Quark Momentum Distributions Research Articles

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.

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.

Single electron yields from semileptonic charm and bottom hadron decays inAu+Aucollisions atsNN=200GeV

The PHENIX Collaboration at the Relativistic Heavy Ion Collider has measured open heavy-flavor production in minimum bias Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV via the yields of electrons from semileptonic decays of charm and bottom hadrons. Previous heavy-flavor electron measurements indicated substantial modification in the momentum distribution of the parent heavy quarks due to the quark-gluon plasma created in these collisions. For the first time, using the PHENIX silicon vertex detector to measure precision displaced tracking, the relative contributions from charm and bottom hadrons to these electrons as a function of transverse momentum are measured in Au$+$Au collisions. We compare the fraction of electrons from bottom hadrons to previously published results extracted from electron-hadron correlations in $p$$+$$p$ collisions at $\sqrt{s_{_{NN}}}=200$ GeV and find the fractions to be similar within the large uncertainties on both measurements for $p_T>4$ GeV/$c$. We use the bottom electron fractions in Au$+$Au and $p$$+$$p$ along with the previously measured heavy flavor electron $R_{AA}$ to calculate the $R_{AA}$ for electrons from charm and bottom hadron decays separately. We find that electrons from bottom hadron decays are less suppressed than those from charm for the region $3<p_T<4$ GeV/$c$.

The role of quark exchange in the structure function of Lithium nucleus

The quark exchange formalism is formulated to calculate the quark momentum distribution in the iso-scalar Lithium nucleus. Then by boosting the nucleus to an infinite momentum frame, the Lithium structure function is evaluated at different nucleon "sizes", i.e., b = 0.7, 0.8, 0.9 and 1 fm and the Bjorken scale (x) values. It is shown that the Lithium structure function becomes narrower, and it is pushed to the smaller x values, as the nucleon size is increased. Similar to our previous works for three nucleon systems, the Lithium nucleus European muon collaboration (EMC) ratio decreases, as we increase the x and b values and it shows larger effect, with respect to the free nucleon and three nucleons iso-scalar nucleus. On the other hand, present calculation of the EMC ratio for Lithium nucleus shows a good agreement with the corresponding NMC data, which is available for 1.4 × 10-4 ≤ x ≤ 0.65. Since the atomic number is still small (A = 6), in this work as usual, we ignore the possibility of simultaneous exchange of quarks between more than two nucleons, which can be important as one moves to the heavy nuclei. Although, according to Hen et al., in the neutron rich nuclei the protons have a greater probability than neutrons to have momentum greater than the Fermi momentum, the three-body contribution may be suppressed.

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.

Top-quark pair production at hadron colliders: differential cross section and phenomenological applications with DiffTop

The results of phenomenological studies of top-quark pair production in proton-proton collisions are presented. Differential cross sections are calculated in perturbative QCD at approximate next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ by using methods of threshold resummation beyond the leading logarithmic accuracy. Predictions for the single-particle inclusive kinematics are presented for transverse momentum and rapidity distributions of final-state top quarks. Uncertainties related to the description of proton structure, top-quark mass and strong coupling constant are investigated in detail. The results are compared to the recent measurements by the ATLAS and CMS collaborations at the LHC at the center of mass energy of 7 TeV. The calculation presented here is implemented in the computer code \textsc{Difftop} and can be applied to the general case of heavy-quark pair production at hadron-hadron colliders. For the first time, a fit of parton distribution functions at NNLO is performed by using the differential cross sections of top-quark pair production together with other data sets. The impact of the top-pair production on the precision of the gluon distribution at high scales is illustrated.

The new spin physics program of the COMPASS experiment

The COMPASS experiment, at CERN SPS, has been compiling for more than a decade successful and precise results on nucleon structure and hadron spectroscopy, leading to statistical errors much smaller than previously measured. The new COMPASS spin physics program, starting this year, aims to a rather complete nucleon structure description; this new representation goes beyond the collinear approximation by including the quark intrinsic transverse momentum distributions. The theoretical framework, for this new picture of the nucleon, is given by the Transverse Momentum Dependent distributions (TMDs) and by the Generalised Parton Distributions (GPDs). The TMDs, in particular Sivers, Boer-Mulders, pretzelosity and transversity functions will be obtained through the polarised Drell-Yan process, for the first time. The results will be complementary to those already obtained via polarised Semi-Inclusive Deep Inelastic Scattering (SIDIS). Also unpolarised SIDIS will be studied, allowing the knowledge improvement of the strange quark PDF and the access to the kaon fragmentation functions (FFs). Deeply Virtual Compton Scattering (DVCS) off an unpolarised hydrogen target will be used to study the GPDs, in a kinematic region not yet covered by any existing experiment.

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.

LEPTONIC DECAY WIDTHS OF VECTOR MESONS IN A RELATIVISTIC POTENTIAL MODEL

Leptonic decay widths and the corresponding decay constants of neutral vector mesons are calculated in the framework of a square-root potential model of independent quarks. Starting with the assumption that a strong correlation exists between the momenta of the quark and anti-quark inside the meson so as to have their total momenta identically zero in the center-of-mass frame of the meson, we find the quark and anti-quark momentum distribution amplitude which is used to determine the transition probability amplitude for the leptonic decay of mesons. The calculated results for leptonic decay widths and the electromagnetic decay constants for the vector mesons \rho, \omega, \phi and \psi are in good agrement with the corresponding experimental values. The results for the heavy meson \Upsilon are somewhat lower than the experimental values.

