Gluon Parton Distribution Functions Research Articles

Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction

We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.

Impact of dijet and D-meson data from 5.02 TeV p+Pb collisions on nuclear PDFs

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 D0-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 D0 data, reaching down to x ∼ 10−5 and derived in a NLO perturbative QCD approach, provide a remarkable reduction of the small-x uncertainties with a strong direct evidence of gluon shadowing. Furthermore, we find a good description of the data even down to zero D0-meson transverse momentum within a purely DGLAP-based approach without a need for imposing any non-linear effects. Importantly, the constraints obtained from the dijet and D0 data are mutually fully consistent, supporting the universality of nuclear PDFs in hard-scattering processes.

An exploratory study of the impact of CMS double-differential top distributions on the gluon parton distribution function

LHC data have the potential to provide constraints on the gluon distribution, especially at high x, with both ATLAS and CMS performing differential measurements. Recently, CMS has measured double-differential distributions at 8 TeV. In this paper we examine the impact of this data set on the gluon distribution. To that end we develop novel, double-differential NNLO predictions for that data. No significant impact is found when the CMS data is added to the CT14HERA2 global PDF fit, due to the larger impact of the inclusive jet data from both the Tevatron and the LHC. If the jet data are removed from the fit, then an impact is observed. If the CMS data is scaled by a larger weight, representing the greater statistical power of the jet data, a roughly equal impact on the gluon distribution is observed for the as for the inclusive jet data. For data samples with higher integrated luminosity at 13 TeV, a more significant impact of the double-differential data may be observed.

Gluon pseudo-distributions at short distances: Forward case

We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone z2→0 limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the ln⁡(−z2)-dependence at short distances z2. The UV terms cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF. We also show that our results may be used for a rather straightforward calculation of the one-loop matching relations for quasi-PDFs.

Measurement of hbox {t}{bar{hbox {t}}} normalised multi-differential cross sections in {text {p}}{text {p}} collisions at sqrt{s}=13,{text {TeV}} , and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions

Normalised multi-differential cross sections for top quark pair (hbox {t}{bar{hbox {t}}}) production are measured in proton-proton collisions at a centre-of-mass energy of 13,{text {TeV}} using events containing two oppositely charged leptons. The analysed data were recorded with the CMS detector in 2016 and correspond to an integrated luminosity of 35.9{,{text {fb}}^{-1}} . The double-differential hbox {t}{bar{hbox {t}}} cross section is measured as a function of the kinematic properties of the top quark and of the hbox {t}{bar{hbox {t}}} system at parton level in the full phase space. A triple-differential measurement is performed as a function of the invariant mass and rapidity of the hbox {t}{bar{hbox {t}}} system and the multiplicity of additional jets at particle level. The data are compared to predictions of Monte Carlo event generators that complement next-to-leading-order (NLO) quantum chromodynamics (QCD) calculations with parton showers. Together with a fixed-order NLO QCD calculation, the triple-differential measurement is used to extract values of the strong coupling strength alpha _{S} and the top quark pole mass (m_{{text {t}}}^{{text {pole}}}) using several sets of parton distribution functions (PDFs). The measurement of m_{{text {t}}}^{{text {pole}}} exploits the sensitivity of the hbox {t}{bar{hbox {t}}} invariant mass distribution to m_{{text {t}}}^{{text {pole}}} near the production threshold. Furthermore, a simultaneous fit of the PDFs, alpha _{S}, and m_{{text {t}}}^{{text {pole}}} is performed at NLO, demonstrating that the new data have significant impact on the gluon PDF, and at the same time allow an accurate determination of alpha _{S} and m_{{text {t}}}^{{text {pole}}}. The values alpha _{S}(m_{{text {Z}}}) = 0.1135{}^{+0.0021}_{-0.0017} and m_{{text {t}}}^{{text {pole}}} = 170.5 pm 0.8 ,{text {GeV}} are extracted, which account for experimental and theoretical uncertainties, the latter being estimated from NLO scale variations. Possible effects from Coulomb and soft-gluon resummation near the hbox {t}{bar{hbox {t}}} production threshold are neglected in these parameter extractions. A rough estimate of these effects indicates an expected correction of m_{{text {t}}}^{{text {pole}}} of the order of +1 ,{text {GeV}} , which can be regarded as additional theoretical uncertainty in the current m_{{text {t}}}^{{text {pole}}} extraction.

