$. This has put some question marks on the robustness of LHC heavy-flavored-meson measurements in studying the partonic structure of the colliding hadrons and nuclei. Here, we introduce SACOT-$m_{\rm T}$ - a novel scheme for open heavy-flavour had…

Nuclear PDFs in the beginning of the LHC era

The status of the global fits of nuclear parton distributions (nPDFs) is reviewed. In addition to comparing the contemporary analyses of nPDFs, difficulties and controversies posed by the neutrino-nucleus deeply inelastic scattering data is overviewed. At the end, the first dijet data from the LHC proton+lead collisions is briefly discussed.

EPPS16 : Bringing nuclear PDFs to the LHC era

We report on EPPS16, the first global analysis of nuclear parton distribution functions (nPDFs) to include LHC data. Also for the first time, a full flavour dependence of nPDFs is allowed. While the included Z and W data are found to have insufficient statistics to yield stringent constraints, the CMS 5.02 TeV proton-lead dijet data prove crucial in setting the shape of nuclear gluon modifications. With these and other observables being measured in proton-lead runs, we are experiencing a shift of nPDFs to the LHC precision era.

Electron-ion physics with the LHeC

The Large Hadron Electron Collider (LHeC) project is the proposal to use the existing LHC proton/ion beams and construct a new electron beam line to perform high-energy electron-proton/ion collisions. In this talk, we consider some of the physics topics that could be studied in the electron-ion mode. In particular, we estimate how much the current nuclear parton distribution fits could be improved with the deeply inelastic scattering measurements at the LHeC by including pseudodata into a global analysis. In addition, we discuss briefly other topics that would help to better understand some aspects of heavy-ion collisions, namely small-$x$ physics and hadron production with a nuclear target.

Agreement of Neutrino Deep Inelastic Scattering Data with Global Fits of Parton Distributions

The compatibility of neutrino-nucleus deep inelastic scattering data within the universal, factorizable nuclear parton distribution functions has been studied independently by several groups in the past few years. The conclusions are contradictory, ranging from a violation of the universality up to a good agreement, most of the controversy originating from the use of the neutrino-nucleus data from the NuTeV Collaboration. Here, we pay attention to non-negligible differences in the absolute normalization between different neutrino data sets. We find that such variations are large enough to prevent a tensionless fit to all data simultaneously and could therefore misleadingly point towards non…

The LHC p+Pb run from the nuclear PDF perspective

The p+Pb and Pb+Pb runs at the LHC have opened a possibility to investigate the validity of collinear factorization in a clearly higher center-of-mass energy scale than earlier in nuclear collisions. Indeed, some processes that have been measured routinely in p+p(p) collisions and utilized for years in free proton PDF fits, can now finally be reached also in the nuclear case. Such new data are expected to provide conclusive answers concerning the universality of the nuclear PDFs. In this talk, I will contrast some of the first p+Pb and Pb+Pb measurements to the predictions based on the nuclear PDFs.

Impact of CMS 5.02 TeV dijet measurements on gluon PDFs - a preliminary view

We discuss the implications of the preliminary CMS dijet data from 5.02 TeV pp and pPb collisions for gluon PDFs of the proton and nuclei. The preliminary pp data show a discrepancy with NLO predictions using for example the CT14 PDFs. We find that this difference cannot be accommodated within the associated scale uncertainties and debate the possible changes needed in the gluon PDF. A similar discrepancy is found between the CMS pPb data and NLO predictions e.g. with the EPPS16 nuclear modifications imposed on the CT14 proton PDFs. When a nuclear modification ratio of the pp and pPb data is constructed, the uncertainties in the scale choices and in proton PDFs effectively cancel and a good…

Constraining nPDFs with inclusive pions and direct photons at forward rapidities in p+Pb collisions at the LHC

In this talk, we present NLO pQCD predictions for inclusive pion and direct photon nuclear modifications in p+Pb collisions at mid- and forward rapidities at the LHC. In addition to the minimum bias predictions, we also address the centrality dependence with spatially dependent nuclear PDFs. To understand which regions of the nuclear momentum fraction $x_2$ these observables predominantly probe, we present also the underlying $x_2$ distributions at different rapidities. We are led to conclude that the isolated photons at forward rapidities are more sensitive to the small-$x_2$ dynamics than the inclusive pions.

An update on nuclear PDFs at the LHeC

The prospects for a measurement of nuclear parton distribution functions (PDFs) at the Large Hadron--Electron Collider are discussed in the light of recent progress made in the front of global analysis of nuclear PDFs.

