We compare the cross section for exclusive $J/ψ$ photoproduction calculated at NLO in the collinear factorization approach with HERA and LHCb data. Using the optimum scale formalism together with the subtraction of the low $k_t<Q_0$ contribution from the NLO coefficient function to avoid double counting we show that the existing global parton distribution functions (PDFs) are consistent with the data within their uncertainties. However, at low $x$ the uncertainties of the present global PDFs are large. On the other hand, the accuracy of the LHCb data are rather good. Therefore, these data provide the possibility to directly measure the gluon PDF over the very large interval of $x$, $10^{-6}<x<10^{-2}$, at a fixed low scale.
We discuss the exclusive $J/ψ$ photoproduction process, as measured recently at LHCb, as a means of constraining and ultimately determining the low $x$ and low $Q$ gluon PDF. The scale dependence of the theoretical prediction for this process is shown to be systematically improved via a taming of the known $\bar{\text{MS}}$ result, this amounts to resumming logarithmically enhanced small-$x$ terms and implementing a small-$Q$ power correction. The cross section level predictions allow the behaviour of the gluon PDF in the low $(x, Q)$ domain to be determined.
We discuss the potential to constrain the small-$x$ PDFs using the exclusive production of heavy vector mesons. The calculation of $J/ψ$ and $Υ$ photoproduction at NLO in collinear factorisation is described. The different behaviour of the NLO corrections for $J/ψ$ and $Υ$ is highlighted and we outline what might be expected from the inclusion of these processes in a PDF fit.
We discuss exclusive $J/ψ$ photoproduction, initially in conventional collinear factorisation at NLO and then subsequently in a refined approach with a programme of low $x$ resummation and implementation of a crucial low $Q_0$ subtraction included. We compare and contrast predictions in both frameworks and remark about the possibility to constrain and ultimately determine the low $x$ and low scale gluon PDF, emphasising the significance of this for future global PDF analyses.
We survey some of the recent developments in the extraction and application of heavy quark Parton Distribution Functions (PDFs). We also highlight some of the key HERA measurements which have contributed to these advances.
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 exclusive vector meson photoproduction, $γp \to V + p$ with $V=J/ψ$ or $Υ$, at NLO in collinear factorisation, in order to examine what may be learnt about the gluon distribution at very low $x$. We examine the factorisation scale dependence of the predictions. We argue that, using knowledge of the NLO corrections, terms enhanced by a large $\ln(1/ξ)$ can be reabsorbed in the LO part by a choice of the factorisation scale. (In these exclusive processes $ξ$ takes the role of Bjorken-$x$.) Then, the scale dependence coming from the remaining NLO contributions has no $\ln(1/ξ)$ enhanceme…
We study the sensitivity of our recent MSTW 2008 NLO and NNLO PDF analyses to the values of the charm- and bottom-quark masses, and we provide additional public PDF sets for a wide range of these heavy-quark masses. We quantify the impact of varying m_c and m_b on the cross sections for W, Z and Higgs production at the Tevatron and the LHC. We generate 3- and 4-flavour versions of the (5-flavour) MSTW 2008 PDFs by evolving the input PDFs and alpha_S determined from fits in the 5-flavour scheme, including the eigenvector PDF sets necessary for calculation of PDF uncertainties. As an example of …
The next-to-leading order (NLO) evolution of the parton distribution functions (PDFs) in QCD is a common tool in the lepton-hadron and hadron-hadron collider data analysis. The standard NLO DGLAP evolution is formulated for inclusive (integrated) PDFs and done using inclusive NLO kernels. We report here on the ongoing project, called KRKMC, in which NLO DGLAP evolution is performed for the exclusive multiparton (fully unintegrated) distributions (ePDFs) with the help of the exclusive kernels. These kernels are calculated within the two-parton phase space for the non-singlet evolution, using Cu…
We present the first next-to-leading-order (NLO) perturbative QCD (pQCD) study of rapidity-differential cross sections of coherent exclusive photoproduction of $J/ψ$ mesons in heavy-ion ultraperipheral collisions (UPCs) at the LHC, $dσ/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/ψ+ \text{Pb})$. For this, we account for the photon-nucleon NLO cross sections at the forward limit, the $t$ dependence using a standard nuclear form factor, and the photon fluxes of the colliding nuclei. Approximating the generalized parton distributions with their forward-limit parton distribution functions (P…
Due to the large masses of the charm and bottom quarks, their production cross sections are calculable within the perturbative QCD. This makes the heavy-quark mesons important observables in high-energy collisions of protons and nuclei. However, the available calculations for heavy-flavored-meson hadroproduction have been somewhat problematic in reliably describing the cross sections across the full kinematic range from zero to very high $p_{\rm T}$. This has put some question marks on the robustness of LHC heavy-flavored-meson measurements in studying the partonic structure of the colliding h…