How to include exclusive J/ψ production data in global PDF analyses

We compare the cross section for exclusive $J/\psi$ 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.

Single top production in PDF fits

We study the impact of recent LHC t-channel single top-quark and top-antiquark measurements at centre-of-mass energies of 7, 8 and 13 TeV on the parton distribution functions (PDFs) of the proton. We consider, namely, total cross sections, top-antitop cross section ratios, and differential distributions. We present a critical appraisal of the data, studying in particular how their description is affected by the theoretical details that enter the computation of the corresponding observables: QCD and electroweak higher-order corrections, the flavour scheme, and the value of the bottom-quark threshold. We perform a series of fits to the data within the NNPDF3.1 framework, whereby next-to-next-to-leading order QCD corrections are applied to single top measurements in a systematic way. We find that there exists an optimal combination of data that maximises consistency with the rest of the dataset, and efficiency in constraining the up, down and, partially, gluon PDFs.

Machine-learning prediction for quasiparton distribution function matrix elements

There have been rapid developments in the direct calculation in lattice QCD (LQCD) of the Bjorken-$x$ dependence of hadron structure through large-momentum effective theory (LaMET). LaMET overcomes the previous limitation of LQCD to moments (that is, integrals over Bjorken-$x$) of hadron structure, allowing LQCD to directly provide the kinematic regions where the experimental values are least known. LaMET requires large-momentum hadron states to minimize its systematics and allow us to reach small-$x$ reliably. This means that very fine lattice spacing to minimize lattice artifacts at order $(P_z a)^n$ will become crucial for next-generation LaMET-like structure calculations. Furthermore, such calculations require operators with long Wilson-link displacements (in finer lattice units), increasing the communication costs relative to that of the propagator inversion. In this work, we explore whether machine-learning (ML) algorithms can make correlator predictions to reduce the computational cost of these LQCD calculations. We consider two algorithms, gradient-boosting decision tree and linear models, applied to LaMET data, the matrix elements needed to determine the kaon and $\eta_s$ unpolarized parton distribution functions (PDFs), meson distribution amplitude (DA), and the nucleon gluon PDF. We find that both algorithms can reliably predict the target observables with different fit quality and systematic errors. The predictions from smaller displacement $z$ to larger ones work better than those for momentum $p$ due to the higher correlation among the data.

Complete matching for quasidistribution functions in large momentum effective theory

We complete the procedure of extracting parton distribution functions (PDFs) using large momentum effective theory (LaMET) at leading power accuracy in the hadron momentum. We derive a general factorization formula for the quasi PDFs in the presence of mixing, and give the corresponding hard matching kernel at $\mathcal O(\alpha_s)$, both for the unpolarized and for the polarized quark and gluon quasi-PDFs. Our calculation is performed in a regularization-independent momentum subtraction scheme. The results allow us to match the nonperturbatively renormalized quasi-PDFs to normal PDFs in the presence of mixing, and therefore can be used to extract flavor-singlet quark PDFs as well as gluon PDFs from lattice simulations.

Accessing Gluon Parton Distributions in Large Momentum Effective Theory.

Gluon parton distribution functions (PDFs) in the proton can be calculated directly on Euclidean lattices using large momentum effective theory (LaMET). To realize this goal, one has to find renormalized gluon quasi-PDFs in which power divergences and operator mixing are thoroughly understood. For the unpolarized distribution, we identify four independent quasi-PDF correlators that can be multiplicatively renormalized on the lattice. Similarly, the helicity distribution can be derived from three independent multiplicatively renormalizable quasi-PDFs. We provide a LaMET factorization formula for these renormalized quasi-PDFs from which one can extract the gluon PDFs.

Resummation for rapidity distributions in top-quark pair production

We extend our framework for the simultaneous resummation of soft and small-mass logarithms to rapidity distributions in top quark pair production. We give numerical results for the rapidity distribution of the top quark or the anti-top quark, as well as the rapidity distribution of the toverline{t} pair, finding that resummation effects stabilize the dependence of the differential cross sections on the choice of factorization scale. We compare our results with recent measurements at the Large Hadron Collider and find good agreement. Our results may be useful in the extraction of the gluon parton distribution function from toverline{t} production.

