Since quarks are regarded as the most fundamental particles which constitute hadrons that we observe in the real world, there are many theories about how many of them are needed and what quantum numbers they carry. Another important question is what keeps them inside the hadron, which is known to have space-time extension. Since they are relativistic objects, how would the hadron appear to observers in different Lorentz frames? The hadron moving with speed close to that of light appears as a collection of Feynman's partons. In other words, the same object looks differently to observers in two different frames, as Einstein's energy-momentum relation takes different forms for those observers. In order to explain this, it is necessary to construct a quantum bound-state picture valid in all Lorentz frames. It is noted that Paul A. M. Dirac studied this problem of constructing relativistic quantum mechanics beginning in 1927. It is noted further that he published major papers in this field in 1945, 1949, 1953, and in 1963. By combining these works by Dirac, it is possible to construct a Lorentz-covariant theory which can explain hadronic phenomena in the static and high-speed limits, as well as in between. It is shown also that this Lorentz-covariant bound-state picture can explain what we observe in high-energy laboratories, including the parton distribution function and the behavior of the proton form factor.
Anisotropies of hadronic distribution in nuclear collisions are used for determination of properties of the nuclear matter. At the LHC it is important to account for the contribution to the flow due to momentum transferred from hard partons to the quark-gluon plasma.
Evolution of anisotropy in momentum and coordinate space of the parton system produced in relativistic heavy-ion collisions is discussed within the free-streaming approximation. The momentum distribution evolves from the prolate shape - elongated along the beam - to the oblate one - squeezed along the beam. At the same time the eccentricity in the coordinate space, which occurs at finite values of impact parameter, decreases. It is argued that the parton system reaches local thermodynamic equilibrium before the momentum distribution becomes oblate.
We investigate the processes leading to phase-space equilibration of parton distributions in nuclear interactions at collider energies. We derive a set of rate equations describing the chemical equilibration of gluons and quarks including medium effects on the relevant QCD transport coefficients, and discuss their consequences for parton equilibration in heavy ion collisions.
The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is applied to Pb+Pb collisions from 20 to 160 A GeV in order to explore the space-time regions of 'partonic matter'. We find that even central collisions at the top-SPS energy of 158 A GeV show a large fraction of non-partonic, i.e. hadronic or string-like matter, which can be viewed as a hadronic corona. Furthermore, we observe that the partonic phase has a very low impact on rapidity distributions of hadrons but a …
In this paper we consider double parton distribution functions (dPDFs) which are the main non perturbative ingredients appearing in the double parton scattering cross section formula in hadronic collisions. By using recent calculation of dPDFs by means of constituent quark models within the so called Light-Front approach, we investigate the role of relativistic effects on dPDFs. We find, in particular, that the so called Melosh operators, which allow to properly convert the LF spin into the canonical one and incorporate a proper treatment of boosts, produce sizeable effects on dPDFs. We discus…
The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results - including the partonic equation of state - in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neut…
Longitudinal and transverse parton distributions for pion and nucleon are calculated from hadron vertexes obtained by a study of form factors within relativistic quark models. The relevance of the one-gluon-exchange dominance at short range for the behavior of the form factors at large momentum transfer and of the parton distributions at the end points is stressed.
The quark gluon plasma produced in ultra-relativistic heavy-ion collisions exhibits remarkable features. It behaves like a nearly perfect liquid with a small shear viscosity to entropy density ratio and leads to the quenching of highly energetic particles. We show that both effects can be understood for the first time within one common framework. Employing the parton cascade Boltzmann Approach to Multi-Parton Scatterings (BAMPS), the microscopic interactions and the space-time evolution of the quark gluon plasma are calculated by solving the relativistic Boltzmann equation. Based on cross sect…
We investigate the impact parameter dependent parton distributions for a relativistic composite system in light-front framework. We take an effective two-body spin-1/2 state, namely an electron dressed with a photon in QED. We express the impact parameter dependent parton distributions in terms of overlaps of light-cone wave functions. We obtain the scale dependence of both fermion and gauge boson distributions and show the distortion of the pdfs in the transverse space for transverse polarization of the state at one loop level.