We present the first NLO pQCD study of coherent exclusive $J/ψ$ photoproduction in ultraperipheral heavy-ion collisions (UPCs) at the LHC. Taking the generalized parton distributions (GPDs) in their forward limit, as parton distribution functions (PDFs), we quantify the NLO contributions in the rapidity-differential cross section, show that the real part of the amplitude must not be neglected, study the gluon and quark contributions, chart the scale-choice and PDF uncertainties, and compare the NLO results with LHC and HERA data. We show that the scale dependence is significant but a scale cho…
Low-$x$ parton densities accounting for absorptive effects and exclusive $J/ψ$ and $Υ$ data from the LHC
IRFU, CEA, Université Paris-Saclay（巴黎萨克雷大学）；Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain（鲁汶天主教大学）；Institute for Particle Physics Phenomenology, Durham University（杜伦大学）；NRC Kurchatov Institute, PNPI（库尔恰托夫研究所）
The H1 and ZEUS published PDF analyses are compared, including a discussion of the different treatments of correlated systematic uncertainties. Differences in the data sets and the analyses are investigated by putting the H1 data set through both PDF analyses and by putting the ZEUS and H1 data sets through the same (ZEUS) analysis, separately. Finally the HERA averaged data set is put through the ZEUS PDF analysis and the result is compared to that obtained when putting the ZEUS and H1 data sets through this analysis together, using both the Offset and the Hessian methods of treating correlat…
We determine the uncertainty on the strong coupling alpha_S due to the experimental errors on the data fitted in global analysis of hard-scattering data, within the standard framework of leading-twist fixed-order collinear factorisation in the MSbar scheme, finding that alpha_S(M_Z^2) = 0.1202^{+0.0012}_{-0.0015} at next-to-leading order (NLO) and alpha_S(M_Z^2) = 0.1171^{+0.0014}_{-0.0014} at next-to-next-to-leading order (NNLO). We do not address in detail the issue of the additional theory uncertainty on alpha_S(M_Z^2), but an estimate is +/-0.003 at NLO and at most +/-0.002 at NNLO. We inv…
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.
We address the question as to whether data for J/ψmesons produced exclusively in the forward direction at the LHC can be used in global parton analyses (based on collinear factorization) to pin down the low x gluon PDF. We show that it may be possible to overcome the problems that (i) the process is described by a skewed or Generalized Parton Distribution (GPD), (ii) it is very sensitive to the choice of factorization scale and (iii) there is bad LO, NLO,... perturbative stability to the predictions. However, we start by briefly explaining how the alternative k_T factorization approach has bee…
In this talk, we present our recent next-to-leading order (NLO) nuclear parton distribution functions (nPDFs), which we call EPS09. As an extension to earlier NLO analyses, we supplement the deep inelastic scattering and Drell-Yan dilepton data by inclusive midrapidity pion measurements from RHIC in order to reduce the otherwize large freedom in the nuclear gluon densities. Our Hessian-type error analysis leading to a collection of nPDF error sets, is the first of its kind among the nPDF analyses.
The low $x$ behaviour of the gluon density $xg(x,μ^2)$ at scale $μ^2=2.4$ GeV$^2$ is determined using exclusive $J/ψ$ production data from HERA and LHCb within the framework of collinear factorisation at next-to-leading order (NLO). It is shown that in the interval $3\times 10^{-6} < x <10^{-3}$ the gluon distribution function grows as $xg(x,μ^2)\propto x^{-λ}$ with $λ=0.135\pm 0.006 $. The impact this experimental data will have for the global parton distribution function (PDF) analyses in this low $x$ domain is quantified. No indication in favour of parton density saturation is observed.
I review recent progress in the NNPDF global analyses of parton distributions (PDFs) focusing on developments contributing to its new upcoming release: NNPDF4.0. The NNPDF4.0 determination represents unprecedented progress in three main directions: i) the systematic inclusion of LHC Run II data at 13 TeV and of new processes from dijets to single top distributions, ii) the deployment of state-of-the-art machine learning algorithms, from automated hyperparameter optimisation to stochastic gradient descent training; and iii) the complete statistical validation of PDF uncertainties, both in the d…
We present the software framework underlying the NNPDF4.0 global determination of parton distribution functions (PDFs). The code is released under an open source licence and is accompanied by extensive documentation and examples. The code base is composed by a PDF fitting package, tools to handle experimental data and to efficiently compare it to theoretical predictions, and a versatile analysis framework. In addition to ensuring the reproducibility of the NNPDF4.0 (and subsequent) determination, the public release of the NNPDF fitting framework enables a number of phenomenological application…
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.
