Heavy quarks, which are produced at the earliest stage of relativistic heavy-ion collisions, probe the entire history of the quark-gluon plasma that is created in the collision. Initially the plasma is populated with chromodynamic fields which can be treated as classical. We study the transport of heavy quarks across such a system, which is called glasma, using a Fokker-Planck equation where the quarks interact with long wavelength chromodynamic fields. We compute field correlators which are used to calculate the collision terms of the transport equation. Finally, the energy loss and momentum broadening of heavy quarks in the glasma are studied. Both of these quantities are sizable and strongly directionally dependent.
We extend the impact parameter dependent Glasma model (IP-Glasma) to three dimensions using explicit small x evolution of the two incoming nuclear gluon distributions. We compute rapidity distributions of produced gluons and the early time energy momentum tensor as a function of space-time rapidity and transverse coordinates. We study rapidity correlations and fluctuations of the initial geometry and multiplicity distributions and compare to existing models for the three dimensional initial state.
In relativistic heavy ion collisions, a highly occupied gluonic matter is created shortly after initial impact, which is in a non-thermal state and often referred to as the Glasma. Successful phenomenology suggests that the glasma evolves rather quickly toward the thermal quark-gluon plasma and a hydrodynamic behavior emerges at very early time $\sim \hat{o}(1)$ fm/c. Exactly how such "apparent thermalization" occurs and connects the initial conditions to the hydrodynamic onset, remains a significant challenge for theory as well as phenomenology. We briefly review various ideas and recent prog…
We compute initial conditions in heavy-ion collisions within the Color Glass Condensate (CGC) framework by combining the impact parameter dependent saturation model (IP-Sat) with the classical Yang-Mills description of initial Glasma fields. In addition to fluctuations of nucleon positions, this IP-Glasma description includes quantum fluctuations of color charges on the length-scale determined by the inverse nuclear saturation scale Q_s. The model naturally produces initial energy fluctuations that are described by a negative binomial distribution. The ratio of triangularity to eccentricity is…
When two sheets of Color Glass Condensate collide in a high energy heavy ion collision, they form matter with very high energy densities called the Glasma. We describe how this matter is formed, its remarkable properties and its relevance for understanding thermalization of the Quark Gluon Plasma in heavy ion collisions. Long range rapidity correlations contained in the near side ridge measured in heavy ion collisions may allow one to directly infer the properties of the Glasma.
Relativistic nuclear collisions offer a unique way to study strong interactions at very high energy. The collision process can be described within the gluon saturation framework as the interaction of two colored glasses, and because of this interaction strong longitudinal gluon fields, namely the Glasma, are produced immediately after the collision. Besides, heavy quarks are also produced in the very early stage and because of their large mass and small concentration, their motion does not affect the evolution of the Glasma, thus behaving as ideal probes of the Glasma itself. We study the evol…
We study the transverse momentum, $p_T$, broadening of charm and beauty quarks in the early stage of high energy nuclear collisions. We aim to compare the diffusion in the evolving Glasma fields with that of a standard, Markovian-Brownian motion in a thermalized medium with the same energy density of the Glasma fields. The Brownian motion is studied via Langevin equations with diffusion coefficients computed within perturbative Quantum Chromodynamics. We find that for small values of the saturation scale, $Q_s$, the average $p_T$ broadening in the two motions is comparable, that suggests that …
We develop the formalism discussed previously in hep-ph/0601209 and hep-ph/0605246 to construct a kinetic theory that provides insight into the earliest ``Glasma'' stage of a high energy heavy ion collision. Particles produced from the decay of classical fields in the Glasma obey a Boltzmann equation whose novel features include an inhomogeneous source term and new contributions to the collision term. We discuss the power counting associated with the different terms in the Boltzmann equation and outline the transition from the field dominated regime to the particle dominated regime in high ene…
We perform a calculation of the one- and two-point correlation functions of energy density and axial charge deposited in the glasma in the initial stage of a heavy ion collision at finite proper time. We do this by describing the initial stage of heavy ion collisions in terms of freely evolving classical fields whose dynamics obey the linearized Yang-Mills equations. Our approach allows us to systematically resum the contributions of high momentum modes that would make a power series expansion in proper time divergent. We evaluate the field correlators in the McLerran-Venugopalan model using t…
We present analytic results that describe the gluon field, or glasma, at very early times after a collision of relativistic heavy ions at proper time $τ=0$. We use a Colour Glass Condensate approach, and perform an expansion in $τ$. The full details of our method are described in our previous paper [1]. In this paper we present an analysis of various physical quantities that can be obtained from the energy-momentum tensor. We show that the expansion to order $τ^6$ can be trusted to about $τ=0.05$ fm. For times small enough that the expansion converges, the transverse and longitudinal pressures…
Recent classical-statistical numerical simulations have established the "bottom-up" thermalization scenario of Baier et al. as the correct weak coupling effective theory for thermalization in ultrarelativistic heavy-ion collisions. We perform a parametric study of photon production in the various stages of this bottom-up framework to ascertain the relative contribution of the off-equilibrium "Glasma" relative to that of a thermalized Quark-Gluon Plasma. Taking into account the constraints imposed by the measured charged hadron multiplicities at RHIC and the LHC, we find that Glasma contributio…
We compute three particle correlations in the Glasma flux tube model of high energy heavy ion collisions. We obtain a simple geometrical picture of these correlations; when convoluted with final state radial flow, it results in distinct predictions for the near side three particle correlation in central heavy ion collisions.
