Gluon Distribution Function Research Articles

Evolution of the color dipole cross section

Using Laplace transform techniques, we describe the evolution of the color dipole cross section at the leading-order and next-to-leading-order approximations from the Bartels–Golec-Biernat–Kowalski model in a kinematic region of low values of the Bjorken variable x and a wide range of transverse dipole size r. This evolution method shows that the saturation scale and geometric scaling are retained. We derived analytical results for the integrated and unintegrated color dipole gluon distribution functions and compared them with the CJ15 parameterization group and the unintegrated color dipole gluon distribution models, respectively. The Sudakov form factor in the evolution of the unintegrated color dipole gluon distribution is incorporated, and the results are considered at small and large values of kt2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_{t}^{2}$$\\end{document}.

B-meson production at forward rapidities in pp collisions at the LHC: estimating the intrinsic bottom contribution

The production of B mesons at forward rapidities is strongly sensitive to the behavior of the gluon and bottom distribution functions for small and large values of the Bjorken-x variable. In this exploratory study, we estimate the cross-section for the B±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^{\\pm }$$\\end{document} meson production in the kinematic range probed by the LHCb detector and that will be analyzed by the future Forward Physics Facility (FPF) considering the hybrid formalism, the solution of the running coupling Balitsky–Kovchegov equation and distinct descriptions for the bottom distribution function. We assume an ansatz for the intrinsic bottom component in the proton wave function, and estimate its impact on the transverse momentum, rapidity and Feynman-x distributions. Our results indicate that the presence of an intrinsic bottom strongly modifies the magnitude of the cross-section at ultra-forward rapidities (y≥6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y \\ge 6$$\\end{document}), which implies an enhancement of the B±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^{\\pm }$$\\end{document} production at the FPF. Possible implications on the prompt neutrino flux at ultra-high energies are also briefly discussed.

Exploring the impact of anti-shadowing effect on unintegrated gluon distributions in the MD-BFKL equation* *Supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030301), the Major Project of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008), the Education Department of Guizhou Province, China (QJJ[2022]016), and the Basic Research Program (Natural Science) of Guizhou Province, China

This paper presents a comprehensive analysis of the MD-BFKL equation, considering both shadowing and anti-shadowing effects in gluon recombination processes. By deriving analytical expressions for unintegrated gluon distributions through the solution of the MD-BFKL equation, with and without the incorporation of the anti-shadowing effect, we offer new insights into the influence of these effects on the behavior of unintegrated gluon distributions. Our results, when compared to those from the CT18NLO gluon distribution function, demonstrate that the anti-shadowing effect has a notably stronger impact on the characteristics of unintegrated gluon distributions, particularly in regions of high rapidity and momentum. This work significantly contributes to the understanding of gluon recombination mechanisms and their implications in high energy physics.

Gluon distribution and mass decomposition of the pion and kaon

We present the gluon distribution functions of the pion and kaon in small-x and large-x regions, and compare them with the results obtained from lattice QCD and continuum Schwinger function methods. Whether in the small-x region or the large-x region, our gluon distribution of the pion is consistent with the results of lattice QCD and continuum Schwinger function methods. We also calculate the first four moments of gluon distributions of the pion and kaon at different Q2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^{2}$$\\end{document} scales. In addition, we present the mass decomposition of the pion and kaon with the dynamical parton distribution functions calculated by the DGLAP equation with parton–parton recombination corrections. The mass structures of the pion and kaon are completely different from that of the proton.

Updated analyses of gluon distribution functions for the pion and kaon from the gauge-invariant nonlocal chiral quark model

In this work, we investigate the gluon distribution functions for the pion and kaon, in addition to the improved result of the valence-quark ones, in the gauge-invariant nonlocal chiral-quark model, in which the momentum dependence of the quark interactions is properly taken into account. We then analyze the gluon distribution functions, generated dynamically through the splitting functions in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi QCD evolution. By comparing with the recent lattice QCD results and Jefferson Lab angular momentum global analyses, it is found that the present numerical results for the gluon parton distribution functions for the pion exhibit a good agreement and the valence up-quark distribution results for the pion by reproducing the reanalyzed experimental data with a remarkable agreement. Our prediction on the gluon distribution functions for the kaon is also consistent with the recent lattice data for the kaon within the errors. Published by the American Physical Society 2024

Exploring the impact of high-precision top-quark pair production data on the structure of the proton at the LHC