Evidence of shadowing in inelastic nucleon-nucleon cross section

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…

Probing the small- x nuclear gluon distributions with isolated photons at forward rapidities in p+Pb collisions at the LHC

Inclusive direct photon production in p+Pb collisions at the LHC is studied within the NLO perturbative QCD. Our aim is to quantify the dominant $x$ regions probed at different rapidities and to identify the best conditions for testing the nuclear gluon parton distribution functions (nPDFs) at small $x$. A comparison to the inclusive pion production reveals that from these two processes the photons carry more sensitivity to the small-$x$ partons and that this sensitivity can be further increased by imposing an isolation cut for the photon events. The details of the isolation criteria, however, seem to make only a small difference to the studied $x$ sensitivity and have practically no effect…

Hessian PDF reweighting meets the Bayesian methods

We discuss the Hessian PDF reweighting - a technique intended to estimate the effects that new measurements have on a set of PDFs. The method stems straightforwardly from considering new data in a usual $\chi^2$-fit and it naturally incorporates also non-zero values for the tolerance, $\Delta\chi^2>1$. In comparison to the contemporary Bayesian reweighting techniques, there is no need to generate large ensembles of PDF Monte-Carlo replicas, and the observables need to be evaluated only with the central and the error sets of the original PDFs. In spite of the apparently rather different methodologies, we find that the Hessian and the Bayesian techniques are actually equivalent if the $\Delta…

Dijets in p + Pb collisions and their quantitative constraints for nuclear PDFs

We present a perturbative QCD analysis concerning the production of high-pT dijets in p+Pb collisions at the LHC. The next-to-leading order corrections, scale variations and free-proton PDF uncertainties are found to have only a relatively small influence on the normalized dijet rapidity distributions. Interestingly, however, these novel observables prove to retain substantial sensitivity to the nuclear effects in the PDFs. Especially, they serve as a more robust probe of the nuclear gluon densities at $x>0.01$, than e.g. the inclusive hadron production. We confront our calculations with the recent data by the CMS collaboration. These preliminary data lend striking support to the gluon a…

The impact of the LHC nuclear program on nPDFs

Volume: 612 The proton-lead and lead-lead runs at the LHC are providing an enormous amount of data sensitive to the nuclear modifications of the initial state. The measurements explore a region of phase space not probed by previous experiments opening a possibility to test and hopefully, also improve the current knowledge of nuclear parton densities. In this talk, we discuss to what extent the present quantitative results for the charge asymmetry in electroweak boson production show sensitivity to the nuclear parton distributions. Peer reviewed

nPDF constraints from the large hadron electron collider

An updated analysis regarding the expected nuclear PDF constraints from the future Large Hadron Electron Collider (LHeC) experiment is presented. The new study is based on a more flexible small-$x$ parametrization which provides less biased uncertainty estimates in the region where there are currently no data constraints. The effect of the LHeC is quantified by directly including a sample of pseudodata according to the expected precision of this planned experiment. As a result, a significant reduction of the small-$x$ uncertainties in sea quarks and gluons is observed.

Electron Ion Collider: The Next QCD Frontier - Understanding the glue that binds us all

This White Paper presents the science case of an Electron-Ion Collider (EIC), focused on the structure and interactions of gluon-dominated matter, with the intent to articulate it to the broader nuclear science community. It was commissioned by the managements of Brookhaven National Laboratory (BNL) and Thomas Jefferson National Accelerator Facility (JLab) with the objective of presenting a summary of scientific opportunities and goals of the EIC as a follow-up to the 2007 NSAC Long Range plan. This document is a culmination of a community-wide effort in nuclear science following a series of workshops on EIC physics and, in particular, the focused ten-week program on "Gluons and quark sea a…

Saturation and forward jets in proton-lead collisions at the LHC

We investigate the forward-jet energy spectrum within the Color Glass Condensate framework at 5 TeV center-of-mass energy. In particular, we focus on the kinematic range covered by the CMS-CASTOR calorimeter. We show that our saturation-model calculations are compatible with the CASTOR measurements and that to optimally reproduce the data, effects of multi-parton interactions need to be included. We predict a significant nuclear suppression - reaching down to 50% at the lowest considered jet energies $E_{\rm jet} \sim 500 \, {\rm GeV}$.

