Nuclear 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 $x$. We find that the data are in a good agreement with the EPPS16 and nCTEQ15 nuclear PDFs whereas they disagree with TuJu19. The implications on flavour separation, higher-twist contributions and models of EMC effect are discussed.
As data become more precise, estimating theoretical uncertainties in global PDF determinations is likely to become increasingly necessary to obtain correspondingly precise PDFs. Here we present a next generation of global proton PDFs (NNPDF4.0) that include theoretical uncertainties due to the use of heavy nuclear and deuteron data in the fit. We estimate these uncertainties by comparing the values of the nuclear observables computed with the nuclear PDFs against those computed with proton PDFs. For heavy nuclear PDFs we use the nuclear nNNPDF2.0 set, while for deuteron PDFs we develop an iter…
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.
We compare predictions of nCTEQ15 nuclear parton distribution functions with proton-lead vector boson production data from the LHC. We select data sets that are most sensitive to nuclear PDFs and have potential to constrain them. We identify the kinematic regions and flavours where these data can bring new information and will have largest impact on the nuclear PDFs. Finally, we estimate the effect of including these data in a global analysis using a reweighting method.
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 larg…
Nuclear parton distribution functions (nuclear PDFs), collinearly factorizable in perturbative QCD (pQCD), are currently extracted most reliably from global analyses of experimental data. Recently, the progress in this field has been driven mainly by the new data from LHC proton-lead collisions. I will review the progress in using data from LHC Run 1 and 2 and also hint at some opportunities and challenges that we face during LHC Run 3.
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.
We quantify the impact of unpolarized lepton-proton and lepton-nucleus inclusive deep-inelastic scattering (DIS) cross section measurements from the future Electron-Ion Collider (EIC) on the proton and nuclear parton distribution functions (PDFs). To this purpose we include neutral- and charged-current DIS pseudodata in a self-consistent set of proton and nuclear global PDF determinations based on the NNPDF methodology. We demonstrate that the EIC measurements will reduce the uncertainty of the light quark PDFs of the proton at large values of the momentum fraction $x$, and, more significantly…
We show how theoretical uncertainties due to nuclear effects may be incorporated into global fits of proton parton distribution functions (PDFs) that include deep-inelastic scattering and Drell-Yan data on nuclear targets. We specifically consider the CHORUS, NuTeV and E605 data included in the NNPDF3.1 fit, which used Pb, Fe and Cu targets, respectively. We show that the additional uncertainty in the proton PDFs due to nuclear effects is small, as expected, and in particular that the effect on the $\bar{d}/\bar{u}$ ratio, the total strangeness $s+\bar{s}$, and the strange valence distribution…
We present updated nCTEQ nuclear parton distribution functions with errors including pion production data from RHIC. We compare them with the results of other groups and present selected LHC applications.
A brief overview of the global DGLAP analyses of the nuclear parton distribution functions is given. Although all the current global nPDF sets describe $R_{F_2}^A(x,Q^2)$ well in the large-$x$ region where the data exist, variations between their parton distributions can be substantial.
We study nuclear effects in charged current deep inelastic neutrino-iron scattering in the frame-work of a chi^2 analysis of parton distribution functions. We extract a set of iron PDFs and show that under reasonable assumptions it is possible to constrain the valence, light sea and strange quark distributions. Our iron PDFs are used to compute x_{Bj}-dependent and Q^2-dependent nuclear correction factors for iron structure functions which are required in global analyses of free nucleon PDFs. We compare our results with nuclear correction factors from neutrino-nucleus scattering models and cor…
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 $χ^2$ 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.
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 …
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 ultra-peripheral heavy-ion collisions the nuclei pass with such a large impact parameter that no strong interaction can take place. However, a photon emitted by one nucleus can still interact either with the other nucleus or with a photon from the another nucleus. The former event type corresponds to photoproduction, earlier studied e.g. in electron-proton collisions at HERA, but now with a nuclear target. This provides an unique opportunity to study the nuclear modifications of the PDFs with the photo-nuclear processes measured in lead-lead collisions at the LHC. Here we present our recent…
The LHC heavy ion data for W/Z production can provide new incisive information on the PDFs. This data is sensitive to the heavier quark flavors (strange and charm) in a high energy kinematic region; this can facilitate the determination of PDFs in the small x region where previous data was limited. At present, the flavor separation of the proton PDFs is dependent on DIS data from nuclear targets. Therefore, improved nuclear corrections can also yield enhanced flavor determination of both the proton and nuclear PDFs.
