Momentum Distributions Of Gluons Research Articles

Proton generalized parton distributions from lattice QCD

Momentum and spatial distributions of quarks and gluons inside hadrons are typically encoded in the so-called generalized parton distributions (GPDs). GPDs are multi-dimensional quantities that are very challenging to extract, both experimentally and within lattice QCD. We present the first lattice results on the x-dependence of isovector unpolarized, helicity and transversity GPDs of the proton, obtained from lattice QCD using an ensemble of Nf = 2 + 1 + 1 maximally twisted mass fermions, with pion mass Mπ = 260 MeV and lattice spacing a ' 0.093 fm. Our calculations use the quasi-distribution formalism and the final distributions are presented in the MS scheme at a renormalization scale of 2 GeV.

Many-Body Correlation Effects on the <i>x</i><sub>Bjorken</sub>-Dependence of Cross Section Ratios off Nuclei for 1 < <i>x</i><sub>Bjorken</sub> < 2

Many-body correlations in nuclei determine the behavior of Deep-Inelastic-Scattering (DIS) and Quasi-Elastic Scattering (QES) cross section ratios off heavy over light nuclei especially for xBjorken > 1, obtained at Jefferson Lab. They can be described in terms of quark-cluster formation in nuclei due to wave-function overlapping, manifesting itself when the momentum transfer is high so that the partonic degrees of freedom are resolved. In clusters (correlated nucleons) the quark and gluon momentum distributions are softer than in single nucleons and extend to xBjorken > 1. The cluster formation probabilities are computed using a network-defining algorithm in which the initial nucleon density is either standard Woods-Saxon or is input from lower energy data while the critical radius for nucleon merging is an adjustable parameter. The exact choice of critical radius depends on the specific nucleus and it is anti-correlated to the rescaling of the xBjorken needed for bound nucleons. The calculations show that there is a strong dependence of the cross section ratios on the xBjorken in agreement with the data and that four-body correlations are needed to explain the experimental results even in the range 1 xBjorken < 2. The dependence on the specific exponents of parton distributions in high-order clusters is weak.

Screening properties of quark-gluon plasma obtained from distribution and correlation functions of the constituent quasiparticle model

Based on the constituent quasiparticle model of quark-gluon plasma (QGP), the matrix elements of the density operator and the Wigner function in the color phase space are presented in form of color path integrals over Wiener and SU(3) group Haar measures. Monte Carlo calculations of quark and gluon momentum distributions and spatial pair distribution functions have been carried out for the strongly coupled QGP plasma in thermal equilibrium at zero baryon chemical potential. The Debye screening mass and the running coupling constant have been obtained from the spatial pair distribution function and are in agreement with the available lattice QCD data. At densities related to the average interparticle distance more than 0.4 fm the gluon bound states in the form of glueballs have been found. Comparison with the Maxwell Boltzmann distribution shows significant influence of interparticle interaction on high energy asymptotics of the momentum distribution functions, resulting in appearance of quantum tails. The new color pair correlation function has been introduced, and related new color screening mass has been discussed.

QCD evolution of the orbital angular momentum of quarks and gluons: Genuine twist-three part

We present the numerical solution of the one-loop QCD evolution equation for the genuine twist-three part of the orbital angular momentum (OAM) distributions of quarks and gluons inside a longitudinally polarized nucleon. This is based on the observation that the evolution is identical to that of the Efremov-Teryaev-Qiu-Sterman function for transverse single spin asymmetry. Together with the known evolution of the Wandzura-Wilczek part, the one-loop evolution of OAM distributions is now practically under control. We also study, for the first time, the scale dependence of the potential angular momentum defined as the difference between the Ji and Jaffe-Manohar definitions of OAM.

Pinning down the linearly-polarised gluons inside unpolarised protons using quarkonium-pair production at the LHC

We show that the production of J/ψ or ϒ pairs in unpolarised pp collisions is currently the best process to measure the momentum distribution of linearly-polarised gluons inside unpolarised protons through the study of azimuthal asymmetries. Not only the short-distance coefficients for such reactions induce the largest possible cos⁡4ϕ modulations, but analysed data are already available. Among the various final states previously studied in unpolarised pp collisions within the TMD approach, di-J/ψ production exhibits by far the largest asymmetries, in the region studied by the ATLAS and CMS experiments. In addition, we use the very recent LHCb data at 13 TeV to perform the first fit of the unpolarised transverse-momentum-dependent gluon distribution.