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 present the general rules for double-Reggeon production of objects with different spins and parities. The existing experimental information on resonance production in these central exclusive diffractive processes is discussed. The absorptive corrections are calculated and found to depend strongly on the quantum numbers of the produced states. The central exclusive diffractive production of 0^+ and 0^- Higgs bosons is studied as an illustrative topical example of the use of the general rules. The signal for diffractive 0^+ and 0^- Higgs production at the LHC is evaluated using, as an example…
Heavy quark parton distribution functions (PDFs) play an important role in several Standard Model and New Physics processes. Most PDF analyses rely on the assumption that the charm and bottom PDFs are generated perturbatively by gluon splitting and do not include any non-perturbative degrees of freedom. However, a non-perturbative, intrinsic heavy quark PDFs have been predicted in the literature. We demonstrate that to a very good approximation the scale-evolution of the intrinsic heavy quark content of the nucleon is governed by non-singlet evolution equations, and use this approximation to m…
We discuss heavy-flavor production at hadron colliders in recent global QCD analyses to determine parton distribution functions (PDFs) in the proton. We discuss heavy-flavor treatments in precision theory predictions at the LHC. In particular, we discuss factorization schemes in presence of heavy flavors in proton-proton collisions, as well as the impact of heavy-flavor production at the LHC on PDFs. We show results of recent updates beyond CT18, the latest global QCD analysis from the CTEQ-TEA group.
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）
University of Cambridge（剑桥大学）；Nikhef Theory Group（尼赫夫理论组）；Instituto de Física Corpuscular (IFIC), Universidad de Valencia-CSIC（瓦伦西亚大学-西班牙国家科学研究理事会物质物理研究所）；Institute for Theoretical Physics, ETH（苏黎世联邦理工学院理论物理研究所）；INFN, Sezione di Trieste, SISSA（意大利国家核物理研究院的里雅斯特分部，的里雅斯特国际高等研究学院）
Measurements of the deep-inelastic scattering (DIS) of leptons and nucleons, $e+p\to e+X$, allow the extraction of Parton Distribution Functions (PDFs) which describe the longitudinal momentum carried by the quarks, anti-quarks and gluons that make up the fast-moving nucleons. While PDFs provide crucial input to perturbative Quantum Chromodynamic (QCD) calculations of processes involving hadrons, they do not provide a complete picture of the partonic structure of nucleons. In particular, PDFs contain neither information on the correlations between partons nor on their transverse motion. Hard e…
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…
The NNPDF collaboration has recently presented NNPDF3.1, a new determination of the parton distribution functions (PDFs) of the proton including a number of new data, some of which are particularly sensitive to the gluon PDF at large x. In this contribution, we present the results of two new analyses based on NNPDF3.1. First, we study the impact of the ATLAS 2011 7 TeV inclusive jet data on the gluon PDF including different rapidity bins. Second, we quantitatively compare the constraints provided by all measurements sensitive to the large-x gluon PDF, namely inclusive jet cross sections, the t…
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…
Transverse momentum dependent (TMD) distributions match collinear parton density functions (PDF) in the limit of small transverse distances, which is accounted for by global extractions of TMD distributions. We study the influence of the collinear PDF value and uncertainties on the determination of unpolarized TMD distributions and the description of Drell-Yan (DY) and Z-boson production measurements at low transverse momenta. We take into account, for the first time, flavor-dependent non-perturbative TMD profiles. We carry out a Bayesian analysis to incorporate the propagation of PDF uncertai…
Parton distribution functions (pdfs) are an important ingredient for LHC phenomenology. Recent progress in determining pdfs from global analyses is reviewed, and some of the most important outstanding issues are highlighted. Particular attention is paid to the precision with which predictions for LHC `standard-candle' cross sections can be made, and also to new information that LHC can provide on pdfs.
Using the new schemes provided by the CTEQ and MRST collaborations and by Alekhin, we analyse the uncertainties due to the parton distribution functions (PDFs) on the next-to-leading-order cross sections of the four main production processes of the Standard Model Higgs boson at the LHC and the Tevatron. In the Higgs mass range where the production rates are large enough, the spread in the uncertainties when the three sets of PDFs are compared is of about 15% in all processes and at both colliders. However, within one given set of PDFs, the deviations from the values obtained with the reference…
We discuss the two most recent global analyses of nuclear parton distribution functions within the nCTEQ approach. LHC data on $W/Z$-boson, single-inclusive hadron and heavy quark/quarkonium production are shown to not only significantly reduce the gluon uncertainty down to $x\geq10^{-5}$, but to also influence the strange quark density. The latter is further constrained by neutrino deep-inelastic scattering and charm dimuon production data, whose consistency with neutral-current experiments is also re-evaluated.