Scaling properties of inclusive W $$^\pm $$ ± production at hadron colliders

We consider the hadroproduction of W gauge bosons in their leptonic decay mode. Starting from the leading-order expressions, we show that by defining a suitable scaling variable the centre-of-mass dependence of the cross sections at the LHC energies can be essentially described by a simple power law. The scaling exponent is directly linked to the small-$x$ behaviour of parton distribution functions (PDF) which, at the high virtualities involved in W production, is largely dictated by QCD evolution equations. This entails a particularly simple scaling law for the lepton charge asymmetry and also predicts that measurements in different collision systems (p-p, p-$\bar{\rm p}$, p-Pb Pb-Pb) are …

Signatures of gluon saturation from structure-function measurements

We study experimentally observable signals for nonlinear QCD dynamics in deep inelastic scattering (DIS) at small Bjorken variable $x$ and moderate virtuality $Q^2$, by quantifying differences between the linear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution and nonlinear evolution with the Balitsky-Kovchegov (BK) equation. To remove the effect of the parametrization freedom in the initial conditions of both equations, we first match the predictions for the DIS structure functions $F_2$ and $F_{\rm L}$ from both frameworks in a region in $x,Q^2$ where both frameworks should provide an accurate description of the relevant physics. The differences in the dynamics are then quanti…

Shadowing in Inelastic Nucleon-Nucleon Cross Section?

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 phe…

Features of W production in p-p, p-Pb and Pb-Pb collisions

We consider the production of inclusive W bosons in variety of high-energy hadronic collisions: p--p, p--$\overline{\rm p}$, p--Pb, and Pb--Pb. In particular, we focus on the resulting distributions of charged leptons from W decay that can be measured with relatively low backgrounds. The leading-order expressions within the collinearly factorized QCD indicate that the center-of-mass energy dependence at forward/backward rapidities should be well approximated by a simple power law. The scaling exponent is related to the small-$x$ behaviour of the quark distributions, which is largely driven by the parton evolution. An interesting consequence is the simple scaling law for the lepton charge as…

Re-weighting at the LHC: the p–Pb data impact

Abstract In this work we present selected results of a comprehensive analysis of the medium modifications in proton-lead LHC Run I data, and discuss the implications on different sets of nuclear parton densities. We find that the nuclear environment has a non-negligible relevance on the experimental results. We incorporate the information from Run I into the current nuclear densities and provide novel sets of nPDFs that will be useful for future predictions.

Top-quark production in proton–nucleus and nucleus–nucleus collisions at LHC energies and beyond

Single and pair top-quark production in proton-lead (p-Pb) and lead-lead (Pb-Pb) collisions at the CERN Large Hadron Collider (LHC) and future circular collider (FCC) energies, are studied with next-to-leading-order perturbative QCD calculations including nuclear parton distribution functions. At the LHC, the pair-production cross sections amount to sigma(t-tbar) = 3.4 mub in Pb-Pb at sqrt(s) = 5.5 TeV, and sigma(t-tbar) = 60 nb in p-Pb at sqrt(s) = 8.8 TeV. At the FCC energies of sqrt(s) = 39 and 63 TeV, the same cross sections are factors of 90 and 55 times larger respectively. In the leptonic final-state t-tbar --> W+b W-bbar --> b bbar l+l- nu+nu-, after typical acceptance and eff…

Nuclear PDFS today

I review the current status of global analysis of nuclear parton distributions and discuss some near-future prospects. I also advocate proton-nucleus (p-$A$) measurements at the LHC with $A\ll 208$ from the viewpoint of nuclear parton distributions.

Neutron-skin effect in direct-photon and charged hadron-production in Pb+Pb collisions at the LHC

A well-established observation in nuclear physics is that in neutron-rich spherical nuclei the distribution of neutrons extends farther than the distribution of protons. In this work, we scrutinize the influence of this so called neutron-skin effect on the centrality dependence of high-$p_{\rm T}$ direct-photon and charged-hadron production. We find that due to the estimated spatial dependence of the nuclear parton distribution functions, it will be demanding to unambiguously expose the neutron-skin effect with direct photons. However, when taking a ratio between the cross sections for negatively and positively charged high-$p_{\rm T}$ hadrons, even centrality-dependent nuclear-PDF effects …

B-meson hadroproduction in the SACOT-mT scheme

We apply the SACOT-mT general-mass variable flavour number scheme (GM-VFNS) to the inclusive B-meson production in hadronic collisions at next-to-leading order in perturbative Quantum Chromodynamics. In the GM-VFNS approach one matches the fixed-order heavy-quark production cross sections, accurate at low transverse momentum (pT), with the zero-mass cross sections, accurate at high pT. The physics idea of the SACOT-mT scheme is to do this by accounting for the finite momentum transfer required to create a heavy quark-antiquark pair throughout the calculation. We compare our results with the latest LHC data from proton-proton and proton-lead collisions finding a very good agreement within th…

EPS09 - Nuclear PDFs and Their Uncertainties at NLO

In this talk, we present our recent next-to-leading order (NLO) nuclear parton distribution functions (nPDFs), which we call EPS09. As an extension to earlier NLO analyses, we supplement the deep inelastic scattering and Drell-Yan dilepton data by inclusive midrapidity pion measurements from RHIC in order to reduce the otherwize large freedom in the nuclear gluon densities. Our Hessian-type error analysis leading to a collection of nPDF error sets, is the first of its kind among the nPDF analyses.