We investigate the impact parameter dependent parton distributions for a relativistic composite system in light-front framework. We express them in terms of overlaps of light-cone wave functions for a self consistent two-body spin-1/2 state, namely an electron dressed with a photon in QED. The pdfs are distorted in the transverse space for transverse polarization of the state at one loop level.
We study the energy-momentum deposited by fast moving partons within a medium using linearized viscous hydrodynamics. The particle distribution produced by this energy-momentum is computed using the Cooper-Frye formalism. We show that for the conditions arising in heavy-ion collisions, energy momentum is preferentially deposited along the head shock of the fast moving partons. We also show that the double hump in the away-side of azimuthal correlations can be produced by two (instead of one) away-side partons that deposit their energy-momentum along their directions of motion. These partons ar…
The novel Parton-Hadron-String Dynamics (PHSD) transport approach is applied to nucleus-nucleus collisions at RHIC energies with respect to differential hadronic spectra in comparison to available data. The PHSD approach is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results from the Wuppertal-Budapest group in thermodynamic equilibrium. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor cu…
We explore parton collisional effects on the conversion of geometry eccentricities into azimuthal anisotropies in Pb+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV using a multi-phase transport model. The initial eccentricity $\varepsilon_{n}$ (n = 2,3) and flow harmonics $v_{n}$ (n = 2,3) are investigated as a function of the number of parton collisions ($N_{coll}$) during the source evolution of partonic phase. It is found that partonic collisions leads to generate elliptic flow $v_{2}$ and triangular flow $v_{3}$ in Pb+Pb collisions. On the other hand, partonic collisions also result in an evo…
We study momentum imbalance as a function of jet asymmetry in high-energy heavy-ion collisions. To implement parton production during the collision, we include all Leading Order (LO) $2\to 2$ and $2\to 3$ parton processes in pQCD. The produced partons lose energy within the quark gluon plasma and hadronize collinearly when they leave it. The energy and momentum deposited into the plasma is described using linear viscous hydrodynamics with a constant energy loss per unit length and a total energy loss given by a Gaussian probability centered around a mean value $\bar{\mathcal{E}}$ and a half-wi…
The angular structure of collisional and radiative energy losses of a hard parton jet propagating through the quark-gluon plasma is analyzed. The possibility to observe the energy losses of quark- and gluon-initiated jets in dense QCD-matter (jet quenching) measuring the characteristics of real hadronic jets in ultra-relativistic collisions of nuclei is investigated. In particular, using calorimetric studies of jet + jet, gamma + jet and Z + jet channels is discussed.
We analyze the recent data from the BRAHMS Collaboration on the pseudorapidity dependence of nuclear modification factors in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV by using the full three dimensional hydrodynamic simulations for the density effects on parton energy loss. We first compute the transverse spectra at $η=0$ and 2.2, and next take a ratio $R_η=R_{AA}(η=2.2)/R_{AA}(η=0)$, where $R_{AA}$ is a nuclear modification factor. It is shown that hydrodynamic components account for $R_η\simeq 1$ at low $p_\mathrm{T}$ and that quenched pQCD components lead $R_η < 1$ at high $p_\mathrm{T}…
Higher-order anisotropic flows $v_{4}$ and $v_{6}$ in heavy ion collisions at the Relativistic Heavy Ion Collider are studied in a multiphase transport model that has previously been used successfully for describing the elliptic flow $v_2$ in these collisions. We find that the same parton scattering cross section of about 10 \textrm{mb} used in explaining the measured $v_2$ can also reproduce the recent data on $v_{4}$ and $v_{6}$ from Au + Au collisions at $\sqrt{s}=200$ \textrm{AGeV}. It is further found that the $% v_{4}$ is a more sensitive probe of the initial partonic dynamics in these c…
We study cluster and hypernuclei production in heavy-ion collisions at relativistic energies employing the Parton-Hadron-Quantum-Molecular-Dynamics (PHQMD) approach, a microscopic n-body transport model based on the QMD propagation of the baryonic degrees of freedom with density dependent 2-body potential interactions. All other ingredients of PHQMD, including the collision integral and the treatment of the quark-gluon plasma (QGP) phase, are adopted from the Parton-Hadron-String Dynamics (PHSD) approach. In PHQMD the cluster formation occurs dynamically, caused by the interactions. The cluste…
The effects of color screening on the hadronization of a parton plasma into a hadron gas are examined at the energies of the relativistic heavy ion collider. It is found to have the tendency to prevent hadronization and therefore delaying the conversion of the partons into a hadron gas. Because of the continual expansion, the resulting hadron gas number densities are lower when screening is included. This should reduce the hadronic noise to genuine signals of the quark-gluon plasma. In this sense, color screening is favorable and should be included in numerical models. In any case, we advocate…