Gluon Shadowing in Heavy-Flavor Production at the LHC.

We study the relevance of experimental data on heavy-flavor [D^{0}, J/ψ, B→J/ψ and ϒ(1S) mesons] production in proton-lead collisions at the LHC to improve our knowledge of the gluon-momentum distribution inside heavy nuclei. We observe that the nuclear effects encoded in both most recent global fits of nuclear parton densities at next-to-leading order (nCTEQ15 and EPPS16) provide a good overall description of the LHC data. We interpret this as a hint that these are the dominant ones. In turn, we perform a Bayesian-reweighting analysis for each particle data sample which shows that each of the existing heavy-quark(onium) data set clearly points-with a minimal statistical significance of 7σ-to a shadowed gluon distribution at small x in the lead. Moreover, our analysis corroborates the existence of gluon antishadowing. Overall, the inclusion of such heavy-flavor data in a global fit would significantly reduce the uncertainty on the gluon density down to x≃7×10^{-6}-where no other data exist-while keeping an agreement with the other data of the global fits. Our study accounts for the factorization-scale uncertainties which dominate for the charm(onium) sector.

On the small-x behavior of the orbital angular momentum distributions in QCD

We present the numerical solution of the leading order QCD evolution equation for the orbital angular momentum distributions of quarks and gluons and discuss its implications for the nucleon spin sum rule. We observe that at small-x, the gluon helicity and orbital angular momentum distributions are roughly of the same magnitude but with opposite signs, indicating a significant cancellation between them. A similar cancellation occurs also in the quark sector. We explain analytically the reason for this cancellation.

Transport coefficients of a hot QCD medium and their relative significance in heavy-ion collisions

The main focus of this article is to obtain various transport coefficients for a hot QCD medium that is produced while colliding two heavy nuclei ultra-relativistically. As the hot QCD medium follows dissipative hydrodynamics while undergoing space-time evolution, the knowledge of the transport coefficients such as thermal conductivity, electrical conductivity, shear and bulk viscosities are essential to understand the underlying physics there. The approach adopted here is semi-classical transport theory. The determination of all these transport coefficients requires knowledge of the medium away from equilibrium. In this context, we setup the linearized transport equation employing the Chapman-Enskog technique from kinetic theory of many particle system with a collision term that includes the binary collisions of quarks/antiquarks and gluons. In order to include the effects of a strongly interacting, thermal medium, a quasi-particle description of realistic hot QCD equation of state has been employed through the equilibrium modeling of the momentum distributions of gluons and quarks with non-trivial dispersion relations while extending the model for finite but small quark chemical potential. The effective coupling for strong interaction has been redefined following the charge renormalization under the scheme of the quasiparticle model. The consolidated effects on transport coefficients are seen to have significant impact on their temperature dependence. The relative significances of momentum and heat transfer as well as charge diffusion processes in hot QCD have been investigated by studying the ratios of the respective transport coefficients.

Full jet evolution in quark–gluon plasma and nuclear modification of jet structure in Pb+Pb collisions at 2.76A TeV

We study the evolution of full jet shower in quark-gluon plasma via solving a set of coupled differential transport equations for the three-dimensional momentum distributions of quarks and gluons contained in the full jets. The evolution equations include all partonic splitting processes as well as the collisional energy loss and transverse momentum broadening for both the leading and radiated partons of the full jets. Combining with realistic hydrodynamic simulation for the space-time evolution of the fireball created in Pb+Pb collisions at 2.76A TeV, we calculate the nuclear modification of single inclusive full jet spectra, the momentum imbalance of photon-jet and dijet pairs, and jet shape function (at partonic level). The roles of various jet-medium interaction mechanisms on the modification of full jet energy and internal structure are studied.

