Nuclear Parton Distribution Functions Research Articles

Nuclear Parton Distribution Functions After the First Decade of LHC Data

We present a review of the conceptual basis, current knowledge, and recent progress regarding global analysis of nuclear parton distribution functions (PDFs). After introducing the theoretical foundations and methodological approaches for the extraction of nuclear PDFs from experimental data, we discuss how different measurements in fixed-target and collider experiments provide increasingly precise constraints on various aspects of nuclear PDFs, including shadowing, antishadowing, the EMC effect, Fermi motion, flavor separation, deuteron binding, and target-mass and other higher-twist effects. Particular emphasis is given to measurements carried out in proton–lead collisions at the Large Hadron Collider, which have revolutionized the global analysis during the past decade. These measurements include electroweak boson, jet, light hadron, and heavy flavor observables. Finally, we outline the expected impact of the future Electron Ion Collider and discuss the role and interplay of nuclear PDFs with other branches of nuclear, particle, and astroparticle physics.

Predictions for exclusive varUpsilon photoproduction in ultraperipheral {textrm{Pb}}+{textrm{Pb}} collisions at the LHC at next-to-leading order in perturbative QCD

We present predictions for the rapidity-differential cross sections of exclusive varUpsilon 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). Our direct NLO predictions depend significantly on nPDF uncertainties and on the choices of the factorization and renormalization scales, but to a much lesser degree on GPD modeling. 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 {textrm{Pb}}+{textrm{Pb}} collisions at the LHC.

Measurement of the Z boson production cross-section in proton-lead collisions at sqrt{s_{textrm{NN}}} = 8.16 TeV

This article presents the first measurement of the differential Z-boson production cross-section in the forward region using proton-lead collisions with the LHCb detector. The dataset was collected at a nucleon-nucleon centre-of-mass energy of sqrt{s_{textrm{NN}}} = 8.16 TeV in 2016, corresponding to an integrated luminosity of 30.8 nb−1. The forward-backward ratio and the nuclear modification factors are measured together with the differential cross-section as functions of the Z boson rapidity in the centre-of-mass frame, the transverse momentum of the Z boson and a geometric variable ϕ*. The results are in good agreement with the predictions from nuclear parton distribution functions, providing strong constraining power at small Bjorken-x.

W±-boson production in p–Pb collisions at sqrt{s_{textrm{NN}}} = 8.16 TeV and Pb–Pb collisions at sqrt{s_{textrm{NN}}} = 5.02 TeV

The production of the W± bosons measured in p–Pb collisions at a centre-of-mass energy per nucleon–nucleon collision sqrt{s_{textrm{NN}}} = 8.16 TeV and Pb–Pb collisions at sqrt{s_{textrm{NN}}} = 5.02 TeV with ALICE at the LHC is presented. The W± bosons are measured via their muonic decay channel, with the muon reconstructed in the pseudorapidity region −4 < {eta}_{textrm{lab}}^{mu } < −2.5 with transverse momentum {p}_{textrm{T}}^{mu } > 10 GeV/c. While in Pb–Pb collisions the measurements are performed in the forward (2.5 < {y}_{textrm{cms}}^{mu } < 4) rapidity region, in p–Pb collisions, where the centre-of-mass frame is boosted with respect to the laboratory frame, the measurements are performed in the backward (−4.46 < {y}_{textrm{cms}}^{mu } < −2.96) and forward (2.03 < {y}_{textrm{cms}}^{mu } < 3.53) rapidity regions. The W− and W+ production cross sections, lepton-charge asymmetry, and nuclear modification factors are evaluated as a function of the muon rapidity. In order to study the production as a function of the p–Pb collision centrality, the production cross sections of the W− and W+ bosons are combined and normalised to the average number of binary nucleon–nucleon collision 〈Ncoll〉. In Pb–Pb collisions, the same measurements are presented as a function of the collision centrality. Study of the binary scaling of the W±-boson cross sections in p–Pb and Pb–Pb collisions is also reported. The results are compared with perturbative QCD calculations, with and without nuclear modifications of the Parton Distribution Functions (PDFs), as well as with available data at the LHC. Significant deviations from the theory expectations are found in the two collision systems, indicating that the measurements can provide additional constraints for the determination of nuclear PDFs and in particular of the light-quark distributions.