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.
We quantify the impact of LHC dijet production measurements on the nNNPDF2.0 nuclear PDFs in twofold. First, from a proton baseline based on NNPDF3.1 and augmented by pp dijet production measurements from ATLAS and CMS at 7 and 8 TeV. Second, from a new nNNPDF2.0 global analysis including the ratio of pPb to pp dijet spectra from CMS at 5 TeV. We show that as opposed to the CMS at 5 TeV absolute pp and pPb dijet spectra, the pPb/pp ratio is well described in a nPDFs fit and provides strong constraints on the gluon of lead.
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 nuclea…
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 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 pro…
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.
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 fr…
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…
We perform a next-to-next-to-leading order (NNLO) analysis of nuclear parton distribution functions (nPDFs) using neutral current charged-lepton ($\ell ^\pm$ + nucleus) deeply inelastic scattering (DIS) data and Drell-Yan (DY) cross-section ratios $σ_{DY}^{A}/σ_{DY}^{A^\prime}$ for several nuclear targets. We study in detail the parametrizations and the atomic mass (A) dependence of the nuclear PDFs at this order. The present nuclear PDFs global analysis provides us a complete set of nuclear PDFs, $f_i^{(A,Z)}(x,Q^2)$, with a full functional dependence on $x$, A, Q$^2$. The uncertainties of th…
We present a detailed phenomenological study of direct photon production in association with a heavy-quark jet in pA collisions at the Relativistic Heavy Ion Collider (RHIC) and at the Large Hadron Collider (LHC) at next-to-leading order in QCD. The dominant contribution to the cross-section comes from the gluon--heavy-quark (gQ) initiated subprocess, making γ+ Q production a process very sensitive to both the gluon and the heavy-quark parton distribution functions (PDFs). Additionally, the RHIC and LHC experiments are probing complementary kinematic regions in the momentum fraction x_2 carrie…
In this talk we apply the photoproduction framework recently implemented into the Pythia 8 Monte Carlo event generator to study the potential of photo-nuclear dijets in ultra-peripheral Pb+Pb collisions at the LHC to further constrain the nuclear PDFs. These events can be described as $γ$A collisions where the relevant part of the flux of quasi-real photons from heavy-ions is obtained by using the equivalent photon approximation and cutting out impact-parameter values which would lead to hadronic interactions between the beam particles. In particular, we quantify the small-$x$ reach with diffe…
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.
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 investigate the effect of including the HERA run I + II combined cross section data on the MMHT2014 PDFs. We present the fit quality within the context of the global fit and when only the HERA data are included. We examine the changes in both the central values and uncertainties in the PDFs. We find that the prediction for the data is good, and only relatively small improvements in $χ^2$ and changes in the PDFs are obtained with a refit at both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small dependence of the fit quality on the value of $Q^2_{\min}$. This can be impro…
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.
We perform a global fit of parton distribution functions (PDFs) together with the strong coupling constant $α_s$ and the quark masses $m_c$, $m_b$ and $m_t$ at next-to-leading order (NLO) in QCD. The analysis applies the $\overline{\mathrm{MS}}\, $ renormalization scheme for $α_s$ and all quark masses. It is performed in the fixed-flavor number scheme for $n_f=3, 4, 5$ and uses the same data as the previous fit of the ABMP16 PDF at next-to-next-to-leading order (NNLO). The new NLO PDFs complement the set of ABMP16 PDFs and are to be used consistently with NLO QCD predictions for hard scatterin…
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, rea…
We study nuclear effects of charged current deep inelastic neutrino-iron scattering in the framework of a chi^2 analysis of parton distribution functions (PDFs). We extract a set of iron PDFs which are used to compute x_Bj-dependent and Q^2-dependent nuclear correction factors for iron structure functions which are required in global analyses of free nucleon PDFs. We compare our results with nuclear correction factors from neutrino-nucleus scattering models and correction factors for charged-lepton--iron scattering. We find that, except for very high x_Bj, our correction factors differ in both…
The progress in constraining proton and nuclear parton distribution functions is briefly summarised. Some persistent uncertainties are pointed out and recent experimental advancements highlighted.