The present status of the EPS nuclear PDFs

The recent global analyses of the nuclear parton distribution functions (nPDFs) lend support to the validity of the factorization theorem of QCD in high-energy processes involving bound nucleons. With a special attention on our latest global analysis EPS09, we review the recent developements in the domain of nuclear PDFs.

EPPS21: a global QCD analysis of nuclear PDFs

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 p…

Predictions for cold nuclear matter effects in p+Pb collisions at s N N = 8.16 TeV

A global reanalysis of nuclear parton distribution functions

We determine the nuclear modifications of parton distribution functions of bound protons at scales $Q^2\ge 1.69$ GeV$^2$ and momentum fractions $10^{-5}\le x\le 1$ in a global analysis which utilizes nuclear hard process data, sum rules and leading-order DGLAP scale evolution. The main improvements over our earlier work {\em EKS98} are the automated $\chi^2$ minimization, simplified and better controllable fit functions, and most importantly, the possibility for error estimates. The resulting 16-parameter fit to the N=514 datapoints is good, $\chi^2/{\rm d.o.f}=0.82$. Within the error estimates obtained, the old {\em EKS98} parametrization is found to be fully consistent with the present an…

Centrality and rapidity dependence of inclusive pion and prompt photon production in p+Pb collisions at the LHC with EPS09s nPDFs

The centrality dependencies of the inclusive neutral pion and prompt photon nuclear modification factors for p+Pb collisions at the LHC are studied using a spatially dependent set of nuclear PDFs, EPS09s. The calculations are performed at mid- and forward rapidities searching for an observable which would optimally probe the spatial dependence of the nuclear PDFs. In addition, we discuss to which $x$ values of the nucleus the different observables are sensitive.

Status of nuclear PDFs after the first LHC p–Pb run

In this talk, I overview the recent progress on the global analysis of nuclear parton distribution functions (nuclear PDFs). After first introducing the contemporary fits, the analysis procedures are quickly recalled and the ambiguities in the use of experimental data outlined. Various nuclear-PDF parametrizations are compared and the main differences explained. The effects of nuclear PDFs in the LHC p-Pb hard-process observables are discussed and some future prospects sketched.

Applicability of pion-nucleus Drell-Yan data in global analysis of nuclear parton distribution functions

Despite the success of modern nuclear parton distribution functions (nPDFs) in describing nuclear hard-process data, they still suffer from large uncertainties. One of the poorly constrained features is the possible asymmetry in nuclear modifications of valence $u$ and $d$ quarks. We study the possibility of using pion-nucleus Drell-Yan dilepton data as a new constraint in the global analysis of nPDFs. We find that the nuclear cross-section ratios from the NA3, NA10 and E615 experiments can be used without imposing significant new theoretical uncertainties and, in particular, that these datasets may have some constraining power on the $u$/$d$ -asymmetry in nuclei.

An analysis of the impact of LHC Run I proton–lead data on nuclear parton densities

We report on an analysis of the impact of available experimental data on hard processes in proton-lead collisions during Run I at the Large Hadron Collider on nuclear modifications of parton distribution functions. Our analysis is restricted to the EPS09 and DSSZ global fits. The measurements that we consider comprise production of massive gauge bosons, jets, charged hadrons and pions. This is the first time a study of nuclear PDFs includes this number of different observables. The goal of the paper is twofold: i) checking the description of the data by nPDFs, as well as the relevance of these nuclear effects, in a quantitative manner; ii) testing the constraining power of these data in eve…

Nuclear structure functions at a future electron-ion collider

The quantitative knowledge of heavy nuclei's partonic structure is currently limited to rather large values of momentum fraction $x$---robust experimental constraints below $x\ensuremath{\sim}{10}^{\ensuremath{-}2}$ at low resolution scale ${Q}^{2}$ are particularly scarce. This is in sharp contrast to the free proton's structure which has been probed in Deep Inelastic Scattering (DIS) measurements down to $x\ensuremath{\sim}{10}^{\ensuremath{-}5}$ at perturbative resolution scales. The construction of an electron-ion collider (EIC) with a possibility to operate with a wide variety of nuclei, will allow one to explore the low-$x$ region in much greater detail. In the present paper we simula…