Numerical evaluation of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu evolution equations for nuclear parton distribution functions

We numerically study for the first time the nonlinear GLR-MQ evolution equations for nuclear parton distribution function (nPDFs) to next-to-leading order accuracy and quantify the impact of gluon recombination at small $x$. Using the nCTEQ15 nPDFs as input, we confirm the importance of the nonlinear corrections for small $x \lesssim 10^{-3}$, whose magnitude increases with a decrease of $x$ and an increase of the atomic number $A$. We find that at $x=10^{-5}$ and for heavy nuclei, after the upward evolution from $Q_0=2$ GeV to $Q=10$ GeV, the quark singlet $\Omega(x,Q^2)$ and the gluon $G(x,Q^2)$ distributions become reduced by $9-15$%, respectively. The relative effect is much stronger for the downward evolution from $Q_0=10$ GeV to $Q=2$ GeV, where we find that $\Omega(x,Q^2)$ is suppressed by 40%, while $G(x, Q^2)$ is enhanced by 140%. These trends propagate into the $F_2^A(x,Q^2)$ nuclear structure function and the $F_L^A(x,Q^2)$ longitudinal structure function, which after the downward evolution become reduced by 45% and enhanced by 80%, respectively. Our analysis indicates that the nonlinear effects are most pronounced in $F_L^A(x,Q^2)$ and are already quite sizable at $x \sim 10^{-3}$ for heavy nuclei. We have checked that our conclusions very weakly depend on the choice of input nPDFs. In particular, using the EPPS21 nPDFs as input, we obtain quantitatively similar results.

Understanding the initial state effects by the measurement of the Drell-Yan process in pPb collisions with CMS

The Drell-Yan process is considered as an essential probe to understand initial-state protons, usually described by the parton distribution functions (PDFs) for stand-alone protons and by the nuclear PDFs (nPDFs) for protons confined in the nucleus. In the LHC era, Z and W boson production in pPb and PbPb collisions have been used to investigate the initial-state effects. In this presentation, we report results for the Drell-Yan process in pPb collisions at a center-of-mass energy of 8.16 TeV with the CMS detector. Differential cross sections are presented as functions of dimuon pT, rapidity and ϕ∗ in a wider dimuon mass region which includes not only the Z boson mass range but also the lower mass region down to 15 GeV. In addition, the forward-backward asymmetries are shown in both mass regions, and the uncertainties are found to be smaller than in the model calculations. The results in the Z mass region are the most precise to date, while the measurements in the lower mass region allow access to a new phase space of nPDF studies at a lower longitudinal momentum fraction x and lower energy scale Q2. The results are compared to the EPPS16 and nCTEQ15WZ nPDFs, and the free-proton PDF CT14. An improved understanding of the nuclear PDF and the modeling of pPb collisions is achieved.

Impact of parton energy loss and nPDFs on J/ψ production in proton-nucleus collisions

The impact of parton energy loss and nuclear parton distribution functions (nPDFs) on J/ψ production in proton-nucleus collisions are investigated by means of the E866, LHC and RHIC experimental data. By the recent EPPS21 nPDFs, a leading order phenomenological analysis of J/ψ production cross-section ratios is performed for E866 experimental data with considering the parton energy loss effect following Landau-Pomeranchuk-Migdal (LPM) regime. The gluon transport coefficient qˆg extracted from the E866 data in 0.20<xF<0.65 region is qˆg=0.35±0.01 GeV2/fm with χ2/ndf=1.01, which indicates that the significantly better-constrained gluon distributions provided by EPPS21 contribute to accurately determining the gluon energy loss. It is founded that for E866 data in 0.20<xF<0.65 the depletion induced by cc¯ energy loss is the largest, gluon energy loss is the second, and quark energy loss is the smallest. In addition, it can be seen that for LHC and RHIC experiment the role of nPDFs and gluon energy loss on J/ψ production are both significant, which indicates that operating more precise measurements at LHC and RHIC in the future can facilitate significantly better-constrained gluon energy loss and nPDFs.

