Nuclear Parton Distribution Research Articles

Nuclear suppression of coherent J/ψ photoproduction in heavy-ion ultraperipheral collisions and leading twist nuclear shadowing

We determine the nuclear suppression factor SPb(x), where x=MJ/ψ2/Wγp2 with MJ/ψ the J/ψ mass and Wγp the photon-nucleon energy, for the cross section of coherent J/ψ photoproduction in heavy-ion ultraperipheral collisions at the Large Hadron Collider and Relativistic Heavy Ion Collider by performing the χ2 fit to all available data on the cross section dσAA→J/ψAA/dy as a function of the J/ψ rapidity y and the photoproduction cross section σγA→J/ψA(Wγp) as a function of Wγp. We find that while the dσAA→J/ψAA/dy data alone constrain SPb(x) for x≥10−3, the combined dσAA→J/ψAA/dy and σγA→J/ψA(Wγp) data allow us to determine SPb(x) in the wide interval 10−5<x<0.05. In particular, the data favor SPb(x), which decreases with a decrease of x in the 10−4<x<0.01 interval and can be both decreasing or constant for x<10−4. Identifying SPb(x) with the ratio of the gluon distributions in Pb and the proton Rg(x,Q02)=gA(x,Q02)/[Agp(x,Q02)], we demonstrate that the leading twist approximation for nuclear shadowing provides a good description of all the data on dσAA→J/ψAA/dy and σγA→J/ψA(Wγp) as well as on the experimental values for SPb(x) derived from σγA→J/ψA(Wγp). We also show that modern nuclear parton distributions reasonably reproduce SPb(x) as well. Published by the American Physical Society 2024

Dimuons from neutrino-nucleus collisions in the semi-inclusive DIS approach

We present a next-to-leading order perturbative QCD calculation of dimuon production in neutrino-nucleus collisions. This process is typically calculated by assuming it to be proportional to inclusive charm production, which requires an effective acceptance correction to take the experimental cuts on the decay-muon kinematics into account. Here, we instead compute the dimuon production cross section directly as a convolution of semi-inclusive deep inelastic scattering to produce charmed hadrons, and a decay function fitted to e+e− data to produce a muon from the charmed hadrons. The presented approach is in a good agreement with available experimental data and will serve as a starting point for higher-order QCD calculations without an external acceptance correction. The uncertainties arising from the decay function and scale dependence are sizeably smaller than those from the nuclear parton distribution functions. We also calculate the effective acceptances within our approach and compare them to those usually used in global fits of parton distribution functions, finding differences of the order of 10 %, depending on the kinematics, perturbative order, and applied parton distributions.

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.

Measurement of the Prompt D^{0} Nuclear Modification Factor in p-Pb Collisions at sqrt[s_{NN}]=8.16 TeV.

The production of prompt D^{0} mesons in proton-lead collisions in both the forward and backward rapidity regions at a center-of-mass energy per nucleon pair of sqrt[s_{NN}]=8.16 TeV is measured by the LHCb experiment. The nuclear modification factor of prompt D^{0} mesons is determined as a function of the transverse momentum p_{T}, and the rapidity in the nucleon-nucleon center-of-mass frame y^{*}. In the forward rapidity region, significantly suppressed production with respect to pp collisions is measured, which provides significant constraints on models of nuclear parton distributions and hadron production down to the very low Bjorken-x region of ∼10^{-5}. In the backward rapidity region, a suppression with a significance of 2.0-3.8 standard deviations compared to parton distribution functions in a nuclear environment expectations is found in the kinematic region of p_{T}>6 GeV/c and -3.25<y^{*}<-2.5, corresponding to x∼0.01.

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.

Neutrino structure functions from GeV to EeV energies

The interpretation of present and future neutrino experiments requires accurate theoretical predictions for neutrino-nucleus scattering rates. Neutrino structure functions can be reliably evaluated in the deep-inelastic scattering regime within the perturbative QCD (pQCD) framework. At low momentum transfers (Q2 ≲ few GeV2), inelastic structure functions are however affected by large uncertainties which distort event rate predictions for neutrino energies Eν up to the TeV scale. Here we present a determination of neutrino inelastic structure functions valid for the complete range of energies relevant for phenomenology, from the GeV region entering oscillation analyses to the multi-EeV region accessible at neutrino telescopes. Our NNSFν approach combines a machine-learning parametrisation of experimental data with pQCD calculations based on state-of-the-art analyses of proton and nuclear parton distributions (PDFs). We compare our determination to other calculations, in particular to the popular Bodek-Yang model. We provide updated predictions for inclusive cross sections for a range of energies and target nuclei, including those relevant for LHC far-forward neutrino experiments such as FASERν, SND@LHC, and the Forward Physics Facility. The NNSFν determination is made available as fast interpolation LHAPDF grids, and it can be accessed both through an independent driver code and directly interfaced to neutrino event generators such as GENIE.