Proton-PDF uncertainties in extracting nuclear PDFs from W± production in p+Pb collisions

We discuss the recent CMS Collaboration measurement of W± 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, co…

Global analysis of nuclear parton distribution functions at leading and next-to-leading order perturbative QCD

The EPPS16 nuclear PDFs

We report on EPPS16 - the first analysis of NLO nuclear PDFs where LHC p-Pb data (Z, W, dijets) have been directly used as a constraint. In comparison to our previous fit EPS09, also data from neutrino-nucleus deeply-inelastic scattering and pion-nucleus Drell-Yan process are now included. Much of the theory framework has also been updated from EPS09, including a consistent treatment of heavy quarks in deeply-inelastic scattering. However, the most notable change is that we no longer assume flavour-blind nuclear modifications for valence and sea quarks. This significantly reduces the theoretical bias. All the analysed data are well reproduced and the analysis thereby supports the validity o…

Neutron-skin effect and centrality dependence of high-$p_{\mathrm{T}}$ observables in nuclear collisions

We report on our studies of the neutron-skin effects in high-$p_{\mathrm{T}}$ observables at the LHC. We study the impact of the neutron-skin effect on the centrality dependence of inclusive direct photon, high-$p_{\mathrm{T}}$ hadron and $W^{\pm}$ production in nuclear collisions at the LHC. The neutron-skin effect refers to the observation that in spherical heavy nuclei, the tail of the neutron distribution extends farther than the distribution of protons, which can affect observables sensitive to electroweak phenomena in very peripheral collisions. We quantify this effect for direct photons, charged hadrons and W bosons as a function of the collision centrality. In the case of direct pho…

Non-quadratic improved Hessian PDF reweighting and application to CMS dijet measurements at 5.02 TeV

Hessian PDF reweighting, or "profiling", has become a widely used way to study the impact of a new data set on parton distribution functions (PDFs) with Hessian error sets. The available implementations of this method have resorted to a perfectly quadratic approximation of the initial $\chi^2$ function before inclusion of the new data. We demonstrate how one can take into account the first non-quadratic components of the original fit in the reweighting, provided that the necessary information is available. We then apply this method to the CMS measurement of dijet pseudorapidity spectra in proton-proton (pp) and proton-lead (pPb) collisions at 5.02 TeV. The measured pp dijet spectra disagree…

Nuclear PDFs at NLO - status report and review of the EPS09 results

We review the current status of the global DGLAP analysis of nuclear parton distribution functions, nPDFs, focusing on the recent EPS09 analysis, whose output, EPS09NLO, is the best-constrained NLO nPDF set on the market. Collinear factorization is found to work very well in the kinematical region studied. With the error sets released in the EPS09 package one can compute how the nPDF-related uncertainties propagate into factorizable nuclear hard-process cross sections. A comparison with the other existing NLO nPDF sets is shown, and the BRAHMS forward-$\eta$ hadron data from d+Au collisions are discussed in the light of the EPS09 nPDFs and their error sets.

Confronting current NLO parton fragmentation functions with inclusive charged-particle spectra at hadron colliders

The inclusive spectra of charged particles measured at high transverse momenta ($p_T\gtrsim$2GeV/c) in proton-proton and proton-antiproton collisions in the range of center-of-mass energies $\sqrt{s}=200-7000$GeV are compared with next-to-leading order perturbative QCD calculations using seven recent sets of parton-to-hadron fragmentation functions (FFs). Accounting for the uncertainties in the scale choices and in the parton distribution functions, we find that most of the theoretical predictions tend to overpredict the measured LHC and Tevatron cross sections by up to a factor of two. We identify the currently too-hard gluon-to-hadron FFs as the probable source of the problem, and justify…

Inclusive prompt photon production in nuclear collisions at RHIC and LHC

Nuclear modification factors of inclusive prompt photon production in d-Au collisions at RHIC and p-Pb collisions at the LHC are provided at different rapidities. The calculations are performed at NLO accuracy using the EPS09 NLO nuclear parton distribution functions (nPDFs) and their error sets. The results are compared to the ones obtained with the nDS and HKN07 NLO nPDFs, and to the corresponding nuclear modification factors of neutral pion production in these collisions. The sensitivity of these results to the scale choice is also investigated. Interestingly, the predictions using the different nPDF sets differ from each other to the extent that this observable can be expected to become…