Gluon orbital angular momentum at small x

We present a general analysis of the orbital angular momentum (OAM) distribution of gluons ${L}_{g}(x)$ inside the nucleon with particular emphasis on the small-$x$ region. We derive a novel operator representation of ${L}_{g}(x)$ in terms of Wilson lines and argue that it is approximately proportional to the gluon helicity distribution ${L}_{g}(x)\ensuremath{\approx}\ensuremath{-}2\mathrm{\ensuremath{\Delta}}G(x)$ at small $x$. We also compute longitudinal single-spin asymmetry in exclusive diffractive dijet production in lepton-nucleon scattering in the next-to-eikonal approximation and show that the asymmetry is a direct probe of the gluon helicity/OAM distribution as well as the QCD odderon exchange.

Impact of momentum anisotropy and turbulent chromo-fields on thermal particle production in quark\u2013gluon-plasma medium

Momentum anisotropy present during the hydrodynamic evolution of the Quark–Gluon Plasma (QGP) in RHIC may lead to the chromo-Weibel instability and turbulent chromo-fields.The dynamics of the quark and gluon momentum distributions in this case is governed by an effective diffusive Vlasov equation (linearized). The solution of this linearized transport equation for the modified momentum distribution functions lead to the mathematical form of non-equilibrium momentum distribution functions of quarks/antiquarks and gluons. The modifications to these distributions encode the physics of turbulent color fields and momentum anisotropy. In the present manuscript, we employ these distribution functions to estimate the thermal dilepton production rate in the QGP medium. The production rate is seen to have appreciable sensitivity to the strength of the anisotropy.

Full jet evolution in quark-gluon plasma and nuclear modification of jet production and jet shape inPb+Pbcollisions at2.76ATeVat the CERN Large Hadron Collider

We study the evolution of full jet shower in quark-gluon plasma via solving a set of coupled differential transport equations for the three-dimensional momentum distributions of quarks and gluons contained in the full jets. In our jet evolution equations, we include all partonic splitting processes as well as the collisional energy loss and transverse momentum broadening for both the leading and radiated partons of the full jets. Combining with a realistic (2+1)-dimensional viscous hydrodynamic simulation for the space-time profiles of the hot and dense nuclear medium produced in heavy-ion collisions, we apply our formalism to calculate the nuclear modification of single inclusive full jet spectra, the momentum imbalance of photon-jet and dijet pairs, and jet shape function (at partonic level) in Pb+Pb collisions at 2.76 ATeV. The roles of various jet-medium interaction mechanisms on the full jet modification are studied. We find that the nuclear modification of jet shape is sensitive to the interplay of different interaction mechanisms as well as the energies of the full jets.

Gluon TMD studies at EIC

A high-energy Electron-Ion Collider (EIC) would offer a most promising tool to study in detail the transverse momentum distributions of gluons inside hadrons. This applies to unpolarized as well as linearly polarized gluons inside unpolarized protons, and to left-right asymmetric distributions of gluons inside transversely polarized protons, the so-called gluon Sivers effect. The inherent process dependence of these distributions can be studied by comparing to similar, but often complementary observables at LHC.

Average Transverse Momentum Quantities Approaching the Lightfront

In this contribution to Light Cone 2014, three average transverse momentum quantities are discussed: the Sivers shift, the dijet imbalance, and the $p_T$ broadening. The definitions of these quantities involve integrals over all transverse momenta that are overly sensitive to the region of large transverse momenta, which conveys little information about the transverse momentum distributions of quarks and gluons inside hadrons. TMD factorization naturally suggests alternative definitions of such integrated quantities, using Bessel-weighting and rapidity cut-offs, with the conventional definitions as limiting cases. The regularized quantities are given in terms of integrals over the TMDs of interest that are well-defined and moreover have the advantage of being amenable to lattice evaluations.