The impact of recent LHC top-quark pair production single differential cross section measurements at 13 TeV collision energy on the structure of the proton is explored. In particular, the impact of these high-precision data on the gluon and other parton distribution functions (PDFs) of the proton at intermediate and large partonic momentum fraction x is analyzed. This study extends the CT18 global analysis framework to include these new data. The interplay between top-quark pair and inclusive jet production as well as other processes at the LHC, is studied. In addition, a study of the impact of scale choice on the theory description of the new 13 TeV tt¯ measurements is performed. Published by the American Physical Society 2024

Nonlinear corrections for the nuclear gluon distribution in eA processes

Abstract An analytical study with respect to the nonlinear corrections for the nuclear gluon distribution function in the next-to-leading order approximation at small x is presented. We consider the nonlinear corrections to the nuclear gluon distribution functions at low values of x and using the parametrization and the nuclear modification factors obtained from the Khanpour-Soleymaninia-Atashbar-Spiesberger-Guzey model. The CT18 gluon distribution is used for the baseline proton gluon density at . We discuss the behavior of the gluon densities in the next-to-leading order and the next-to-next-to-leading order approximations at the initial scale , as well as the modifications due to the nonlinear corrections. We find that the QCD nonlinear corrections are more significant for the next-to-leading order accuracy than the next-to-next-to-leading order for light and heavy nuclei. The results of the nonlinear GLR-MQ evolution equation are similar to those obtained with the Rausch-Guzey-Klasen gluon upward and downward evolutions within the uncertainties. The magnitude of the gluon distribution with the nonlinear corrections increases with a decrease in x and an increase in atomic number A.

Adiabatic hydrodynamization: A natural framework to find and describe prehydrodynamic attractors

The adiabatic hydrodynamization framework [1, 2] is a promising framework within which to describe and characterize pre-hydrodynamic attractors in a model-independent fashion. Using this framework, we define a procedure to identify a time-dependent change in coordinates which reveals a dynamical reduction in the number of active degrees of freedom. Applying this procedure to the kinetic theory of a Bjorken-expanding gas of gluons in the small angle elastic scattering limit, we are able to intuitively explain the selfsimilar evolution of the gluon distribution function long before the applicability of hydrodynamics, as well as the loss of memory of its initial condition.

Impact of charge symmetry breaking on gluon and sea quark distributions in the pion and kaon

In this exploratory study, I present, for the first time, the implications of the charge symmetry breaking (CSB) that arise from the [Formula: see text] and [Formula: see text] quark-mass differences on gluon and sea quark distribution functions of the pion and kaon in the framework of the Nambu–Jona-Lasino (NJL) model, which is a quark-level chiral effective theory of QCD, with the help of the proper-time regularization scheme to simulate color confinement of QCD. From the analysis, one finds that the charge symmetry (CS) gluon distribution for the pion has a good agreement with the prediction results obtained from the recent lattice QCD simulation and JAM global fit QCD analysis at a higher scale of [Formula: see text][Formula: see text]GeV2. The size of the CSB effects on gluon and sea quark distributions for the pion with the realistic ratios of [Formula: see text] at [Formula: see text][Formula: see text]GeV2 are, respectively, estimated by 1.3% and 2.0% at [Formula: see text] in comparison with those for [Formula: see text], while those for the kaon are approximately about 0.3% and 0.5% at [Formula: see text], respectively. A remarkable result is found that the CSB effects on gluon distribution for the kaon are smaller than that for the pion, which has a similar prediction result as that for the CS case.

Measurement of exclusive vector meson photoproduction in pPb collisions with the CMS experiment

The exclusive photoproduction of vector mesons provides a unique opportunity to constrain the gluon distribution function within protons and nuclei. Measuring vector mesons of various masses over a wide range of rapidity and as a function of transverse momentum provides important information on the evolution of the gluon distribution within nuclei. A variety of measurements, including the exclusive J/ψ, ρ, and Υ meson production in pPb (at nucleonnucleon center of mass energies of 5.02 and 8.16 TeV) and PbPb (5.02 TeV) collisions, are presented as a function of squared transverse momentum and the photon-proton center of mass energy. Finally, compilations of these data and previous measurements are compared to various theoretical predictions.

Determination of Parton Distribution Functions with Jets at Forward Rapidity Region Using xFitter Analysis Framework

Parton distribution functions (PDF), which have to be determined from the measurements, are one of the main components to define the physics that occurs at the hadron colliders. In this study, a quantum chromodynamics (QCD) analysis was performed at the next-to-leading order (NLO) in the xFitter framework which is an open source QCD fit platform. Along with the HERA1+2 DIS and the jet differential cross-section data measured in the forward rapidity region (3.2 < |y| < 4.7) of the CMS detector in the LHC in proton-proton collisions at s = 8 TeV were used in xFitter analysis framework. Particularly gluon distribution functions were emphasized.