We study the production of heavy quarks, charm at BNL-RHIC ($\sqrt{s}$=200 GeV/nucleon) and CERN-LHC ($\sqrt{s}$=5.5 TeV/nucleon) and bottom at CERN-LHC from heavy ions colliding at relativistic energies. We consider initial fusion of gluons (and quark- anti-quark annihilation), pre-thermal parton interactions and interactions in thermalized quark gluon plasma. We also consider free-streaming partons as another extreme and compare the results with those from a thermalized plasma of partons. The pre-thermal contribution is calculated by considering interaction among partons having large transve…
We examine Pb+Pb collisions at CERN SPS energy 158 A GeV, by employing the earlier developed and recently refined parton-cascade/cluster-hadronization model and its Monte Carlo implementation. This space-time model involves the dynamical interplay of perturbative QCD parton production and evolution, with non-perturbative parton-cluster formation and hadron production through cluster decays. Using computer simulations, we are able to follow the entwined time-evolution of parton and hadron degrees of freedom in both position and momentum space, from the instant of nuclear overlap to the final yi…
In the theory of deep inelastic scattering (DIS) the final state interaction (FSI) between the struck quark and the remnants of the target is usually assumed to be negligible in the Bjorken limit. This assumption, still awaiting a full validation within nonperturbative QCD, is investigated in a model composed by two relativistic particles, interacting via a relativistic harmonic oscillator potential, within light-cone hamiltonian dynamics. An electromagnetic current operator whose matrix elements behave properly under Poincaré transformations is adopted. It is shown that: i) the parton model i…
Wounded parton scaling of multiplicities in ultra-relativistic light- and heavy-ion collisions
Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院核物理研究所）；AGH University of Kraków, Faculty of Physics and Applied Computer Science（克拉科夫AGH科技大学物理与应用计算机科学学院）
The measurement of nuclear Generalized Parton Distributions (GPDs) represents a valuable tool to understand the structure of bound nucleons and the phenomenology of hard scattering off nuclei. By using a realistic, non-relativistic microscopic approach for the evaluation of GPDs of 3He, it will be shown that conventional nuclear effects, such as isospin and binding ones, or the uncertainty related to the use of a given nucleon-nucleon potential, are bigger than in the forward case so that, if great attention is not paid, conventional nuclear effects can be easily mistaken for exotic ones. It i…
From the correlation structure of transverse momentum $p_t$ in relativistic nuclear collisions we observe for the first time temperature/velocity structure resulting from low-$Q^2$ partons. Our novel analysis technique does not invoke an {\em a priori} jet hypothesis. $p_t$ autocorrelations derived from the scale dependence of $<p_t>$ fluctuations reveal a complex parton dissipation process in RHIC heavy ion collisions. We also observe structure which may result from collective bulk-medium recoil in response to parton stopping.
We analyze the suppression of particle production at large transverse momenta in ($0-5%$ most) central collisions of gold nuclei at $\sqrt{s_\textrm{NN}}=$ 200 GeV and lead nuclei at $\sqrt{s_{\textrm{NN}}}=$ 2.76 TeV. Full next-to-leading order radiative corrections at ${\cal{O}}(α_s^3)$, and nuclear effects like shadowing and parton energy loss are included. The parton energy loss is implemented in a simple multiple scattering model, where the partons lose an energy $ε=λ\times dE/dx$ per collision, where $λ$ is their mean free path. We take $ε=κE$ for a treatment which is suggestive of the B…
The event generator based on the higher-twist energy loss formalism -- Modular All Twist Transverse-scattering Elastic-drag and Radiation (MATTER) -- is further developed and coupled to a hydrodynamic model for studying jet modification in relativistic nuclear collisions. The probability of parton splitting is calculated using the Sudakov form factor that is constructed by a combination of vacuum and medium-induced splitting functions; and the full parton showers are simulated, including both energy-momentum and space-time evolutions of all jet partons. With the assumption that partons below a…
We investigate the suppression factor and the azimuthal correlation function for high $p_T$ hadrons in central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV by using a dynamical model in which hydrodynamics is combined with explicitly traveling jets. We study the effects of parton energy loss in a hot medium, intrinsic $k_T$ of partons in a nucleus, and $p_{\perp}$ broadening of jets on the back-to-back correlations of high $p_T$ hadrons. Parton energy loss is found to be a dominant effect on the reduction of the away-side peaks in the correlation function.
