The neutrino deep inelastic scattering (DIS) data is very interesting for global analyses of proton and nuclear parton distribution functions (PDFs) since they provide crucial information on the strange quark distribution in the proton and allow for a better flavor decompositon of the PDFs. In order to use neutrino DIS data in a global analysis of proton PDFs nuclear effects need to be understood. We study these effects with the help of nuclear PDFs extracted from global analyses of charged-lepton DIS, Drell-Yan and neutrino DIS data at next-to-leading order in QCD.
We perform a global chi^2-analysis of nuclear parton distribution functions using data from charged current neutrino-nucleus deep-inelastic scattering (DIS), charged-lepton-nucleus DIS, and the Drell-Yan (DY) process. We show that the nuclear corrections in nu-A DIS are not compatible with the predictions derived from l^+A DIS and DY data. We quantify this result using a hypothesis-testing criterion based on the chi^2 distribution which we apply to the total chi^2 as well as to the chi^2 of the individual data sets. We find that it is not possible to accommodate the data from nu-A and l^+A DIS…
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 C…
The progress in constraining proton and nuclear parton distribution functions is briefly summarised. Some persistent uncertainties are pointed out and recent experimental advancements highlighted.
The associated production of direct photons and heavy quarks at the LHC is presented. Predictions for the nuclear modification factor to the cross-section at ALICE are shown. It is demonstrated that this process is a great probe of the gluon and heavy quark nuclear PDFs, as over 80 % of its nPDF dependence at NLO comes from those nPDFs. Therefore measurements of this process will provide an excellent constraint on the gluon nPDF, and will distinguish between different nPDF sets currently out on the market.
So far the nuclear PDFs (nPDFs) in the global DGLAP fits have been taken to be spatially independent. In this work, using the $A$-dependence of the globally fitted sets EPS09 and EKS98, we have determined the spatial dependence of the nPDFs in terms of powers of the nuclear thickness functions. New spatially dependent nPDF sets EPS09s (NLO, LO, error sets) and EKS98s (LO) are released. As an application, we consider the nuclear modification factor $R_{dAu}^{π^0}$ at midrapidity for neutral pion production in deuteron-gold collisions at RHIC in NLO. Comparison with the PHENIX data in different …
By globally analyzing nuclear Drell-Yan data including all incident energies, the nuclear effects of nPDFs and initial-state parton energy loss are investigated. Based on Landau-Pomeranchuk-Migdal (LPM) regime, the calculations are carried out by means of the analytic parametrizations of quenching weights derived from the Baier-Dokshitzer-Mueller-Peign$\acute{e}$-Schiff (BDMPS) formalism and using the new EPPS16 nPDFs. It is found that the results are in good agreement with the data and the role of the energy loss effect on the suppression of Drell-Yan ratios is prominent, especially for low-m…
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 pa…
We use the nCTEQ analysis framework to investigate nuclear Parton Distribution Functions (nPDFs) in the region of large x and intermediate-to-low $Q$, with special attention to recent JLab Deep Inelastic Scattering data on nuclear targets. This data lies in a region which is often excluded by $W$ and $Q$ cuts in global nPDF analyses. As we relax these cuts, we enter a new kinematic region, which requires new phenomenology. In particular, we study the impact of i) target mass corrections, ii) higher twist corrections, iii) deuteron corrections, and iv) the shape of the nuclear PDF parametrizati…
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 diff…
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 $Ω(x,Q^2)$ and the gluon $G(x,Q^2)$ …
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-$η$ hadron data from d+Au collisions are d…
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 th…
We present a first determination of the nuclear parton distribution functions (nPDF) based on the NNPDF methodology: nNNPDF1.0. This analysis is based on neutral-current deep-inelastic structure function data and is performed up to NNLO in QCD calculations with heavy quark mass effects. For the first time in the NNPDF fits, the $χ^2$ minimization is achieved using stochastic gradient descent with reverse-mode automatic differentiation (backpropagation). We validate the robustness of the fitting methodology through closure tests, assess the perturbative stability of the resulting nPDFs, and com…
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.