The NNLO QCD analysis of gluon density at small-x

In this paper, a next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) calculation of gluon distribution function at small-[Formula: see text] is presented. The gluon distribution function is explored analytically in the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi approach by a Taylor expansion at small-[Formula: see text] as two first-order partial differential equations in two variables: Bjorken [Formula: see text] and [Formula: see text][Formula: see text]. We have solved the system of equations at LO, NLO and NNLO, respectively, by Lagrange’s method. The resulting analytical expressions are compared with the available global parton distribution function fits as well as with the results of the Block–Durand–McKay model. We have further performed an [Formula: see text] test to check the compatibility of our predictions and observed that our results can be consistently described in the context of perturbative QCD. A comparative analysis of the obtained results at LO, NLO and NNLO reveals that the NNLO approximation has a significant contribution to the gluon distribution function particularly in the small-[Formula: see text] region.

First glimpse into the kaon gluon parton distribution using lattice QCD

In this work, we present the first results on the gluon parton distribution of the kaon from lattice quantum chromodynamics. We carry out the lattice calculation at pion mass around 310~MeV and two lattice spacings, 0.15 and 0.12~fm, using $2+1+1$-flavor HISQ ensembles generated by MILC Collaboration. The kaon correlators are calculated using clover fermions and momentum-smearing sources with maximum boost momentum around 2~GeV and high statistics (up to 324,000 measurements). We study the dependence of the resulting reduced Ioffe-time pseudo-distributions at multiple boost momenta and lattice spacings. We then extract the kaon gluon distribution function in the $\overline{\text{MS}}$ scheme at $\mu = 2$~GeV, neglecting the mixing between the gluon and singlet-quark sectors. Our results at the smaller lattice spacing are consistent with phenomenological determinations.

Universality aspects of quantum corrections to transverse momentum broadening in QCD media

We study non-linear quantum corrections to transverse momentum broadening (TMB) of a fast parton propagating in dense QCD matter in the leading logarithmic approximation. These non-local corrections yield an anomalous super-diffusive behavior characterized by a heavy tailed distribution which is associated with Lévy random walks. Using a formal analogy with the physics of traveling waves, we show that at late times the transverse momentum distribution tends to a universal scaling regime. We derive analytic solutions in terms of an asymptotic expansion around the scaling limit for both fixed and running coupling. We note that our analytic approach yields a good agreement with the exact numerical solutions down to realistic values of medium length. Finally, we discuss the interplay between system size and energy dependence of the diffusion coefficient hat{q} and its connection with the gluon distribution function that is manifest at large transverse momentum transfer.

Longitudinal double-spin asymmetry for inclusive jet and dijet production in polarized proton collisions at s=510 GeV

We report measurements of the longitudinal double-spin asymmetry, ALL, for inclusive jet and dijet production in polarized proton-proton collisions at midrapidity and center-of-mass energy s=510 GeV, using the high luminosity data sample collected by the STAR experiment in 2013. These measurements complement and improve the precision of previous STAR measurements at the same center-of-mass energy that probe the polarized gluon distribution function at partonic momentum fraction 0.015≲x≲0.25. The dijet asymmetries are separated into four jet-pair topologies, which provide further constraints on the x dependence of the polarized gluon distribution function. These measurements are in agreement with previous STAR measurements and with predictions from current next-to-leading-order global analyses. They provide more precise data at low dijet invariant mass that will better constrain the shape of the polarized gluon distribution function of the proton.Received 21 October 2021Accepted 4 April 2022DOI:https://doi.org/10.1103/PhysRevD.105.092011Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuark & gluon jetsPhysical SystemsGluonsPropertiesSpinTechniquesHadron collidersParticles & FieldsNuclear Physics