Gluon Quasi-Parton-Distribution Functions from Lattice QCD.

We present the first attempt to access the x dependence of the gluon unpolarized parton-distribution function (PDF), based on lattice simulations using the large-momentum effective theory approach. The lattice calculation is carried out with pion masses of 340 and 678MeV on a (2+1)-flavor domain-wall fermion configuration with lattice spacing a=0.111 fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93GeV. Taking the normalization from similar matrix elements in the rest frame of the nucleon and pion, our results for these matrix elements are consistent with the Fourier transform of the global fit CT14 and PDF4LHC15 NNLO of the gluon PDF, within statistical uncertainty and the systematic one up to power corrections, perturbative O(α_{s}) matching and the mixing from the quark PDFs.

Impact of the top quark cross-section data on parton distribution functions

Recent measurements of top quark pair production cross-section, which is performed at the LHC and the Tevatron collider, are studied using Hessian profiling technique to obtain their impact on the parton distribution functions (PDFs). The top quark production data covers different center-of-mass energies [Formula: see text], 5.02, 7, 8 and 13 TeV in either [Formula: see text] or [Formula: see text] collisions. It is explained how the Hessian profiling method may be used to assess the impact of these new data on PDFs and consequently on their predictions. In this research, the impact of recent measurements of top quark pair cross-sections on different CT14, MMHT2014 and NNPDF3.0 PDF sets is investigated. The analysis results show that the recent top quark production at the LHC and Tevatron data provide significant constraints in particular on the central value, relative uncertainties or both for the [Formula: see text]-quark distribution and the gluon PDFs in both CT14 and MMHT2014 PDF sets and are insensitive to valence-quark PDFs. A small constraint on the [Formula: see text]-sea quark distribution for CT14 PDF is also observed. There is no impact on the NNPDF3.0 PDF set in presence of these data.

Constraining Gluon Distributions in Nuclei Using Dijets in Proton-Proton and Proton-Lead Collisions at sqrt[s_{NN}]=5.02 TeV.

The pseudorapidity distributions of dijets as functions of their average transverse momentum (p_{T}^{ave}) are measured in proton-lead (pPb) and proton-proton (pp) collisions. The data samples were collected by the CMS experiment at the CERN LHC, at a nucleon-nucleon center-of-mass energy of 5.02TeV. A significant modification of the pPb spectra with respect to the pp spectra is observed in all p_{T}^{ave} intervals investigated. The ratios of the pPb and pp distributions are compared to next-to-leading order perturbative quantum chromodynamics calculations with unbound nucleon and nuclear parton distribution functions (PDFs). These results give the first evidence that the gluon PDF at large Bjorken x in lead ions is strongly suppressed with respect to the PDF in unbound nucleons.

Proton PDFs constraints from measurements using the ATLAS experiment

High-precision measurements of Standard Model (SM) processes provide information on different aspects contributing to the process, such as parton distribution functions (PDFs), and comparisons with the current precision reached theoretically on the calculations of the cross sections of such processes. This document describes ATLAS measurements, performed at different centre-of-mass energies, of vector boson (W and Z) cross sections and cross-section ratios. It also discusses measurements of ratios of Z-boson and top-quark pair production cross sections, which provide important information on the proton PDFs. Finally, a measurement involving the di-lepton decay channel of top-quark pairs at 8 TeV is presented, because of its direct sensitivity to the gluon PDF.

Measurement of differential cross sections and W+/W\u2212 cross-section ratios for W boson production in association with jets at sqrt{s}=8 TeV with the ATLAS detector

This paper presents a measurement of the W boson production cross section and the W+/W− cross-section ratio, both in association with jets, in proton-proton collisions at sqrt{s}=8 TeV with the ATLAS experiment at the Large Hadron Collider. The measurement is performed in final states containing one electron and missing transverse momentum using data corresponding to an integrated luminosity of 20.2 fb−1. Differential cross sections for events with at least one or two jets are presented for a range of observables, including jet transverse momenta and rapidities, the scalar sum of transverse momenta of the visible particles and the missing transverse momentum in the event, and the transverse momentum of the W boson. For a subset of the observables, the differential cross sections of positively and negatively charged W bosons are measured separately. In the cross-section ratio of W+/W− the dominant systematic uncertainties cancel out, improving the measurement precision by up to a factor of nine. The observables and ratios selected for this paper provide valuable input for the up quark, down quark, and gluon parton distribution functions of the proton.