We perform the next-to-next-leading-order (NNLO) QCD global fit of PDFs using inclusive charged-lepton and neutrino DIS data down to Q = 1 GeV. We also consider the data on neutrino-nucleon dimuon production, that allows us to disentangle the strange sea distribution. The fit results in χ^2/NDP = 5150/4338 = 1.2 that demonstrates a good consistency of the data sets used in analysis. The resulting value of α_s(M_Z) = 0.1136+- 0.0007(exp.) is in a good agreement with the previous version of the fit with a more stringent cut on Q. This analysis allows us to improve the accuracy of PDFs. The HT te…
We study nuclear effects of charged current deep inelastic neutrino-iron scattering in the framework of a chi^2 analysis of parton distribution functions (PDFs). We extract a set of iron PDFs which are used to compute x_Bj-dependent and Q^2-dependent nuclear correction factors for iron structure functions which are required in global analyses of free nucleon PDFs. We compare our results with nuclear correction factors from neutrino-nucleus scattering models and correction factors for charged lepton-iron scattering. We find that, except for very high x_Bj, our correction factors differ in both …
We investigate the influence of modified nuclear parton distribution functions (PDFs) on high-pT hadron production at RHIC and LHC energies using a pQCD-improved parton model. For application at RHIC, we focus on the possible contribution of the EMC modification of the nuclear PDFs in the x > 0.3 region to the observed suppression of pi0 production at pT > 10 GeV/c in dAu collisions. We study three different parameterizations of the nuclear PDF modifications and find that they give consistent results for R_dAu(pT) for neutral pions in the region 10 GeV/c < pT < 20 GeV/c. We find that the EMC s…
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 hea…
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 r…
We introduce a generalized definition of parton distribution functions (PDFs) for a more consistent all-order treatment of power corrections. We present a new set of modified DGLAP evolution equations for nuclear PDFs, and show that the resummed $α_s A^{1/3}/Q^2$-type of leading nuclear size enhanced power corrections significantly slow down the growth of gluon density at small-$x$. We discuss the relation between the calculated power corrections and the saturation phenomena.
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 theoretic…
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 {\…
In this talk, we introduce our recently completed next-to-leading order (NLO) global analysis of the nuclear parton distribution functions (nPDFs) called EPS09 - a higher order successor to the well-known leading-order (LO) analysis EKS98 and also to our previous LO work EPS08. As an extension to similar global analyses carried out by other groups, we complement the data from deep inelastic $l+A$ scattering and Drell-Yan dilepton measurements in p+$A$ collisions by inclusive midrapidity pion production data from d+Au collisions at RHIC, which results in better constrained gluon distributions t…
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.
In this talk, we discuss the compatibility of different deeply inelastic neutrino-nucleus data sets and the universal nuclear PDFs. This is an issue that has lately been investigated by different groups but the conclusions have been surprisingly contradictory. While some studies have found a good overall agreement between the nuclear PDFs and the neutrino data, others have claimed for an incompatibility. Here, we demonstrate that the independent neutrino data sets from NuTeV, CHORUS and CDHSW collaborations differ in the absolute overall normalization and that it is not possible to accurately …
We present a new global QCD analysis of nuclear parton distribution functions. In addition to the most commonly analyzed data sets for deep inelastic scattering of charged leptons off nuclei and Drell Yan di-lepton production, we include also measurements for neutrino-nuclei scattering as well as inclusive pion production in deuteron-gold collisions. The emerging picture is one of consistency, where universal nuclear modification factors for each parton flavor reproduce the main features of all data without any significant tension among the different sets.
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.
We analyze experimental data of nuclear structure function ratios $F_2^A/F_2^D$ for obtaining optimum parton distribution functions (PDFs) in nuclei. Then, uncertainties of the nuclear PDFs are estimated by the Hessian method. Parametrization of nuclear parton distribution is investigated in the leading order of $α_s$. The parton distribution are provided at $Q^2=1 GeV^2$ with a number of parameters, which are determined by a $χ^2$ analysis of the data on nuclear structure function. From the analysis, we propose parton distributions at $Q^2=1 GeV^2$ for nuclei from deuteron to heavy ones with …