Compatibility of neutrino DIS data and its impact on nuclear parton distribution functions

In global analyses of nuclear parton distribution functions (nPDFs), neutrino deep-inelastic scattering (DIS) data have been argued to exhibit tensions with the data from charged-lepton DIS. Using the nCTEQ framework, we investigate these possible tensions both internally and with the data sets used in our recent nPDF analysis nCTEQ15WZSIH. We take into account nuclear effects in the calculation of the deuteron structure function $F_2^D$ using the CJ15 analysis. The resulting nPDF fit, nCTEQ15WZSIHdeut, serves as the basis for our comparison with inclusive neutrino DIS and charm dimuon production data. Using $\chi^2$ hypothesis testing, we confirm evidence of tensions with these data and study the impact of the proton PDF baseline as well as the treatment of data correlation and normalization uncertainties. We identify the experimental data and kinematic regions that generate the tensions and present several possible approaches how a consistent global analysis with neutrino data can be performed. We show that the tension can be relieved using a kinematic cut at low $x$ ($x>0.1$) and also investigate a possibility of managing the tensions by using uncorrelated systematic errors. Finally, we present a different approach identifying a subset of neutrino data which leads to a consistent global analysis without any additional cuts. Understanding these tensions between the neutrino and charged-lepton DIS data is important not only for a better flavor separation in global analyses of nuclear and proton PDFs, but also for neutrino physics and for searches for physics beyond the Standard Model.

Inclusive and diffractive dijet photoproduction in ultraperipheral heavy ion collisions at the LHC

We calculate the cross section of inclusive dijet photoproduction in ultraperipheral collisions (UPCs) of heavy ions at the CERN Large Hadron Collider using next-to-leading order perturbative QCD and demonstrate that it provides a good description of the ATLAS data. We study the role of this data in constraining nuclear parton distribution functions (nPDFs) using the Bayesian reweighting technique and find that it can reduce current uncertainties of nPDFs at small x by a factor of 2. We also make predictions for diffractive dijet photoproduction in UPCs and examine its potential to shed light on the disputed mechanism of QCD factorization breaking in diffraction.

Impact of W and Z Production Data and Compatibility of Neutrino DIS Data in Nuclear Parton Distribution Functions

Vector boson production and neutrino deep-inelastic scattering (DIS) data are crucial for constraining the strange quark parton distribution function (PDF) and more generally for flavor decomposition in PDF extractions. We extend the nCTEQ15 nuclear PDFs (nPDFs) by adding the recent W and Z production data from the LHC in a global nPDF fit. The new nPDF set, referred to as nCTEQ15WZ, is used as a starting point for a follow-up study in which we assess the compatibility of neutrino DIS data with charged lepton DIS data. Specifically, we re-analyze neutrino DIS data from NuTeV, Chorus, and CDHSW, as well as dimuon data from CCFR and NuTeV. To scrutinize the level of compatibility, different kinematic regions of the neutrino data are investigated. Fits to the neutrino data alone and a preliminary global fit are performed and compared to nCTEQ15WZ.

Constraining the nuclear gluon PDF with inclusive hadron production data

The nuclear parton distribution functions (nPDFs) of gluons are known to be difficult to determine with fits of deep inelastic scattering (DIS) and Drell-Yan (DY) data alone. Therefore, the nCTEQ15 analysis of nuclear PDFs added inclusive neutral pion production data from RHIC to help in constraining the gluon. In this analysis, we present a new global analysis of nuclear PDFs based on a much larger set of single inclusive light hadron data from RHIC and the LHC. Using our new nCTEQ code (nCTEQ++) with an optimized version of INCNLO we study systematically the limitations of the theory and the impact of the fragmentation function uncertainty.