Measurement of lepton differential distributions and the top quark mass in tbar{t} production in pp collisions at sqrt{s}=8\xa0TeV with the ATLAS detector

This paper presents single lepton and dilepton kinematic distributions measured in dileptonic tbar{t} events produced in 20.2hbox {fb}^{-1} of sqrt{s}=8 TeV pp collisions recorded by the ATLAS experiment at the LHC. Both absolute and normalised differential cross-sections are measured, using events with an opposite-charge emu pair and one or two b-tagged jets. The cross-sections are measured in a fiducial region corresponding to the detector acceptance for leptons, and are compared to the predictions from a variety of Monte Carlo event generators, as well as fixed-order QCD calculations, exploring the sensitivity of the cross-sections to the gluon parton distribution function. Some of the distributions are also sensitive to the top quark pole mass; a combined fit of NLO fixed-order predictions to all the measured distributions yields a top quark mass value of {m_t^{mathrm {pole}}}=173.2pm 0.9pm 0.8pm 1.2 GeV, where the three uncertainties arise from data statistics, experimental systematics, and theoretical sources.

The impact of CMS inclusive jet data on parton distribution functions and their uncertainties

It is well known that the jet production data at LHC provide important constraints on the medium and large-[Formula: see text] gluon parton distribution function (PDF), as well as on the large-[Formula: see text] sea quarks. In this work, we study the impact of recent CMS measurements for the inclusive jet production at center-of-mass energy of [Formula: see text][Formula: see text]=[Formula: see text]13 TeV on the PDFs and their uncertainties. To this aim, with use of the FastNLO and xFitter framework, we apply the parton distribution re-weighting procedure to study the impact of CMS data on two NLO modern CT14 and MMHT PDF sets. As a result, we found that the fit quality obtained using both of these PDF sets is very good. Moreover, the CMS data can impact both the central values and uncertainties of some PDFs especially at low and large [Formula: see text] regions. Overall, it is indicated that the CT14 PDFs compared with the MMHT ones are more affected. We emphasis that the inclusion of these data in a new global analysis of PDFs can improve the determination of the gluon and quark PDFs at both low and large [Formula: see text] regions.

Exclusive J/ψ and ϒ photoproduction and the low x gluon

We study exclusive vector meson photoproduction, with or ϒ, at next-to-leading order (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 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 enhancements. As a result, we find that predictions for the amplitude of ϒ production are stable to within about ±15%. This will allow data for the exclusive process at the Large Hadron Collider (LHC), particularly from LHCb, to be included in global parton analyses to constrain the gluon parton distribution function (PDF) down to Moreover, the study of exclusive photoproduction indicates that the gluon density found in the recent global PDF analyses is too small at low x and low scales.

Constraints on parton distributions and the strong coupling from LHC jet data

Jet production at hadron colliders provides powerful constraints on the parton distribution functions (PDFs) of the proton, in particular on the gluon PDF. Jet production can also be used to extract the QCD coupling [Formula: see text] and to test its running with the momentum transfer up to the TeV region. In this review, I summarize the information on PDFs and the strong coupling that has been provided by Run I LHC jet data. First of all, I discuss why jet production is directly sensitive to the gluon and quark PDFs at large-x, and then review the state-of-the-art perturbative calculations for jet production at hadron colliders and the corresponding fast calculations required for PDF fitting. Then I present the results of various recent studies on the impact on PDFs, in particular the gluon, that have been performed using as input jet measurements from ATLAS and CMS. I also review the available determinations of the strong coupling constant based on ATLAS and CMS jet data, with emphasis on the fact that LHC jet data provides, for the first time, a direct test of the [Formula: see text] running at the TeV scale. I conclude with a brief outlook on possible future developments.