Exclusive J/psi production, gamma* p -> J/psi p, offers a unique opportunity to determine the gluon density of the proton in the small x domain. We use the available HERA data to determine the gluon distribution in the region 10^{-4} <~ x <~ 10^{-2} and 2 <~ Q^2 <~ 10 GeV^2, where the uncertainty on the gluon extracted from the global parton analyses is large. The gluon density is found to be approximately flat at the lower scale; it is compared with those of recent global analyses.
Global analyses of Parton Distribution Functions (PDFs) have provided incisive constraints on the up and down quark components of the proton, but constraining the other flavor degrees of freedom is more challenging. Higher-order theory predictions and new data sets have contributed to recent improvements. Despite these efforts, the strange quark PDF has a sizable uncertainty, particularly in the small x region. We examine the constraints from experiment and theory, and investigate the impact of this uncertainty on LHC observables. In particular, we study W/Z production to see how the s-quark u…
Experimental measurements in deep-inelastic scattering and lepton-pair production on deuterium targets play an important role in the flavor separation of $u$ and $d$ (anti)quarks in global QCD analyses of the parton distribution functions (PDFs) of the nucleon. We investigate the impact of theoretical corrections accounting for the light-nuclear structure of the deuteron upon the fitted $u, d$-quark, gluon, and other PDFs in the CJ15 and CT18 families of next-to-leading order CTEQ global analyses. The investigation is done using the $L_2$ sensitivity statistical method, which provides a common…
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…
The high statistics that will be collected during the LHC Run-II (and beyond) open the path to precision measurements at the TeV scale, where the PDFs will play a crucial role in BSM searches. In the di-lepton final state accurate measurements of the Forward-Backward Asymmetry (AFB) will be available, particularly in the invariant mass region around the Z peak. We show that this observable displays a statistical error which is competitive with that assigned to the existing PDF sets and which will rapidly become smaller than the latter as the integrated luminosity grows, thereby offering a mean…
HEPGEN is a generator of Monte Carlo events, which is dedicated to studies of hard exclusive single photon or meson production processes at the COMPASS experiment kinematic domain. In addition HEPGEN allows to generate also single photon or meson production accompanied by the diffractive dissociation of the nucleon, which is one of the main sources of background in analyses of exclusive processes.
Detailed studies have been carried out on the impact of the LHC top quark pair production data on gluon PDF, in the context of the CTEQ-TEA global PDF fit, with the ePump-updating method. The considered $t\bar{t}$ data include single differential distributions from ATLAS and double differential distributions from CMS, both at 8 TeV. All analyses have been carried out at the NNLO, using fastNNLO tables. We show that the sensitivity per data point of the LHC $t\bar{t}$ data is similar to that of jet data, as included in the CT14HERA2 fit, while the total sensitivity of the present $t\bar{t}$ dat…
The use of machine learning algorithms in theoretical and experimental high-energy physics has experienced an impressive progress in recent years, with applications from trigger selection to jet substructure classification and detector simulation among many others. In this contribution, we review the machine learning tools used in the NNPDF family of global QCD analyses. These include multi-layer feed-forward neural networks for the model-independent parametrisation of parton distributions and fragmentation functions, genetic and covariance matrix adaptation algorithms for training and optimis…
The xFitter project (former HERAFitter project) is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton for many different kinds of analyses in Quantum Chromodynamics (QCD). xFitter version 2.0.0 has recently been released, and offers an expanded set of tools and options. It incorporates experimental data from a wide range of experiments including fixed-target, Tevatron, HERA, and LHC. xFitter can analyze this data up to next-to-next-to-leading-order (NNLO) in perturbation theory with a variety of theoretical calculati…
We investigate the MSHT20 global PDF sets, demonstrating the effects of varying the strong coupling $α_S(M_Z^2)$ and the masses of the charm and bottom quarks. We determine the preferred value, and accompanying uncertainties, when we allow $α_S(M_Z^2)$ to be a free parameter in the MSHT20 global analyses of deep-inelastic and related hard scattering data, at both NLO and NNLO in QCD perturbation theory. We also study the constraints on $α_S(M_Z^2)$ which come from the individual data sets in the global fit by repeating the NNLO and NLO global analyses at various fixed values of $α_S(M_Z^2)$, s…
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.
New physics searches at the LHC or Tevatron typically look for a specific number of hard jets, leptons and photons. To obtain an exclusive N-jet sample, one can measure the event shape "N-jettiness" τ_N and veto additional undesired jets by requiring τ_N <<1. However, this leads to large logarithms of τ_N in the cross section, that need to be summed for reliable theory predictions. For N=0 in hadronic collisions, τ_N reduces to the "beam thrust" eventshape τ_B. We derive a factorization theorem for pp -> XL, where a central jet veto τ_B<<1 is imposed on the hadronic final state X and L is non-…
