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.
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…
The JIMWLK equation with a "daughter dipole" running coupling is solved numerically starting from an initial condition given by the McLerran-Venugopalan model. The resulting Wilson line configurations are then used to compute the spectrum of gluons comprising the glasma inital state of a high energy heavy ion collision. The development of a geometrical scaling region makes the spectrum of produced gluons harder. Thus the ratio of the mean gluon transverse momentum to the saturation scale grows with energy. Also the total gluon multiplicity increases with energy slightly faster than the saturat…
We report on a numerical study of the Boltzmann equation including $2\leftrightarrow 2$ scatterings of gluons and quarks in an overoccupied Glasma undergoing longitudinal expansion. We find that when a cascade of gluon number to the infrared occurs, corresponding to an infrared enhancement analogous to a transient Bose-Einstein condensate, gluon distributions qualitatively reproduce the results of classical-statistical simulations for the expanding Glasma. These include key features of the distributions that are not anticipated in the "bottom-up" thermalization scenario. We also find that quar…
We calculate of the one- and two-point correlation functions of the energy density and the divergence of the Chern-Simons current in the nonequilibrium Glasma state formed in a high-energy nuclear collision. We show that the latter depends on the difference of the total and linearly polarized gluon transverse momentum distributions. Since the divergence of the Chern-Simons current provides the source of axial charge, we infer information about the statistical properties of axial charge production at early times. We further develop a simple phenomenological model to characterize axial charge di…
We study the gluon distribution in nucleus-nucleus collisions in the framework of the Color-Glass-Condensate. Approximate analytical solutions are compared to numerical solutions of the non-linear Yang-Mills equations. We find that the full numerical solution can be well approximated by taking the full initial condition of the fields in Coulomb gauge and using a linearized solution for the time evolution. We also compare kt-factorized approximations to the full solution.
We calculate the triple- and quadruple-gluon inclusive distributions with arbitrary rapidity and azimuthal angle dependences in the gluon saturation regime by using glasma diagrams. Also, we predict higher-dimensional ridges in triple- and quadruple-hadron correlations for p-p and p-Pb collisions at LHC, which have yet to be measured. In p-p and p-Pb collisions at the top LHC energies, gluon saturation is expected to occur since smaller Bjorken-$x$ values are being probed. Glasma diagrams, which are enhanced at small-$x$, include the gluon saturation effects, and they are used for calculating …
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 report recent progress on understanding the thermalization of the quark-gluon plasma during the early stage in a heavy ion collision. The initially high overpopulation in the far-from-equilibrium gluonic matter ("Glasma") is shown to play a crucial role. The strongly interacting nature (and thus fast evolution) naturally arises as an {\em emergent property} of this pre-equilibrium matter where the intrinsic coupling is weak but the highly occupied gluon states coherently amplify the scattering. A possible transient Bose-Einstein Condensate is argued to form dynamically on a rather general g…
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.
We compute the production of gluons from Glasma color flux tubes. We calculate the probability distribution of gluon multiplicities arising from the distribution of color electric and color magnetic flux tubes found in the Glasma. We show that the result corresponds to the negative binomial probability distribution observed in experiments. The parameter k that characterizes this distribution is proportional to the number of colors N_c^2-1 and to the number of flux tubes. For one gluon color and one flux tube, the multiplicity distribution is close to a Bose-Einstein distribution. We call this …
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 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.
The near-side ridge observed in A+A collisions at RHIC has been described as arising from the radial flow of Glasma flux tubes formed at very early times in the collisions. We investigate the viability of this scenario by performing a non-perturbative numerical computation of double inclusive gluon production in the Glasma. Our results support the conjecture that the range of transverse color screening of correlations determining the size of the flux tubes is a semi-hard scale, albeit with non-trivial structure. We discuss our results in the context of ridge correlations in the RHIC heavy ion …
Using the standard Lagrangian of gluons and a model of dual superconductor for magnetic monopoles, we calculate the number densities of the gluons and monopoles produced by the decay of background color electric $E$ and magnetic $B$ fields ( glasma ). We find that gluons are dominant decay products when the initial values of the gauge fields are large such that $gE=gB>(0.5\mbox{GeV})^2$, while they are suppressed and monopoles are dominant decay products when the initial values are small such that $gE=gB<(0.4\mbox{GeV})^2$. The feature of the gluon dominance at large $gE=gB$ and the monopole d…
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…
I discuss a phenomenological model for the Glasma. I introduce over occupied distributions for gluons, and compute their time evolution. I use this model to estimate the ratio of quarks to gluons and the entropy production as functions of time. I then discuss photon production at RHIC and LHC, and how geometric scaling and the Glasma might explain generic features of such production.