Global perturbative QCD analyses, based on large data sets from e-p and hadron collider experiments, provide tight constraints on the parton distribution function (PDF) in the proton. The extension of these analyses to nuclear parton distributions (nPDF) has attracted much interest in recent years. nPDFs are needed as benchmarks for the characterization of hot QCD matter in nucleus-nucleus collisions, and attract further interest since they may show novel signatures of non-linear density-dependent QCD evolution. However, it is not known from first principles whether the factorization of long-r…
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.
In this review talk I discuss the latest developments in the DGLAP-based global analysis of nuclear parton distribution functions (nPDFs), focusing on the recent EPS09, nCTEQ and DSSZ global fits. I also briefly review the recent analysis for assigning a spatial dependence to the globally analysed nPDFs, resulting in the new sets EPS09s and EKS98s ("s" for spatial). With these, one can now compute nuclear hard-process cross sections and estimate their nPDF-originating uncertainties in different centrality classes for the first time consistently with the global nPDF fits.
Global perturbative QCD analyses, based on large data sets from electron-proton and hadron collider experiments, provide tight constraints on the parton distribution function (PDF) in the proton. The extension of these analyses to nuclear parton distributions (nPDF) has attracted much interest in recent years. nPDFs are needed as benchmarks for the characterization of hot QCD matter in nucleus-nucleus collisions, and attract further interest since they may show novel signatures of non-linear density-dependent QCD evolution. However, it is not known from first principles whether the factorizati…
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.
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.
Using QCD calculations of the cross section of inclusive dijet photoproduction in Pb-Pb ultraperipheral collisions in the LHC kinematics as pseudo-data, we study the effect of including these data using the Bayesian reweighting technique on nCTEQ15, nCTEQ15np, and EPPS16 nuclear parton distribution functions (nPDFs). We find that, depending on the assumed error of the pseudo-data, it leads to a significant reduction of the nPDF uncertainties at small values of the momentum fraction $x_A$. Taking the error to be 5\%, the uncertainty of nCTEQ15 and nCTEQ15np nPDFs reduces approximately by a fact…
We present a next-to-leading order QCD calculation of inclusive dijet photoproduction in ultraperipheral Pb-Pb collisions at the LHC and show that the results agree very well with various kinematic distributions measured by the ATLAS collaboration. The effect of including these data in nCTEQ or EPPS16 nuclear parton density functions (nPDFs) is then studied using the Bayesian reweighting technique. For an assumed total error of 5\% on the final data, its inclusion would lead to a significant reduction of the nPDF uncertainties of up to a factor of two at small values of the parton momentum fra…
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.