Measuring the gluon distribution in nuclei at an electron–ion collider

Despite the successes of the HERA collider, where much information was gained on the structure of the nucleon, data on the structure of the nucleus at moderate-to-small x remains elusive, as only fixed-target high- x data currently exist. The small- x region, however, is of great interest. The nucleon structure in this region is dominated by gluons which show a rapid rise with decreasing x . At low- x , this growth must be tamed and the gluon distribution will be saturated. This saturation phenomena is expected to be universal, appearing in both nucleons and nuclei. A knowledge of this regime is of vital importance to understanding the underlying physics which governs the initial conditions of heavy-ion collisions at both the LHC and RHIC, where particle production is dominated by gluons from this unknown region. However, only tantalising hints of this have been observed so far. Therefore, the construction of an Electron–Ion Collider (EIC), colliding polarised electrons with polarised protons and also a wide variety of nuclei, will allow an exploration of the region of small- x in great detail (with luminosities 100 x that of HERA), answering questions on both the spatial and momentum distributions of gluons and sea quarks in nuclei. In particular, the saturation region is more accessible in nuclei due to the amplification of the saturation scale with nuclear size ( Q S ∝ A 1 / 3 ). In this paper I present the current status of measuring the gluon distribution in nuclei in e + A collisions at an EIC.

Jet propagation and medium excitation in a quark–gluon plasma

Abstract We implement the complete set of elastic 2 → 2 parton scattering processes in the Linearized Boltzmann Transport (LBT) model to study the parton propagation inside a hot quark–gluon plasma. We calculate and compare the elastic energy loss and the transverse momentum distribution of quarks and gluons. We further simulate a single jet propagation and the induced medium excitation within a static quark–gluon plasma to study how the jet energy and profiles are modified by the jet-medium interaction and in particular the jet-induced wake. Effects of the recoiled thermal partons and the jet-induced wake on the jet energy loss and profiles are studied in detail.

Studies of the 3D structure of the proton at Jlab

In recent years parton distributions, describing longitudinal momentum, helicity and transversity distributions of quarks and gluons, have been generalized to account also for transverse degrees of freedom. Two new sets of more general distributions, Transverse Momentum Distributions (TMDs) and Generalized Parton Distributions (GPDs) were introduced to describe transverse momentum and spatial distributions of partons. Great progress has been made since then in measurements of different Single Spin Asymmetries (SSAs) in semi-inclusive and hard exclusive processes, providing access to TMDs and GPDs, respectively. Studies of TMDs and GPDs are also among the main driving forces of the JLab 12 GeV upgrade project.

Structure and spin of the nucleon

Parton distribution functions, describing longitudinal momentum, helicity and transversity distributions of quarks and gluons, have been recently generalized to account also for transverse degrees of freedom. Two new sets of more general distributions, Transverse Momentum Distributions and Generalized Parton Distributions, were introduced to describe transverse momentum and space distributions of partons. Great progress has been made since then in measurements of different Single Spin Asymmetries (SSAs) in semi-inclusive and hard exclusive processes providing access to TMDs and GPDs, respectively. Facilities world-wide involved in studies of the 3D structure of nucleon include HERMES, COMPASS, BELLE, BaBar, Halls A, B, and C at JLab, and PHENIX and STAR at RHIC (BNL). TMD studies in the Drell-Yan process are also becoming an important part of the program of hadron scattering experiments. Studies of TMDs are also among the main driving forces of the JLab 12-GeV upgrade project, several of the forward upgrade proposals of STAR and PHENIX at RHIC, and future facilities, such as the Electron Ion Collider (EIC), FAIR in Germany, and NICA in Russia. In this contribution we present an overview of the latest developments in studies of parton distributions and discuss newly released results, ongoing activities, as well as some future measurements.

Medium-induced broadening and softening of a parton shower

The modifications of the angular and transverse momentum distributions of quarks and gluons inside a parton shower due to the presence of a medium are studied within an analytical description that reduces to the modified leading logarithmic approximation (MLLA) of QCD in the absence of medium.

Thermalization of gluon matter including [formula omitted] interactions

Within a pQCD inspired kinetic parton cascade we simulate the space time evolution of gluons which are produced initially in a heavy ion collision at RHIC energy. The inelastic gluonic interactions gg ↔ ggg do play an important role: For various initial conditions it is found that thermalization and the close to ideal fluid dynamical behaviour sets in at very early times. Special emphasis is put on color glass condensate initial conditions and the 'bottom up thermalization' scenario. Off-equilibrium 3 → 2 processes make up the very beginning of the evolution leading to an initial decrease in gluon number and a temporary avalanche of the gluon momentum distribution to higher transversal momenta.