We investigate the azimuthal correlations of the glasma in p-p collisions at $\sqrt{s_{\mathrm{NN}}}=7$ TeV by using the CGC formalism. As expected, the azimuthal correlations show two peaks at $Δϕ=0$ and $π$ which represent collimation production in CGC. Beyond that, azimuthal correlations show fine structures, i.e. bumps or shoulders between the two peaks, when at least one gluon has small $x$. The structures are demonstrated to be associated with saturation momentum, and likely appear at transverse momentum around $2Q_{\mathrm{sp}}=1.8$ GeV$/$c.
A Glasma flux-tube model has been proposed to explain strong elongation on pseudorapidity $η$ of the same-side 2D peak in minimum-bias angular correlations from $\sqrt{s_{NN}} = 200$ GeV \auau collisions. The same-side peak or "soft ridge" is said to arise from coupling of flux tubes to radial flow. Gluons radiated transversely from flux tubes are boosted by radial flow to form a narrow structure or ridge on azimuth. In this study we test the conjecture by comparing predictions for particle production, spectra and correlations from the Glasma model and conventional fragmentation processes with…
We present an ab-initio approach to compute the longitudinal dependence of the initial state in heavy-ion collisions by including small-x evolution of the nuclear gluon distributions. Extending the IP-Glasma model by including JIMWLK rapidity evolution, we compute event-by-event rapidity distributions of produced gluons and the early time energy momentum tensor as a function of space-time rapidity and transverse coordinates. We show how the effects of small-x evolution manifest themselves in longitudinal (rapidity) correlations of event-by-event multiplicities and transverse geometry and compa…
We study the synchrotron-like gluon emission in $AA$-collisions from fast partons due to interaction with the coherent glasma color fields. Our results show that for RHIC and LHC conditions the contribution of this mechanism to parton energy loss is much smaller than the radiative energy loss in the plasma phase.
We study ridge correlations of the glasma in pp collisions at $\sqrt{s_{\mathrm{NN}}}=7$ TeV by using the color glass condensate (CGC) formalism. The azimuthal collimation at long range rapidity is intrinsic to glasma dynamics and is reproduced here. When rapidity window enlarges, ridge correlations in two dimensional $Δy$-$Δϕ$ distribution and one dimensional $Δϕ$ distribution at long range rapidity gap are enhanced. The enhancements are demonstrated to be the contributions of source gluons. The quantum evolution of the gluons presents unique correlation patterns in differential correlation f…
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 estimate the energy density and the gluon distribution associated with the classical fields describing the early-time dynamics of the heavy-ion collisions. We first decompose the energy density into the momentum components exactly in the McLerran-Venugopalan model, with the use of the Wilson line correlators. Then we evolve the energy density with the free-field equation, which is justified by the dominance of the ultraviolet modes near the collision point. We also discuss the improvement with inclusion of nonlinear terms into the time evolution. Our numerical results at RHIC energy are fai…
The collinear color electric and magnetic fields have been discussed to be produced immediately after high energy heavy ion collisions. We discuss anomalous gluon production under the background gauge fields. The gluons are Nielsen-Olesen unstable modes. The production rate of the modes by Schwinger mechanism has recently been found to be anomalously larger than the rate of quarks or other stable gluons. Analyzing classical evolutions of the modes with initial conditions given by vacuum fluctuations, we find that their production makes the color electric field decay very rapidly. The life time…
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 …
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…
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…
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 …
Glasma in high energy heavy ion collisions is longitudinal classical color electric and magnetic fields. The color electric field has been shown to produces quark and anti-quark pairs by the Schwinger mechanism and to oscillate with time in non-expanding glasma, that is, plasma oscillation. On the other hand, in the expanding glasma we show that the field decreases with the plasma oscillation. We can explicitly obtain the solutions representing such temporal behaviors in the system with $τ$ and $η$ coordinates. We show these results by using massless QED as a simplified model of QCD.