Global perturbative QCD analyses, based on large data sets from electron-proton and hadron collider experiments, provide tight constraints on the parton distribution function (PDF) in the proton. The extension of these analyses to nuclear parton distributions (nPDF) has attracted much interest in recent years. nPDFs are needed as benchmarks for the characterization of hot QCD matter in nucleus-nucleus collisions, and attract further interest since they may show novel signatures of non- linear density-dependent QCD evolution. However, it is not known from first principles whether the factorizat…
Determination of Nuclear PDFs using Markov Chain Monte Carlo Methods
Institute of Nuclear Physics Polish Academy of Sciences（波兰科学院核物理研究所）；Southern Methodist University（南方卫理公会大学）；Jefferson Lab（杰斐逊实验室）；Westfälische Wilhelms-Universität Münster（明斯特西法利亚威廉大学）
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 …
University of Münster（明斯特大学）；Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院核物理研究所）；Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心/法国国家粒子物理研究所亚原子与宇宙学实验室）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；Southern Methodist University（南方卫理公会大学）；Theory Center, Jefferson Lab（杰斐逊实验室理论中心）
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 ligh…
We propose a new method to determine the spatially or impact-parameter dependent nuclear parton distribution functions (nPDFs) using the double parton scattering (DPS) processes in high-energy heavy-ion (proton-nucleus and nucleus-nucleus) collisions. We derive a simple generic DPS formula in nuclear collisions by accommodating both the nuclear collision geometry and the spatially dependent nuclear modification effect, under the assumption that the impact-parameter dependence of nPDFs is only related to the nuclear thickness function. While the geometric effect is widely adopted, the impact of…
We present a model-independent determination of the nuclear parton distribution functions (nPDFs) using machine learning methods and Monte Carlo techniques based on the NNPDF framework. The neutral-current deep-inelastic nuclear structure functions used in our previous analysis, nNNPDF1.0, are complemented by inclusive and charm-tagged cross-sections from charged-current scattering. Furthermore, we include all available measurements of W and Z leptonic rapidity distributions in proton-lead collisions from ATLAS and CMS at $\sqrt{s}=5.02$ TeV and 8.16 TeV. The resulting nPDF determination, nNNP…
The presence of nuclear medium and collective phenomena which involve several nucleons modify the parton distribution functions of nuclei (nPDFs) compared to those of a free nucleon. These modifications have been investigated by different groups using global analyses of high energy nuclear reaction world data resulting in modern nPDF parametrizations with error estimates, such as EPS09(s), HKN07 and nDS. These phenomenological nPDF sets roughly agree within their uncertainty bands, but have antiquarks for large-$x$ and gluons for the whole $x$-range poorly constrained by the available data. In…
This work studies collinearly factorizable nuclear parton distribution functions (nPDFs) in perturbative Quantum Chromodynamics (QCD) at next-to-leading order in the light of hadron-nucleus collision data which have not been included in nPDF analyses previously. The aim is at setting new constraints on the nuclear modifications of the gluon distribution and on the flavour separation of quark nuclear modifications. The introductory part provides an outline of the theoretical framework of QCD collinear factorization and the used statistical methods and relates the work presented here to other si…
In this contribution we present a status report on the recent progress towards an analysis of nuclear parton distribution functions (nPDFs) using the NNPDF methodology. We discuss how the NNPDF fitting approach can be extended to account for the dependence on the atomic mass number $A$, and introduce novel algorithms to improve the training of the neural network parameters within the NNPDF framework. Finally, we present preliminary results of a nPDF fit to neutral current deep-inelastic lepton-nucleus scattering data, and demonstrate how one can validate the new fitting methodology by means of…
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 …
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 $W^{\pm},\,Z$ boson production in p+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 TUJ…
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 datase…
The determination of the parton distribution functions (PDFs) is crucial for a complete understanding of the protons and neutrons that make most of the visible matter in the universe. Years of dedicated studies have yielded a quite precise knowledge of the behavior of partons moving collinearly within a proton. However Deep Inelastic Scattering (DIS) experiments off nuclei have shown a non-trivial difference with respect to DIS in protons, hinting that the partons in a nuclear medium do not behave the same way as in a free proton. In this work we will discuss the latest results in nuclear part…
We perform a χ^2-analysis of Nuclear Parton Distribution Functions (NPDFs) using neutral current charged-lepton Deeply Inelastic Scattering (DIS) and Drell-Yan data for several nuclear targets. The nuclear A dependence of the NPDFs is extracted in a next-to-leading order fit. We compare the nuclear corrections factors F2(Fe)/F2(D) for this charged-lepton data with other results from the literature. In particular, we compare and contrast fits based upon the charged-lepton DIS data with those using neutrino-nucleon DIS data.
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.