Impact of heavy quark and quarkonium data on nuclear gluon PDFs

A clear understanding of nuclear parton distribution functions (nPDFs) plays a crucial role in the interpretation of collider data taken at the Relativistic Heavy Ion Collider (RHIC), the Large Hadron Collider (LHC) and in the near future at the Electron-Ion Collider (EIC). Even with the recent inclusions of vector boson and light meson production data, the uncertainty of the gluon PDF remains substantial and limits the interpretation of heavy ion collision data. To obtain new constraints on the nuclear gluon PDF, we extend our recent nCTEQ15WZ+SIH analysis to inclusive quarkonium and open heavy-flavor meson production data from the LHC. This vast new data set covers a wide kinematic range and puts strong constraints on the nuclear gluon PDF down to $x\lesssim 10^{-5}$. The theoretical predictions for these data sets are obtained from a data-driven approach, where proton-proton data are used to determine effective scattering matrix elements. This approach is validated with detailed comparisons to existing next-to-leading order (NLO) calculations in non-relativistic QCD (NRQCD) for quarkonia and in the general-mass variable-flavor-number scheme (GMVFNS) for the open heavy-flavored mesons. In addition, the uncertainties from the data-driven approach are determined using the Hessian method and accounted for in the PDF fits. This extension of our previous analyses represents an important step toward the next generation of PDFs not only by including new data sets, but also by exploring new methods for future analyses.

NNLO nuclear parton distribution functions with electroweak-boson production data from the LHC

We present new sets of nuclear parton distribution functions (nPDFs) at next-to-leading order and next-to-next-to-leading order in perturbative QCD. Our analyses are based on deeply inelastic scattering data with charged-lepton and neutrino beams on nuclear targets, and experimental data from measurements of ${W}^{\ifmmode\pm\else\textpm\fi{}},Z$ boson production in $\mathrm{p}+\mathrm{Pb}$ collisions at the LHC. In addition, a set of proton baseline PDFs is fitted within the same framework and with the same theoretical assumptions. The results of our global QCD analysis are compared to existing nPDF sets and to the previous nPDF set TUJU19, which was based on deep-inelastic scattering data only. Our work is performed using an open-source tool, xFitter, and the required extensions of the code are discussed as well. We find good agreement with the data included in the fit and a lower value for ${\ensuremath{\chi}}^{2}/{N}_{\mathrm{dp}}$ when performing the fit at next-to-next-to-leading order. We apply the resulting nuclear PDFs to electroweak boson production in $\mathrm{Pb}+\mathrm{Pb}$ collisions at the LHC and compare the results to the most recent data from ATLAS and CMS.

Imaging nuclear modifications on parton distributions with triple-differential dijet cross sections in proton-nucleus collisions

Dijet production in proton-nucleus ($p$A) collisions at the LHC provides invaluable information on the underlying parton distributions in nuclei, especially the gluon distributions. Triple-differential dijet cross sections enable a well-controlled kinematic scan (over momentum fraction $x$ and probing scale $Q^2$) of the nuclear parton distribution functions (nPDFs), i.e., $f^\textrm{A}_i(x,Q^2)$. In this work, we study several types of triple-differential cross sections for dijet production in proton-proton ($pp$) and proton-lead ($p$Pb) collisions at the LHC, to next-to-leading order within the framework of perturbative quantum chromodynamics (pQCD). Four sets of nPDF parametrizations, EPPS16, nCTEQ15, TUJU19, and nIMParton16 are employed in the calculations for $p$Pb collisions. We show that the observable nuclear modification factor $R_{p\textrm{Pb}}$ of such cross sections can serve as a nice image of the nuclear modifications on parton distributions, quantified by the ratio $r^{\textrm{A}}_i(x,Q^2)\!=\!f^\textrm{A,proton}_i(x,Q^2)/f^\textrm{proton}_i(x,Q^2)$. Considerable differences among the $R_{p\textrm{Pb}}$ predicted by the four nPDF sets can be observed and intuitively understood. Future measurements of such observables are expected to not only constrain the nPDF parametrizations, but also help confirm various nuclear effects, e.g., shadowing, anti-shadowing, EMC, and Fermi motion in different regions of $x$ and their variations with probing scale $Q^2$.

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: 5 TeV double-differential CMS dijet and LHCb D-meson data, as well as 8 TeV 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.

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

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.