The the initial stage of a relativistic heavy ion collision can be described by a classical color field configuration known as the Glasma. The production of quark pairs from this background field is then computed nonperturbatively by numerically solving the Dirac equation in the classical background. The result seems to point towards an early chemical equilibration of the plasma.
We study the evolution of the angular momentum of the heavy quarks in the very early stage of high energy nuclear collisions, in which the background is made of evolving Glasma fields. Given the novelty of the problem, we limit ourselves to the use of toy heavy quarks with a large, unphysical mass, in order to implement the kinetic equations for the angular momentum in the non-relativistic limit. We find that as a consequence of the anisotropy of the background fields, angular momentum fluctuations are also anisotropic: we understand this in simple terms relating the fluctuations of the angula…
We present results from numerical Classical Yang Mills calculations of the initial stage Glasma field configurations in a relativistic heavy ion collision. We compute the initial gluon multiplicity from RHIC to LHC energies. The initial conditions for the classical field computation are taken from a dipole model parametrization tested on HERA data, meaning that all the parameters, including the normalization and the value of the saturation scale, are fixed from DIS data.
We introduce distribution functions for quarks and gluons in the Glasma and discuss how they satisfy various relationships of statistical physics. We use these distributions to compute photon production in the early stages of heavy ion collisions. Photon rates satisfy geometric scaling, that is, the emission rate per unit area scales as a function of the saturation momenta divided by the transverse momentum of the photon. Photon distributions from the Glasma are steeper than those computed in the Thermalized Quark Gluon Plasma (TQGP). Both the delayed equilibration of the Glasma and a possible…
We extend the weak field approximation for the Glasma beyond the boost-invariant approximation, which allows us to compute rapidity-dependent observables in the early stages of heavy-ion collisions. We show that in the limit of small fields, the weak field approximation agrees quantitatively with non-perturbative lattice simulations. Furthermore, we demonstrate that the rapidity profile of the transverse pressure is determined by longitudinal color correlations within the colliding nuclei.
We review the Color Glass Condensate effective theory, that describes the gluon content of a high energy hadron or nucleus, in the saturation regime. The emphasis is put on applications to high energy heavy ion collisions. After describing initial state factorization, we discuss the Glasma phase, that precedes the formation of an equilibrated quark-gluon plasma. We end this review with a presentation of recent developments in the study of the isotropization and thermalization of the quark-gluon plasma.
Anisotropic flow coefficients v_1-v_5 in heavy ion collisions are computed by combining a classical Yang-Mills description of the early time glasma flow with the subsequent relativistic viscous hydrodynamic evolution of matter through the quark-gluon plasma and hadron gas phases. The glasma dynamics, as realized in the IP-Glasma model, takes into account event-by-event geometric fluctuations in nucleon positions and intrinsic sub-nucleon scale color charge fluctuations; the pre-equilibrium flow of matter is then matched to the MUSIC algorithm describing viscous hydrodynamic flow and particle p…
The initial energy density produced in an ultrarelativistic heavy ion collision can, in the color glass condensate framework, be factorized into a product of the integrated gluon distributions of the nuclei. Although this energy density is well defined without any infrared cutoff besides the saturation scale, it is apparently logarithmically ultraviolet divergent. We argue that this divergence is not physically meaningful and does not affect the behavior of the system at any finite proper time.
We study the diffusion of charm quarks in the early stage of high energy nuclear collisions at the RHIC and the LHC. The main novelty of the present study is the introduction of the color current carried by the heavy quarks that propagate in the evolving Glasma (Ev-Glasma), that is responsible of the energy loss via polarization of the medium. We compute the transverse momentum broadening, $σ_p$, of charm in the pre-thermalization stage, and the impact of the diffusion on the nuclear modification factor in nucleus-nucleus collisions. The net effect of energy loss is marginal in the pre-thermal…
We investigate the effect of nucleon-nucleon correlations on the initial condition of ultra-central heavy ion collisions at LHC energies. We calculate the eccentricities of the MC-Glauber and IP-Glasma models in the 0--1% centrality class and show that they are considerably affected by the inclusion of such type of correlations. For an IP-Glasma initial condition, we further demonstrate that this effect survives the fluid-dynamical evolution of the system and can be observed in its final state azimuthal momentum anisotropy.