EPPS16 – First nuclear PDFs to include LHC data

We present results of our recent EPPS16 global analysis of NLO nuclear parton distribution functions (nPDFs). For the first time, dijet and heavy gauge boson production data from LHC proton–lead collisions have been included in a global fit. Especially, the CMS dijets play an important role in constraining the nuclear effects in gluon distributions. With the inclusion of also neutrino–nucleus deeply-inelastic scattering and pion–nucleus Drell–Yan data and a proper treatment of isospin-corrected data, we were able to free the flavor dependence of the valence and sea quark nuclear modifications for the first time. This gives us less biased, yet larger, flavor by flavor uncertainty estimates. …

Predictions for cold nuclear matter effects in p+Pb collisions at sNN=8.16 TeV

Predictions for cold nuclear matter effects on charged hadrons, identified light hadrons, quarkonium and heavy flavor hadrons, Drell–Yan dileptons, jets, photons, gauge bosons and top quark pairs produced in p +Pb collisions at sNN=8.16 TeV are compiled and, where possible, compared to each other. Predictions of the normalized ratios of p +Pb to p+p cross sections are also presented for most of the observables, providing new insights into the expected role of cold nuclear matter effects. In particular, the role of nuclear parton distribution functions on particle production can now be probed over a wider range of phase space than ever before.

Revisiting the D-meson hadroproduction in general-mass variable flavour number scheme

We introduce a novel realization of the open heavy-flavour hadroproduction in general-mass variable flavour number scheme at next-to-leading order in perturbative QCD. The principal novelty with respect to the earlier works is in the treatment of small-transverse-momentum limit, which has been a particularly challenging kinematic region in the past. We show that by a suitable choice of scheme, it is possible to obtain a well-behaved description of the open heavy-flavour hadroproduction cross sections from zero up to asymptotically high transverse momentum. We contrast our calculation with the available D$^0$-meson data as measured by the LHCb and ALICE collaborations at the LHC, finding a v…

Heavy-flavour production in the SACOT-mT scheme

The hadroproduction of heavy-flavoured mesons has recently attracted a growing interest e.g. within the people involved in global analysis of proton and nuclear parton distribution functions, saturation physics, and physics of cosmic rays. In particular, the D- and B-meson measurements of LHCb at forward direction are sensitive to gluon dynamics at small $x$ and are one of the few perturbative small-$x$ probes before the next generation deep-inelastic-scattering experiments. In this talk, we will concentrate on the collinear-factorization approach to inclusive D-meson production and describe a novel implementation --- SACOT-$m_{\rm T}$ --- of the general-mass variable flavour number scheme …

Heavy flavour production in the SACOT-$m_{\rm T}$ scheme

The hadroproduction of heavy-flavoured mesons has recently attracted a growing interest e.g. within the people involved in global analysis of proton and nuclear parton distribution functions, saturation physics, and physics of cosmic rays. In particular, the D- and B-meson measurements of LHCb at forward direction are sensitive to gluon dynamics at small $x$ and are one of the few perturbative small-$x$ probes before the next generation deep-inelastic-scattering experiments. In this talk, we will concentrate on the collinear-factorization approach to inclusive D-meson production and describe a novel implementation - SACOT-$m_{\rm T}$ - of the general-mass variable flavour number scheme (GM-…

EPS09 - a New Generation of NLO and LO Nuclear Parton Distribution Functions

We present a next-to-leading order (NLO) global DGLAP analysis of nuclear parton distribution functions (nPDFs) and their uncertainties. Carrying out an NLO nPDF analysis for the first time with three different types of experimental input -- deep inelastic $\ell$+A scattering, Drell-Yan dilepton production in p+$A$ collisions, and inclusive pion production in d+Au and p+p collisions at RHIC -- we find that these data can well be described in a conventional collinear factorization framework. Although the pion production has not been traditionally included in the global analyses, we find that the shape of the nuclear modification factor $R_{\rm dAu}$ of the pion $p_T$-spectrum at midrapidity …

Bayesian PDF reweighting meets the Hessian methods

Volume: 273 New data coming from the LHC experiments have a potential to extend the current knowledge of parton distribution functions (PDFs). As a short cut to the cumbersome and time consuming task of performing a new PDF fit, re weighting methods have been proposed. In this talk, we introduce the so-called Hessian re-weighting, valid for PDF fits that carried out a Hessian error analysis, and compare it with the better-known Bayesian methods. We determine the existence of an agreement between the two approaches, and illustrate this using the inclusive jet production at the LHC. Peer reviewed

An improved global analysis of nuclear parton distribution functions including RHIC data

We present an improved leading-order global DGLAP analysis of nuclear parton distribution functions (nPDFs), supplementing the traditionally used data from deep inelastic lepton-nucleus scattering and Drell-Yan dilepton production in proton-nucleus collisions, with inclusive high-$p_T$ hadron production data measured at RHIC in d+Au collisions. With the help of an extended definition of the $\chi^2$ function, we now can more efficiently exploit the constraints the different data sets offer, for gluon shadowing in particular, and account for the overall data normalization uncertainties during the automated $\chi^2$ minimization. The very good simultaneous fit to the nuclear hard process data…

Towards EPPS21 nuclear PDFs

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.