Nuclear modification factor of light neutral-meson spectra up to high transverse momentum in p–Pb collisions at [formula omitted] TeV

Neutral pion (π0) and η meson production cross sections were measured up to unprecedentedly high transverse momenta (pT) in p–Pb collisions at sNN=8.16TeV. The mesons were reconstructed via their two-photon decay channel in the rapidity interval −1.3<y<0.3 in the ranges of 0.4<pT<200 GeV/c and 1.0<pT<50 GeV/c, respectively. The respective nuclear modification factor (RpPb) is presented for pT up to of 200 and 30 GeV/c, where the former was achieved by extending the π0 measurement in pp collisions at s=8TeV using the merged cluster technique. The values of RpPb are below unity for pT<10 GeV/c, while they are consistent with unity for pT>10 GeV/c, leaving essentially no room for final state energy loss. The new data provide strong constraints for nuclear parton distribution and fragmentation functions over a broad kinematic range and are compared to model predictions as well as previous results at sNN=5.02TeV.

Isovector EMC Effect from Global QCD Analysis with MARATHON Data

We report the results of a MonteCarlo global QCD analysis of unpolarized parton distribution functions (PDFs), including for the first time constraints from ratios of ^{3}He to ^{3}H structure functions recently obtained by the MARATHON experiment at Jefferson Lab. Our simultaneous analysis of nucleon PDFs and nuclear effects in A=2 and A=3 nuclei reveals the first indication for an isovector nuclear EMC effect in light nuclei. We find that while the MARATHON data yield relatively weak constraints on the F_{2}^{n}/F_{2}^{p} neutron to proton structure function ratio and on the d/u PDF ratio, they suggest an enhanced nuclear effect on the d-quark PDF in the bound proton, questioning the assumptions commonly made in nuclear PDF analyses.

Impact of inclusive hadron production data on nuclear gluon PDFs

A precise knowledge of nuclear parton distribution functions (nPDFs) is---among other things---important for the unambiguous interpretation of hard process data taken in $pA$ and $AA$ collisions at the Relativistic Heavy Ion Collider (RHIC) and the LHC. The available fixed target data for deep inelastic scattering (DIS) and Drell-Yan (DY) lepton pair production mainly constrain the light quark distributions. It is hence crucial to include more and more collider data in global analyses of nPDFs in order to better pin down the different parton flavors, in particular the gluon distribution at small $x$. To help constrain the nuclear gluon PDF, we extend the nCTEQ15 analysis by including single inclusive hadron (SIH) production data from RHIC (PHENIX and STAR) and LHC (ALICE). In addition to the DIS, DY, and SIH datasets, we will also include LHC $W/Z$ production data. As the SIH calculation is dependent on hadronic fragmentation functions (FFs), we use a variety of FFs available in the literature to properly estimate this source of uncertainty. We study the impact of these data on the PDFs and compare with both the nCTEQ15 and nCTEQ15WZ sets. The calculations are performed using a new implementation of the nCTEQ code (ncteq++) including a modified version of incnlo, which allows faster calculations using precomputed grids. The extension of the nCTEQ15 analysis to include the SIH data represents an important step toward the next generation of PDFs.

Centrality dependence of electroweak boson production in PbPb collisions at the CERN Large Hadron Collider

Recent data on the nuclear modification of W and Z boson production measured by the ATLAS collaboration in PbPb collisions at $\sqrt{s_{\rm nn}}=5.02$ TeV show an enhancement in peripheral collisions, seemingly contradicting predictions of the Glauber model. The data were previously explained by arguing that the nucleon-nucleon cross section may be shadowed in nucleus-nucleus collisions, and hence suppressed compared to the proton-proton cross section at the same collision energy. This interpretation has quite significant consequences for the understanding of heavy-ion data, in particular in the context of the Glauber model. Instead, we provide an alternative explanation of the data by assuming that there is a mild bias present in the centrality determination of the measurement; on the size of the related systematic uncertainty. Using this assumption, we show that the data is in agreement with theoretical calculations using nuclear parton distribution functions. Finally, we speculate that the centrality dependence of the W$^-$/W$^{+}$ ratio may point to the relevance of a larger skin thickness of the Pb nucleus, which, if present, would result in a few percent larger PbPb cross section than currently accounted for in the Glauber model and may hence be the root of the centrality bias.