The physics of the initial conditions of heavy ion collisions is dominated by the nonlinear gluonic interactions of QCD. These lead to the concepts of parton saturation and the Color Glass Condensate (CGC). We discuss recent progress in calculating multi-gluon correlations in this framework, prompted by the observation that these correlations are in fact easier to compute in a dense system (nucleus-nucleus) than a dilute one (proton-proton).
We discuss the transverse momentum broadening of hard probes traversing an evolving glasma, which is the earliest phase of the matter produced in relativistic heavy-ion collisions. The coefficient $\hat q$ is calculated using the Fokker-Planck equation, and an expansion in the proper time $τ$ which is applied to describe the temporal evolution of the glasma. The correlators of the chromodynamic fields that determine the Fokker-Planck collision term, which in turn provides $\hat q$, are computed to fifth order in $τ$. The momentum broadening is shown to rapidly grow in time and reach a magnitud…
We discuss results from 3+1-D numerical simulations of SU(2) Yang--Mills equations for an unstable Glasma expanding into the vacuum after a high energy heavy ion collision. We expand on our earlier work on a non-Abelian Weibel instability in such a system and study the behavior of the instability in greater detail on significantly larger lattices than previously. We establish the time scale for the onset of the instability and demonstrate that the growth rate is robust as one approaches the continuum limit. For large violations of boost invariance, non-Abelian effects cause the growth of soft …
Gauge invariant momentum broadening of hard probes in glasma
Brandon University（布兰登大学）；Winnipeg Institute for Theoretical Physics（温尼伯理论物理研究所）；University of Toronto（多伦多大学）；National Centre for Nuclear Research（国家核研究中心）
In the Color Glass Condensate (CGC) effective field theory, colliding sheets of Colored Glass form a strongly interacting, non-equilibrium state called the Glasma. How Colored Glass shatters to form the Glasma, the properties of the Glasma, and how the Glasma thermalizes into a Quark Gluon Plasma(QGP) are questions of central interest in understanding the properties of the strongly interacting matter produced in heavy ion collisions. We argue that these questions can be addressed in the framework of field theories with strong time dependent external sources. Albeit such field theories are non-…
In heavy ion collisions, transverse momentum broadening quantifies the modification of a hard probe due to interactions with the quark-gluon plasma (QGP). We calculate momentum broadening in the Glasma, which is the highly non-isotropic precursor stage of the QGP right after the collision. We show that the Glasma leads to anisotropic momentum broadening: high energy partons accumulate more momentum along the beam axis than transverse to it. The physical origin of anisotropic broadening can be traced back to differences in the shapes of chromo-electric and chromo-magnetic flux tubes in the Glas…
We consider two-gluon production in dilute-dense collisions within the Color Glass Condensate framework, applicable to both proton-nucleus and heavy-light ion collisions. We go beyond the glasma graph approximation which is valid in the dilute-dilute limit and show the correspondence between the glasma graphs and the $k_T$-factorized approach that we use in our calculation. We then identify the classical uncorrelated, and the Hanbury-Brown-Twiss (HBT) and Bose enhancement correlated contributions, with the Bose enhancement contribution being suppressed by the number of degrees of freedom with …
We study the propagation of charm quarks in the early stage of high energy proton-lead collision, considering the interaction of these quarks with the evolving Glasma by means of the Wong equations. Neglecting quantum fluctuations at the initial time the Glasma is made of longitudinal fields, but the dynamics leads to a quick formation of transverse fields; we estimate such a formation time as $Δt\approx 0.1$ fm/c which is of the same order of the formation time of heavy quark pairs $t_\mathrm{formation}\approx 1/(2m)$. Limiting ourselves to the simple case of a static longitudinal geometry, w…
We present a formulation of the initial state of heavy ion collisions that generalizes the 2+1D boost invariant IP-Glasma \cite{Schenke:2012wb} to 3+1D through JIMWLK rapidity evolution of the pre-collision Wilson lines. The rapidity dependence introduced by the JIMWLK evolution leads us to modify the initial condition for the gauge fields, and to solve Gauss' law iteratively in order to allow for temporal evolution on a 3-dimensional lattice. While the transverse physics of QGP has been studied nearly exhaustively, the effect of longitudinal fluctuations introduced by the JIMWLK evolution has…
We review our progress on 3+1D Glasma simulations to describe the earliest stages of heavy-ion collisions. In our simulations we include nuclei with finite longitudinal extent and describe the collision process as well as the evolution of the strongly interacting gluonic fields in the laboratory frame in 3+1 dimensions using the colored particle-in-cell method. This allows us to compute the 3+1 dimensional Glasma energy-momentum tensor, whose rapidity dependence can be compared to experimental pion multiplicity data from RHIC. An improved scheme cures the numerical Cherenkov instability and pa…