Towards a single scale-dependent Pomeron in holographic light-front QCD

The Pomeron Regge trajectory underlies the dynamics dependence of hadronic total cross sections and diffractive reactions at high energies. The physics of the Pomeron is closely related to the gluon distribution function and the gluon gravitational form factor of the target hadron. In this article we examine the scale dependence of the nonperturbative gluon distribution in the nucleon and the pion, which was derived in a previous article [G. F. de T\'eramond, H. G. Dosch, T. Liu, R. S. Sufian, S. J. Brodsky, and A. Deur, Gluon matter distribution in the proton and pion from extended holographic light-front QCD, Phys. Rev. D 104, 114005 (2021)] in the framework of holographic light-front QCD and the Veneziano model. We argue that the QCD evolution of the gluon distribution function $g(x,\ensuremath{\mu})$ to large ${\ensuremath{\mu}}^{2}$ leads to a single scale-dependent Pomeron. The resulting Pomeron trajectory ${\ensuremath{\alpha}}_{P}(t,\ensuremath{\mu})$ not only depends on the momentum transfer squared $t$, but also on the physical scale $\ensuremath{\mu}$ of the amplitude, such as the virtuality ${Q}^{2}$ of the interacting photon in inclusive diffractive electroproduction, thus unifying the soft and the perturbative Pomeron. This can explain not only the ${Q}^{2}$ evolution of the proton structure function ${F}_{2}(x,{Q}^{2})$ at small $x$, but also the observed energy and ${Q}^{2}$ dependence of high energy diffractive processes involving virtual photons up to LHC energies.

Analytic derivation of the nonlinear gluon distribution function

In the present article, two analytical solutions based on the Laplace transforms method for the linear and non-linear gluon distribution functions have been presented at low values of $x$. These linear and non-linear methods are presented based on the solutions of the Dokshitzer-Gribov- Lipatov-Altarelli-Parisi (DGLAP) evolution equation and the Gribov-Levin-Ryskin Mueller-Qiu (GLR-MQ) equation at the leading-order accuracy in perturbative QCD respectively. The gluon distributions are obtained directly in terms of the parametrization of structure function $F_{2}(x,Q^{2})$ and its derivative and compared with the results from the parametrization models. The $n_{f}$ changes at the threshold are considered in the numerical results. The effects of the non-linear corrections are visible as $Q^{2}$ decreases and vanish as $Q^{2}$ increases. The nonlinear corrections tame the behavior of the gluon distribution function at low $x$ and $Q^{2}$ in comparison with the parametrization models.

Evidence for the maximally entangled low x proton in Deep Inelastic Scattering from H1 data

We investigate the proposal by Kharzeev and Levin of a maximally entangled proton wave function in Deep Inelastic Scattering at low x and the proposed relation between parton number and final state hadron multiplicity. Contrary to the original formulation we determine partonic entropy from the sum of gluon and quark distribution functions at low x, which we obtain from an unintegrated gluon distribution subject to next-to-leading order Balitsky–Fadin–Kuraev–Lipatov evolution. We find for this framework very good agreement with H1 data. We furthermore provide a comparison based on NNPDF parton distribution functions at both next-to-next-to-leading order and next-to-next-to-leading with small x resummation, where the latter provides an acceptable description of data.

Probing gluon helicity with heavy flavor at the Electron-Ion Collider

We propose a new measurement of the heavy flavor hadron double spin asymmetry in deep-inelastic scattering at a future Electron-Ion Collider (EIC) to constrain the polarized gluon distribution function inside the proton. Statistical projection on $D^0$ meson double spin asymmetry is calculated with an EIC central detector using an all-silicon tracker and vertexing subsystem. A first impact study was done by interpreting pseudo-data at next-to-leading order in QCD. The sensitivity of the experimental observable in constraining gluon helicity distribution in a wide range of parton momentum fraction $x$ has been investigated considering different beam energy configurations. This measurement complements the inclusive spin-dependent structure function measurement and provides an opportunity to constrain the gluon helicity distribution in the moderate $x$ region.

Transverse momentum dependent parton densities in processes with heavy quark generations

To study the heavy quark production processes, we use the transverse momentum dependent (TMD, or unintegrated) gluon distribution function in a proton obtained recently using the Kimber-Martin-Ryskin prescription from the Bessel-inspired behavior of parton densities at small Bjorken $x$ values. We obtained a good agreement of our results with the latest HERA experimental data for reduced cross sections $\sigma^{c\overline{c}}_{\rm red}(x,Q^2)$ and $\sigma^{b\overline{b}}_{\rm red}(x,Q^2)$, and also for deep inelastic structure functions $F_2^c(x,Q^2)$ and $F_2^b(x,Q^2)$ in a wide range of $x$ and $Q^2$ values. Comparisons with the predictions based on the Ciafaloni-Catani-Fiorani-Marchesini evolution equation and with the results of conventional pQCD calculations performed at first three orders of perturbative expansion are presented.