A QCD analysis of LHCb D-meson data in p plus Pb collisions

We scrutinize the recent LHCb data for D$^0$-meson production in p+Pb collisions within a next-to-leading order QCD framework. Our calculations are performed in the SACOT-$m_{\rm T}$ variant of the general-mass variable-flavour-number scheme (GM-VFNS), which has previously been shown to provide a realistic description of the LHC p+p data. Using the EPPS16 and nCTEQ15 nuclear parton distribution functions (PDFs) we show that a very good agreement is obtained also in the p+Pb case both for cross sections and nuclear modification ratios in the wide rapidity range covered by the LHCb data. Encouraged by the good correspondence, we quantify the impact of these data on the nuclear PDFs by the Hes…

A Global DGLAP analysis of nuclear PDFs

In this talk, we shortly report results from our recent global DGLAP analysis of nuclear parton distributions. This is an extension of our former EKS98-analysis improved with an automated χ2 minimization procedure and uncertainty estimates. Although our new analysis show no significant deviation from EKS98, a sign of a significantly stronger gluon shadowing could be seen in the RHIC BRAHMS data. nonPeerReviewed

Nuclear PDF constraints from p+Pb collisions at the LHC

As the current nuclear PDF analyses are mainly constrained by fixed-target Drell-Yan and deeply inelastic scattering data only the quark nuclear modifications at fairly large $x$ values are in a good control. Inclusive pion production in d+Au collisions at RHIC provides some constraints for gluons but due to the limited kinematic reach of the data the gluon modifications remain uncertain especially at small values of $x$. In this talk, we discuss how the existing data from p+Pb collisions at the LHC can improve the nuclear PDF fits and which measurements would be sensitive to the small-$x$ gluons. In particular, we consider inclusive hadron production, compare this to direct photons, and sh…

Double D-meson production in proton-proton and proton-lead collisions at the LHC

We consider the simultaneous production of two heavy-flavoured hadrons - particularly D mesons - at the LHC. We base our calculations on collinearly factorized QCD at next-to-leading order, using the contemporary parton distribution functions and D-meson fragmentation functions. The contributions of double-parton scatterings are included in the approximation of independent partonic interactions. Our framework benchmarks well with the available proton-proton data from the LHCb collaboration giving us confidence to make predictions for proton-lead collisions. Our results indicate that the double D-meson production in proton-lead collisions should be measurable at the LHCb kinematics with the …

B-meson hadroproduction in the SACOT-$m_{\rm T}$ scheme

We apply the SACOT-$m_{\rm T}$ general-mass variable flavour number scheme (GM-VFNS) to the inclusive B-meson production in hadronic collisions at next-to-leading order in perturbative Quantum Chromodynamics. In the GM-VFNS approach one matches the fixed-order heavy-quark production cross sections, accurate at low transverse momentum ($p_{\rm T}$), with the zero-mass cross sections, accurate at high $p_{\rm T}$. The physics idea of the SACOT-$m_{\rm T}$ scheme is to do this by accounting for the finite momentum transfer required to create a heavy quark-antiquark pair throughout the calculation. We compare our results with the latest LHC data from proton-proton and proton-lead collisions fin…

A perturbative QCD study of dijets in p+Pb collisions at the LHC

Inspired by the recent measurements of the CMS collaboration, we report a QCD study of dijet production in proton+lead collisions at the LHC involving large-transverse-momentum jets, $p_T \gtrsim 100$ GeV. Examining the inherent uncertainties of the next-to-leading order perturbative QCD calculations and their sensitivity to the free proton parton distributions (PDFs), we observe a rather small, typically much less than 5% clearance for the shape of the dijet rapidity distribution within approximately 1.5 units around the midrapidity. Even a more stable observable is the ratio between the yields in the positive and negative dijet rapidity, for which the baseline uncertainty can be made negl…

Neutron-skin effect and centrality dependence of high-pT observables in nuclear collisions