In the color glass condensate framework the saturation scale measured in deep inelastic scattering of high energy hadrons and nuclei can be determined from the correlator of Wilson lines in the hadron wavefunction. These same Wilson lines give the initial condition of the classical field computation of the initial gluon multiplicity and energy density in a heavy ion collision. In this paper the Wilson line correlator in both adjoint and fundamental representations is computed using exactly the same numerical procedure that has been used to calculate gluon production in a heavy ion collision. I…
Non-perturbative quark production and transport in the evolving glasma: the WAGASHI event generator
Institute of Physics, Academia Sinica（中央研究院物理研究所）；Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University（广岛大学先进理工学研究科物理项目）；Kobayashi Maskawa Institute, Nagoya University（名古屋大学小林-益川研究所）；International Institute for Sustainability with Knotted Chiral Meta Matter, Hiroshima University（广岛大学螺旋手性超物质可持续国际研究所）；Hiyoshi Department of Physics and Research and Education Center for Natural Sciences, Keio University（庆应义塾大学日吉理学部及自然科学研究与教育中心）；iTHEMS, TRIP Headquarters, RIKEN（理化学研究所iTHEMS/TRIP总部）
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.
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…
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 present an analytical calculation of the covariance of the energy-momentum tensor associated to the gluon field produced in ultra-relativistic heavy ion collisions at early times, the Glasma. This object involves the two-point and single-point correlators of the energy-momentum tensor ($\langle T^{μν}(x_{\perp})T^{σρ}(y_{\perp})\rangle$ and $\langle T^{μν}(x_{\perp})\rangle$, respectively) at proper time $τ\!=\!0^+$. Our approach is based on the Color Glass Condensate effective theory, which allows us to map the fluctuations of the valence color sources in the colliding nuclei to those of t…
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…
These two lectures concern the Color Glass Condensate and the Glasma. These are forms of matter which might be studied in high energy hadronic collisions. The Color Glass Condensate is high energy density gluonic matter. It constitutes the part of a hadron wavefunction important for high energy processes. The Glasma is matter produced from the collision of two high energy hadrons. Both types of matter are associated with coherent fields. The Color Glass Condensate is static and related to a hadron wavefunction where the glasma is transient and evolves quickly after a collision. I present the p…
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…
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…
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 …
It has been discussed that quark gluon plasma is produced following the rapid decay of coherent color gauge fields generated immediately after high energy heavy ion collisions. But there are no convincing mechanisms known for the rapid decay of the gauge fields which satisfy phenomenological constraints on their lifetime. We show by using classical statistical field theory that the gauge fields rapidly decay into magnetic monopoles. For comparison, we show how fast they decay into Nielsen-Olesen unstable modes. We find that the rapid decay of the glasma is caused by the monopole production.
In this paper we investigate the role of inelastic collisions in the kinetic evolution of a highly overpopulated gluon system starting from Glasma-type initial condition. Using the Gunion-Bertsch formula we derive the inelastic collision kernel under the collinear and small angle approximations. With both numerics and analytic analysis, we show that the inelastic process has two effects: globally changing (mostly reducing) the total particle number, while locally at small momentum regime always filling up the infrared modes extremely quickly. This latter effect is found to significantly speed …
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 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 …
The Glasma is a gluonic state of matter which can be created in collisions of relativistic heavy ions and is a precursor to the quark-gluon plasma. The existence of this state is a prediction of the color glass condensate (CGC) effective theory. In many applications of the CGC framework, the boost invariant approximation is employed. It assumes that the longitudinal extent of the nuclei can be approximated as infinitesimally thin. Consequently, the Glasma produced from such a collision is boost invariant and can be effectively described in 2+1D. Therefore, observables of the boost invariant Gl…
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…
We use a hybrid model which relies on QCD effective kinetic theory -- K\oMP\oST -- to dynamically bridge the gap between IP-Glasma initial states and viscous hydrodynamics, for the theoretical interpretation of heavy-ion collision results. The hydrodynamic phase is then followed by dynamical freeze-out handled by UrQMD. It is observed that the new pre-equilibrium/pre-hydro phase does influence the extraction of transport coefficients. We also show how the early dynamics is reflected in photon observables.
We propose a new prescription for evaluating a von Neumann entropy in the initial stage of high-energy heavy-ion collisions utilizing the time evolution of classical Yang-Mills (CYM) field: The von Neumann entropy is computed for the quantum coherent states constructed so as to give the classical gluon fields as the expectation values. The entropy is to be liberated when the complete decoherence is achieved. As a demonstration, the time evolution of the CYM dynamics is solved with an initial condition which mimics the Glasma state, though in a non-expanding geometry; the Glasma state is charac…
We discuss different sources of fluctuations in nuclear collisions and their realization in the IP-Glasma model. We present results for multiplicity distributions in p+p and p+A collisions and compare eccentricity distributions in A+A collisions to the flow harmonic distributions in 10 centrality classes measured by the ATLAS collaboration.