Systematic studies on the nuclear parton distribution with photon and hadron productions in nuclear collisions at the LHC* *Supported by the National Key Research and Development Program of China (2018YFE0104700, 2018YFE0104800), the National Natural Science Foundation of China (12061141008, 12175085), and the Fundamental Research Funds for the Central Universities ( CCNU220N003)

A systematic study on the impact of widely-used nuclear-modified parton distribution function (nPDF) parameterizations on the production of direct photons and charged hadrons is performed by employing a next-to-leading order Monte Carlo event generator JETPHOX in hadronic collisions at LHC energies. The nuclear modification factors of photon and charged hadron productions are studied in three types of collision systems, i.e., small ( and ), medium , and large , in a wide rapidity acceptance. The results illustrate that the direct photon production process is a sensitive probe to decipher the difference of the nPDF parameterization implementations, which provides new insights for the experimental measurements to refine the nuclear modifications of the parton distributions. To provide a benchmark for searching for quark gluon plasma in the upcoming small system measurements at LHC energies, we carry out detailed studies on the cold nuclear matter effect in collisions. Our outcomes show that the cold nuclear matter effects are negligible for the charged hadron production in collisions, which can be used as a baseline to subtract the initial state contribution.

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.

Atomic mass, Bjorken variable, and scale dependence of quark transport coefficient in Drell-Yan process for proton incident on nucleus* *Supported in part by the National Natural Science Foundation of China (11975090, 11575052).

By means of the nuclear parton distributions determined without the fixed-target Drell-Yan experimental data and the analytic expression of quenching weight based on the BDMPS formalism, next-to-leading order analyses were performed on the Drell-Yan differential cross section ratios from the Fermilab E906 and E866 collaborations. It was found that the results calculated only with the nuclear effects of the parton distribution were not in agreement with the E866 and E906 experimental data. The incoming parton energy loss effect cannot be ignored in the nuclear Drell-Yan reactions. The predicted results indicate that, with the quark transport coefficient as a constant, the suppression due to the target nuclear geometry effect is approximately% for the quark transport coefficient. It was shown that we should consider the target nuclear geometry effect in studying the Drell-Yan reaction on nuclear targets. On the basis of the Bjorken variable and scale dependence of the quark transport coefficient, the atomic mass dependence was incorporated. The quark transport coefficient was determined as a function of the atomic mass, Bjorken variable, and scale by the global fit of the experimental data. The determined constant factor of the quark transport coefficient is GeV/fm. It was found that the atomic mass dependence has a significant impact on the constant factor in the quark transport coefficient in cold nuclear matter.

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.

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 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.

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.

NNNPDF3.0: evidence for a modified partonic structure in heavy nuclei

We present an updated determination of nuclear parton distributions (nPDFs) from a global NLO QCD analysis of hard processes in fixed-target lepton-nucleus and proton-nucleus together with collider proton-nucleus experiments. In addition to neutral- and charged-current deep-inelastic and Drell–Yan measurements on nuclear targets, we consider the information provided by the production of electroweak gauge bosons, isolated photons, jet pairs, and charmed mesons in proton-lead collisions at the LHC across centre-of-mass energies of 5.02 TeV (Run I) and 8.16 TeV (Run II). For the first time in a global nPDF analysis, the constraints from these various processes are accounted for both in the nuclear PDFs and in the free-proton PDF baseline. The extensive dataset underlying the nNNPDF3.0 determination, combined with its model-independent parametrisation, reveals strong evidence for nuclear-induced modifications of the partonic structure of heavy nuclei, specifically for the small-x shadowing of gluons and sea quarks, as well as the large-x anti-shadowing of gluons. As a representative phenomenological application, we provide predictions for ultra-high-energy neutrino-nucleon cross-sections, relevant for data interpretation at neutrino observatories. Our results provide key input for ongoing and future experimental programs, from that of heavy-ion collisions in controlled collider environments to the study of high-energy astrophysical processes.

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.