We investigate the properties of the QCD matter across the deconfinement phase transition. In the scope of the parton-hadron string dynamics (PHSD) transport approach, we study the strongly interacting matter in equilibrium as well as the out-of equilibrium dynamics of relativistic heavy-ion collisions. We present here in particular the results on the electromagnetic radiation, i.e. photon and dilepton production, in relativistic heavy-ion collisions and the relevant correlator in equilibrium, i.e. the electric conductivity. By comparing our calculations for the heavy-ion collisions to the ava…
We present a consistent calculation of the structure functions within a light-front constituent quark model of the nucleon. Relativistic effects and the relevance of the covariance constraints are analyzed for both polarized and unpolarized parton distributions. Various models, which differ in their gluonic structure at the hadronic scale, are investigated. The results of the full covariant calculation are compared with those of a non-relativistic approximation to show the structure and magnitude of the differences.
PACIAE, a parton and hadron cascade model, is utilized to systematically investigate strange particle production and strangeness enhancement in Au+Au collision and in Pb+Pb collision with the 200GeV at RHIC and 2.76TeV at LHC, respectively. The experimental results at different centrality, which come from the STAR collaboration and the ALICE collaboration, are well described by the PACIAE model. This may represent the importance of the parton and hadron rescatterings, as well as the reduction mechanism of strange quark suppression, added in the PACIAE model.
We discuss predictions for the pion and kaon interferometry measurements in relativistic heavy ion collisions at SPS and RHIC energies. In particular, we confront relativistic transport model calculations that include explicitly a first-order phase transition from a thermalized quark-gluon plasma to a hadron gas with recent data from the RHIC experiments. We critically examine the "HBT-puzzle" both from the theoretical as well as from the experimental point of view. Alternative scenarios are briefly explained.
We get the distributions of shower partons initiated by heavy quarks $c$ and $b$ by studying the fragmentation functions in the framework of the recombination model. The transverse momentum spectra of heavy flavored mesons are predicted with these distributions. We find that the contribution from the recombination of thermal-shower partons is an important part in the total spectrum for the mesons. We predict the heavy flavored meson productions for different centralities with the heavy quark fugacities fitted by the experimental data of $J/ψ$ transverse momentum spectra in Au+Au collisions.
The proper support of generalized parton distributions from relativistic constituent quark models with pointlike constituents is studied. The correct support is guaranteed when the vertex function does not depend on the relative minus-momentum. We show that including quark interactions in models with pointlike constituent quarks might lead to a support problem. A computation of the magnitude of the support problem in the Bonn relativistic constituent quark model is presented.
We report on a new equilibration scenario in relativistic heavy ion collisions, the scenario of the Increasingly Strongly Interacting Parton Plasma, and the effects of this scenario on equilibration and open charm, photon and dilepton production. The parton plasma is shown to be a very special kind of many-body system, which contains new physics concerning the approach towards equilibrium. This is likely to be unique to the parton plasma.
The conventional NLO parton model is enough for the description of total cross sections and one-particle distributions. In the case of two-particle correlations, the collinear approximation has failed, and it is necessary to account for the transverse momenta of initial partons. The different possibilities to do this are discussed.
The relevance of parton interaction rates for observables of a quark- gluon plasma and for testing field theoretical methods is exhibited. Using the Braaten-Pisarski method the interaction rate as well as the transport rate beyond the leading logarithm approximation are estimated. Limts on the validity of perturbative QCD for relativistic heavy ion collisions are discussed.