Tomography of exotic hadrons in high-energy exclusive processes

We investigated the possibility of determining internal structure of exotic hadrons by using high-energy reaction processes, where quarks and gluons are appropriate degrees of freedom. In particular, it should be valuable to investigate the high-energy exclusive processes which include generalized parton distributions (GPDs) and generalized distribution amplitudes (GDAs). The GPDs and GDAs contain momentum distributions of partons and form factors. We found that the exotic nature appears in momentum distributions of quarks as suggested by the constituent-counting rule and in the form factors associated with exotic hadron sizes and the number of constituents. Transition GPDs to exotic hadrons could probe such exotic signatures. We also propose that these exotic signatures should be found in exclusive production processes of exotic hadrons from gamma^* gamma in electron-positron annihilation. For example, the GDAs contain information on a time-like form factor of the energy-momentum tensor of a hadron h. We show that the cross section of e gamma -> e+hbar h is sensitive to the exotic signature by looking at the hbar h invariant-mass dependence by taking light hadrons, h=f_0 (980) and a_0 (980). From such GDA measurements, the tomography of exotic hadrons becomes possible, for example, by Belle and BaBar experiments and by future linear collider.

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.

Short-range correlations of partons &amp; 3D nucleon structure

Dynamical breaking of chiral symmetry in QCD is caused by non- perturbative interactions on a scale �∼ 0.3fm much smaller than the hadronic size R∼ 1fm. This has important consequences for the nucleon structure such as the prediction that the transverse momentum distribution of sea quarks is sig- nificantly broader than the pT-distribution of valence quarks due to short-range correlations between sea quarks in the nucleon's light-cone wave function.

SEA QUARK TRANSVERSE MOMENTUM DISTRIBUTIONS AND DYNAMICAL CHIRAL SYMMETRY BREAKING

Recent theoretical studies have provided new insight into the intrinsic transverse momentum distributions of valence and sea quarks in the nucleon at a low scale. The valence quark transverse momentum distributions ([Formula: see text]) are governed by the nucleon's inverse hadronic size R-1 ~ 0.2 GeV and drop steeply at large pT. The sea quark distributions ([Formula: see text]) are in large part generated by non–perturbative chiral–symmetry breaking interactions and extend up to the scale ρ-1 ~ 0.6 GeV. These findings have many implications for modeling the initial conditions of perturbative QCD evolution of TMD distributions (starting scale, shape of pT distributions, coordinate–space correlation functions). The qualitative difference between valence and sea quark intrinsic pT distributions could be observed experimentally, by comparing the transverse momentum distributions of selected hadrons in semi–inclusive deep–inelastic scattering, or those of dileptons produced in pp and [Formula: see text] scattering.

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.

Experimental Program of the Future COMPASS-II Experiment at CERN

Over the last decade the COMPASS experiment has successfully obtained precise results on nucleon structure and hadron spectroscopy, with statistical errors much lower than previously reported. Recently, the new COMPASS-II program, focused on the study of a more complete nucleon description, was approved by CERN. The goal of the program is to access the nucleon structure beyond the collinear approxi-mation, including the quark intrinsic transverse momentum distributions, which are described by the Transverse Momentum Dependent (TMD) Parton Distribution Functions (PDFs) and by Generalised Parton Distributions (GPDs). The COMPASS collaboration proposes to measure the TMD PDFs, for the first time, via the polarised Drell-Yan process. The results will be complementary to those already obtained in polarised Semi-Inclusive Deep Inelastic Scattering (SIDIS). The GPDs can be accessed using deeply virtual Compton scattering and hard exclusive meson production using an unpolarised hydrogen target in a kinematic region not yet covered by any existing experiment. Also unpolarised SIDIS will be studied, by improving the knowledge of the strange quark PDF and obtaining the kaon fragmentation functions. Another topic covered in this COMPASS-II program is the measurement of the pion and kaon polarisabilities using the Primakoff reaction, which corresponds to a test of the chiral perturbative theory.

Charmonium production from nonequilibrium charm and anticharm quarks in quark-gluon plasma

Parameterizing the charm and anticharm quark momentum distributions by the Tsallis distribution, we study the nonequilibrium effect on the charmonium production rate in a quark-gluon plasma up to the next-to-leading order in perturbative QCD. We find that nonequilibrium charm and anticharm quarks suppress the charmonium production rate compared to that from equilibrated ones. We further show that the suppression factor calculated with the charm quark relaxation time, which has frequently been used in the literature, is close to our results.

Charmed-Hadron Production in ϒ(1S) Semi-inclusive Decay

In the framework of the NRQCD factorization formalism, we calculate the decay rate for the process ϒ(1S) → cc̄gg to the next-to-leading order (NLO) in the relative velocity v of the b quark in the bottomonium rest frame. We also study the momentum distributions of the charm quark and the charmed-hadron in the decay. The momentum distribution of the charmed-hadron is obtained by convolving the charm quark momentum distribution with a fragmentation function of the charm quark into the hadron. In addition, we fit the nonperturbative NRQCD matrix element ⟨v2⟩ϒ through comparing the theoretical prediction with the measurement from the BaBar collaboration for the decay rate of ϒ(1S) → D*+X. In return, taking this matrix element as an input parameter, we predict the decay rates as well as the momentum distributions for a collection of charmed-hadrons in the process ϒ(1S) → cc̄gg → hX.