While current nuclear parton distribution functions (nPDFs) from global fits to experimental data are spatially homogeneous, many experimental observables in nucleus-nucleus collisions are presented in terms of centrality cuts. These cuts can be related to impact parameter using the Glauber theory and it is thus usual in the description of such observables to convolute an assumed impact parameter distribution with the homogeneous nPDFs. In this study we use the Gribov theory of nuclear shadowing supplemented with information from diffraction to model the impact parameter distributions of nucle…
Understanding nuclear effects in parton distribution functions (PDF) is an essential component needed to determine the strange and anti-strange quark contributions in the proton. In addition Nuclear Parton Distribution Functions (NPDF) are critically important for any collider experiment with nuclei (e.g. RHIC, ALICE). Here two next-to-leading order chi^2-analyses of NPDF are presented. The first uses neutral current charged-lepton Deeply Inelastic Scattering (DIS) and Drell-Yan data for several nuclear targets and the second uses neutrino-nucleon DIS data. We compare the nuclear corrections f…
A new QCD analysis for nuclear parton distribution functions (nPDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) is presented. The framework of the analysis, including the form of the parameterization as well as the included DIS data sets, are discussed. The results of this QCD analysis are compared to the existing nPDF sets and to the fitted data. The presented framework is based on an open-source tool, xFitter, which has been modified to be applicable also for a nuclear PDF analysis. The required modifications are covered as well. Finally, an outlook for the next …
We calculate cross sections for inclusive dijet photoproduction in electron-nucleus scattering in the kinematics of the future EIC and the possible LHeC, HE-LHeC, and the FCC using next-to-leading order (NLO) perturbative QCD and nCTEQ15 and EPPS16 nuclear parton density functions (nPDFs). We make predictions for distributions in the dijet average transverse momentum ${\bar p}_T$, the average rapidity $\barη$, the observed nuclear momentum fraction $x_A^{\rm obs}$, and the observed photon momentum fraction $x_γ^{\rm obs}$. Comparing the kinematic reaches of the four colliders, we find that an …
New hard-scattering measurements from the LHC proton-lead run have the potential to provide important constraints on the nuclear parton distributions and thus contributing to a better understanding of the initial state in heavy ion collisions. In order to quantify these constraints, as well as to assess the compatibility with available nuclear data from fixed target experiments and from RHIC, the traditional strategy is to perform a global fit of nuclear PDFs. This procedure is however time consuming and technically challenging, and moreover can only be performed by the PDF fitters themselves.…
We have presented the results of our next-to-next-to-leading order (NNLO) QCD analysis of nuclear parton distribution functions (nuclear PDFs) [Phys. Rev. D 93 (2016) 014026, arXiv:1601.00939 [hep-ph]] using all available neutral current charged-lepton ($\ell ^\pm$ + nucleus) deeply inelastic scattering (DIS) data as well as Drell-Yan (DY) cross-section ratios $σ_{\rm DY}^{A}/σ_{\rm DY}^{A^\prime}$ for a variety of nuclear targets. We have studied in detail the parametrizations and the atomic mass (A) dependence of the nuclear PDFs at NNLO at the input scale, $Q_0^2 = 2 \, {\rm GeV^2}$. Our {\…
We present new sets of nuclear parton distribution functions (nPDFs) at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO). Our analyses are based on deeply inelastic scattering data with charged-lepton and neutrino beams on nuclear targets. In addition, a set of proton baseline PDFs is fitted within the same framework with the same theoretical assumptions. The results of this global QCD analysis are compared to existing nPDF sets and to the fitted cross sections. Also, the uncertainties resulting from the limited constraining power of the included experimental data are prese…
The extraction of the strange quark parton distribution function (PDF) poses a long-standing puzzle. Measurements from neutrino-nucleus deep inelastic scattering (DIS) experiments suggest the strange quark is suppressed compared to the light sea quarks, while recent studies of W/Z boson production at the LHC imply a larger strange component at small x values. As the parton flavor determination in the proton depends on nuclear corrections, e.g. from heavy-target DIS, LHC heavy ion measurements can provide a distinct perspective to help clarify this situation. In this investigation we extend the…