We study the transverse momentum spectrum and the elliptic flow v2 of photons produced in Au+Au collisions at sqrt(s)=200 GeV using the Parton-Hadron-String Dynamics (PHSD) transport approach. As sources for photon production, we incorporate the interactions of off-shell quarks and gluons in the strongly interacting quark-gluon plasma (q+qbar->g+gamma and q/qbar+g->q/qbar+gamma), the decays of hadrons (pi->gamma+gamma, eta->gamma+gamma, omega->pi+gamma, eta'->rho+gamma, phi->eta+gamma, a_1->pi+gamma) as well as their interactions (pi+pi->rho+gamma, rho+pi->pi+gamma, bremsstrahlung m+m->m+m+gam…
We investigate the impact of three-body forces on the transverse-momentum distribution of partons inside the proton. This is achieved by considering the three-body problem in a class of hyper-central quark potential models. Solving the corresponding Schrödinger equation, we determine the quark wave function in the proton and with appropriate transformations and projections we find the transverse-momentum distribution of a single quark. In each case the parameters of the quark potentials are adjusted in order to sufficiently describe observable properties of the proton. Using a factorization an…
The idea that the parton system created in relativistic heavy-ion collisions (i) emerges in a state with transverse momenta close to thermodynamic equilibrium and (ii) its evolution at early times is dominated by the 2-dimensional (transverse) hydrodynamics of the ideal fluid is investigated. It is argued that this mechanism may help to solve the problem of early equilibration.
We present a consistent calculation of the structure functions within a light-front constituent quark model of the nucleon. Relativistic effects and the relevance of the covariance constraints are analyzed for polarized parton distributions. Various models, which differ in their gluonic structure at the hadronic scale, are investigated. The results of the full covariant calculation are compared with those of a non-relativistic approximation to show the structure and magnitude of the differences. It is also shown how measurements of transversity in doubly polarized Drell-Yan lepton pair product…
The dynamics of partons and hadrons in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for the partonic phase (DQPM) including a dynamical hadronization scheme. The PHSD approach is applied to nucleus-nucleus collisions from low SPS to LHC energies. The traces of partonic interactions are found in particular in the elliptic flow of hadrons and in their transverse mass spectra. We investigate also the equilibrium properties of strongly-interacting infinite parton-hadro…
The space-time propagation of heavy quarks in ultra-relativistic heavy ion collisions is studied within the partonic transport model Boltzmann Approach of MultiParton Scatterings (BAMPS). In this model heavy quarks interact with the partonic medium via binary scatterings. The cross sections for these interactions are calculated with leading order perturbative QCD, but feature a more precise Debye screening derived within the hard thermal loop approximation and obey the running of the coupling. Within this framework the elliptic flow and the nuclear modification factor of heavy quarks are compu…
A simple relativistic model is suggested that elucidates the qualitative difference in valence quark distributions of bosons in ground and virtual states. The inelastic diffraction of highly virtual photon in DIS is discussed.
We discuss different sources of hadron correlations in relativistic heavy ion collisions. We show that correlations among partons in a quasi-thermal medium can lead to the correlated emission of hadrons by quark recombination and argue that this mechanism offers a plausible explanation for the dihadron correlations in the few GeV/c momentum range observed in Au+Au collisions at RHIC.