We report on our studies of the neutron-skin effects in high-pT observables at the LHC. We study the impact of the neutron-skin effect on the centrality dependence of inclusive direct photon, highpT hadron and W± production in nuclear collisions at the LHC. The neutron-skin effect refers to the observation that in spherical heavy nuclei, the tail of the neutron distribution extends farther than the distribution of protons, which can affect observables sensitive to electroweak phenomena in very peripheral collisions. We quantify this effect for direct photons, charged hadrons and W bosons as a function of the collision centrality. In the case of direct photons we find that it will be difficu…

Constraining nPDFs with inclusive pions and direct photons at forward rapidities in p+Pb collisions at the LHC

Abstract In this talk, we present NLO pQCD predictions for inclusive pion and direct photon nuclear modifications in p + Pb collisions at mid- and forward rapidities at the LHC. In addition to the minimum bias predictions, we also address the centrality dependence with spatially dependent nuclear PDFs. To understand which regions of the nuclear momentum fraction x 2 these observables predominantly probe, we present also the underlying x 2 distributions at different rapidities. We are led to conclude that the isolated photons at forward rapidities are more sensitive to the small- x 2 dynamics than the inclusive pions.

Constraints for nuclear PDFs from the LHCb D-meson data

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 …

Nuclear gluons at RHIC in a multi-observable approach

We explore the possibility of measuring nuclear gluon distributions at the Relativistic Heavy-Ion Collider (RHIC) with $\sqrt{s}=200 \, {\rm GeV}$ proton-nucleus collisions. In addition to measurements at central rapidity, we consider also observables at forward rapidity, consistent with proposed upgrades to the experimental capabilities of STAR and sPHENIX. The processes we consider consist of Drell-Yan dilepton, dijet, and direct photon-jet production. The Drell-Yan process is found to be an efficient probe of gluons at small momentum fractions. In order to fully utilize the potential of Drell-Yan measurements we demonstrate how the overall normalization uncertainty present in the experim…

Impact of CMS dijets in 5.02 TeV pPb and pp collisions on EPPS16 nuclear PDFs

The CMS measurement of dijet pseudorapidity distributions in pPb versus pp collisions at 5.02 TeV provides a direct probe on nuclear gluon PDFs. We show that while the predicted pPb pseudorapidity distributions suffer from sizable free-proton PDF uncertainties, the ratios of the pPb and pp distributions are practically insensitive to scale and free-proton PDF choices. We find the CMS data on pPb to pp ratios to be in good agreement with the EPPS16 nuclear modifications. Using a non-quadratic extension of the Hessian PDF reweighting method, we study the impact of these data on the EPPS16 nuclear PDFs. Relative to EPPS16, we find stronger evidence for mid-x gluon antishadowing as well as indi…

Predictions for exclusive $\Upsilon$ photoproduction in ultraperipheral ${\rm Pb}+{\rm Pb}$ collisions at the LHC at next-to-leading order in perturbative QCD

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 ac…

Pion–nucleus Drell–Yan data as a novel constraint for nuclear PDFs

We have studied the prospects of using the Drell-Yan dilepton process in pion-nucleus collisions as a novel input in the global analysis of nuclear parton distribution functions (nPDFs). In a NLO QCD framework, we find the measured nuclear cross-section ratios from the NA3, NA10 and E615 experiments to be largely insensitive to the pion parton distributions and also compatible with the EPS09 and nCTEQ15 nPDFs. These data sets can thus be, and in EPPS16 have been, included in global nPDF analyses without introducing significant new theoretical uncertainties or tension with the other data. In particular, we explore the constraining power of these data sets on the possible flavour asymmetry in…

Nuclear PDFs from the LHeC perspective

We study the prospects for constraining the nuclear parton distribution functions by small-x deep inelastic scattering. Performing a global fit of nuclear parton distribution functions including a sample of pseudodata representing expected measurements at the planned LHeC collider, we demonstrate that the accuracy of the present nuclear parton distributions could be be improved substantially. We also discuss the impact of flavour-tagged data.

Neutron skin and centrality classification in high-energy heavy-ion collisions at the LHC

The concept of centrality in high-energy nuclear collisions has recently become a subject of an active debate. In particular, the experimental methods to determine the centrality that have given reasonable results for many observables in high-energy lead-lead collisions at the LHC have led to surprising behaviour in the case of proton-lead collisions. In this letter, we discuss the possibility to calibrate the experimental determination of centrality by asymmetries caused by mutually different spatial distributions of protons and neutrons inside the nuclei --- a well-known phenomenon in nuclear physics known as the neutron-skin effect.