The early-time evolution of the system generated in ultra-relativistic heavy ion collisions is dominated by the presence of strong color fields known as Glasma fields. These can be described following the classical approach embodied in the Color Glass Condensate effective theory, which approximates QCD in the high gluon density regime. In this framework we perform an analytical first-principles calculation of the two-point correlator of the divergence of the Chern-Simons current at proper time $τ\!=\!0^+$, which characterizes the early fluctuations of axial charge density in the plane transver…
We calculate the transverse momentum broadening $\hat q$ and collisional energy loss $dE/dx$ of hard probes traversing an evolving glasma during the earliest phase of a relativistic heavy-ion collision. We use a Fokker-Planck equation and apply a proper time expansion to describe the temporal evolution of the glasma. The correlators of the chromodynamic fields that determine the Fokker-Planck collision terms, which in turn provide $\hat q$ and $dE/dx$, are computed to fifth order. Both transport coefficients are strongly dependent on time. The maximum values they acquire before the proper time…
We investigate the consequences of long range rapidity correlations in the Glasma. Particles produced locally in the transverse plane are correlated by approximately boost invariant flux tubes of longitudinal color electric and magnetic fields that are formed when two sheets of Colored Glass Condensate pass through one another, each acquiring a modified color charge density in the collision. We argue that such long range rapidity correlations persist during the evolution of the Quark Gluon Plasma formed later in the collision. When combined with transverse flow, these correlations reproduce ma…
In the pre-thermal equilibrium stage of relativistic heavy-ion collisions, a strong quasi-classical transverse gluon field emerges at about $τ_0 \simeq 0.1 \, \rm fm/c$ and evolves together with their longitudinal counterparts according to the classical Yang-Mills (CYM) equations. Recently it has been shown that these fields induce a diffusion of charm quarks in momentum space resulting in a tilt of their spectrum without a significant drag. We find that in nucleus-nucleus collisions at LHC such a novel dynamics of charm quarks leads to an initial enhancement of the nuclear modification factor…
In these proceedings, we report on our numerical lattice simulations of partons traversing the boost-invariant, non-perturbative glasma as created at the early stages of collisions at RHIC and LHC. Since these highly energetic partons are produced from hard scatterings during heavy-ion collisions, they are already affected by the first stage of the medium's time evolution, the glasma, which is the pre-equilibrium precursor state of the quark-gluon plasma. We find that partons quickly accumulate transverse momentum up to the saturation momentum during the glasma stage. Moreover, we observe an i…
The initial stage of a heavy ion collision is dominated by nonperturbatively strong chromoelectric and -magnetic fields. The spatial Wilson loop provides a gauge invariant observable to probe the dynamics of the longitudinal chromomagnetic field. We discuss recent results from a real time lattice calculation of the area-dependence of the expectation value of the spatial Wilson loop. We show that at relatively early times after the collision, a universal scaling as a function of the area emerges at large distances for very different initial conditions, with a nontrivial critical exponent. A sim…
Light-front Hamiltonian jet evolution in the Glasma
University of Jyväskylä（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）；Instituto Galego de Fisica de Altas Enerxias (IGFAE)（加利西亚高能物理研究所）；Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）；Axencia Galega de Innovación (GAIN)（加利西亚创新署）
The study of jets in heavy-ion collisions provides important information about the interaction of partons with the medium that they traverse. The seeds of jets are highly energetic partons, which are produced from hard scatterings during the collision event. As such, they are affected by all different stages of the medium's time evolution, including the glasma, which is the pre-equilibrium precursor state of the quark-gluon plasma. Here we report on our numerical lattice simulations of partons traversing the boost-invariant, non-perturbative glasma as created at the early stages of collisions …
Axial charge production at the early stage of heavy-ion collisions is investigated within the framework of real-time lattice simulations at leading order in QCD coupling. Starting from color glass condensate initial conditions, the time evolution of quantum quark fields under classical color gauge fields is computed on a lattice in longitudinally expanding geometry. We consider simple color charge distributions in Lorentz contracted nuclei that realize flux tube-like configurations of color fields carrying nonzero topological charge after a collision. By employing the Wilson fermion extended t…