An approach is proposed to calculate Generalized Parton Distributions (GPDs) in a Constituent Quark Model (CQM) scenario, considering the constituent quarks as complex systems. The GPDs are obtained from the wave functions of the non relativistic CQM of Isgur and Karl, convoluted with the GPDs of the constituent quarks themselves. The latter are modelled by using the structure functions of the constituent quark, the double distribution representation of GPDs, and a recently proposed phenomenological constituent quark form factor. The present approach permits to access a kinematical range corre…
The three well-known forms of relativistic dynamics are unitarily equivalent and the problem of constructing the current operators can be solved in any form. However the notion of the impulse approximation is reasonable only in the point form. In particular, the parton model which is the consequence of the impulse approximation in the front form is incompatible with Lorentz invariance, P invariance and T invariance. The results for deep inelastic scattering based on the impulse approximation in the point form give natural qualitative explanation of the fact that the values given by the parton …
We address dilepton production in Au+Au collisions at sqrt(s_NN)=200 GeV by employing the parton-hadron-string dynamics (PHSD) off-shell transport approach. Within the PHSD one goes beyond the quasiparticle approximation by solving generalized transport equations on the basis of the off-shell Kadanoff-Baym equations for the Green's functions in the phase-space representation. The approach consistently describes the full evolution of a relativistic heavy-ion collision from the initial hard scatterings and string formation through the dynamical deconfinement phase transition to the quark-gluon p…
A general expression for the dead cone of gluons radiated by virtual partons has been derived. The conventional dead cone for massive on-shell quarks and the dead cone for the massless virtual partons have been obtained by using different limits of the general expression. Radiative suppression due to the virtuality of initial parton jets in Heavy-Ion Collisions (HIC) has been discussed. It is observed that the suppression caused by the high virtuality is overwhelmingly large as compared to that on account of conventional dead-cone of heavy quarks. The dead cone due to virtuality may play a cru…
We study the quark angular momentum distribution in the nucleon within a light-front covariant quark model. Special emphasis is put into the orbital angular momentum: a quantity which is very sensitive to the relativistic treatment of the spin in a light-front dynamical approach. Discrepancies with the predictions of the low-energy traditional quark models where relativistic spin effects are neglected, are visible also after perturbative evolution to higher momentum scales. Orbital angular momentum distributions and their contribution to the spin sum rule are calculated for different phenomeno…
The azimuthal anisotropies of the collective transverse flow of hadrons are investigated in a large range of heavy-ion collision energy within the Parton-Hadron-String Dynamics (PHSD) microscopic transport approach which incorporates explicit partonic degrees of freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD as well as dynamical hadronization and hadronic dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow $v_2$ with bombarding energy is successfully described in terms of…
The phenomenon of jet quenching provides essential information about the properties of hot and dense matter created in ultra-relativistic heavy-ion collisions. Recent results from experiments at the Large Hadron Collider (LHC) show evidence for an unexpectedly similar suppression of both light and heavy flavor jets. Furthermore, the role of radiative energy loss of heavy quarks is still under active discussion within the theoretical community. By employing the parton cascade Boltzmann Approach to Multi-Parton Scatterings (BAMPS), which numerically solves the 3+1D Boltzmann equation both for li…
According to recent studies, Parton Distribution Functions (PDFs) and Generalized Parton Distributions (GPDs) can be evaluated in a Constituent Quark Model (CQM) scenario, considering the constituent quarks as composite objects. In here, a fully covariant model for a system of two particles, together with its non relativistic limit, are used to calculate PDFs and GPDs. The analysis permits to realize that by no means the effects of Relativity can be simulated taking into account the structure of the constituent particles, the two effects being independent and necessary for a proper description…
The short parton production phase in high-energy heavy-ion collisions is treated analytically as a nonlinear diffusion process. The initial buildup of the rapidity density distributions of produced charged hadrons within tau_p = 0.25 fm/c occurs in three sources during the colored partonic phase. In a two-step approach, the subsequent diffusion in pseudorapidity space during the interaction time of tau_int = 7-10 fm/c (mean duration of the collision) is essentially linear as expressed in the Relativistic Diffusion Model (RDM) which yields excellent agreement with the data at RHIC energies, and…
Transverse parton momentum dependent distribution functions (TMDs) of the nucleon are studied in a covariant model, which describes the intrinsic motion of partons in terms of a covariant momentum distribution. The consistency of the approach is demonstrated, and model relations among TMDs are studied. As a byproduct it is shown how the approach allows to formulate the non-relativistic limit.
We take hydrodynamic initial conditions in relativistic heavy ion collisions from the Color Glass Condensate (CGC) picture through the kT factorization formula. Gluon distributions produced from the CGC are found to provide good initial conditions for the hydrodynamic simulations in Au + Au collisions at Relativistic Heavy Ion Collider (RHIC) energies. We reproduce the centrality, rapidity, and energy dependences of multiplicity within this approach. We also investigate the energy loss of high pT partons in the dense thermalized medium created from colliding two CGC's. We find that our results…
