Early Time Dynamics of Gluon Fields in High Energy Nuclear Collisions

Abstract

Nuclei colliding at very high energy create a strong, quasi-classical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromo-electric and chromo-magnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. For example, we find that the ratio of longitudinal to transverse pressure very early in the system behaves as $p_L/p_T=-[1-\frac{3}{2a}(Q\tau {)}^2]/[1-\frac{1}{a}(Q\tau {)}^2]+\mathcal{O}(Q\tau {)}^4$ where $\tau$ is the longitudinal proper time, $Q$ is related to the saturation scales $Q_s$ of the two nuclei, and $a=\ln (Q^2/{\hat{m}}^2)$ with $\hat{m}$ a scale to be defined later. Our results are generally applicable if $\tau \lesssim 1/Q$. As already discussed in a previous paper, the transverse energy flow $S^i$ of the gluon field exhibits hydrodynamic-like contributions that follow transverse gradients of the energy density ${\nabla }^i\epsilon$. In addition, a rapidity-odd energy flow also emerges from the non-abelian analog of Gauss' Law and generates non-vanishing angular momentum of the field. We will discuss the space-time picture that emerges from our analysis and its implications for observables in heavy ion collisions.

26 pages, 9 figures

References in corpus (45)

• An Introduction to PYTHIA 8.2
• A Brief Introduction to PYTHIA 8.1
• Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
• Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration
• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Glauber Modeling in High Energy Nuclear Collisions
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• The Color Glass Condensate
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Hydrodynamic Modeling of Heavy-Ion Collisions
• The Intrinsic Glue Distribution at Very Small x
• Fluctuating Glasma initial conditions and flow in heavy ion collisions
• Event-by-event anisotropic flow in heavy-ion collisions from combined Yang-Mills and viscous fluid dynamics
• Globally Polarized Quark-gluon Plasma in Non-central A+A Collisions
• 200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid
• Some Features of the Glasma
• First Results from Pb+Pb collisions at the LHC
• Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus
• Gluon Production from Non-Abelian Weizsäcker-Williams Fields in Nucleus-Nucleus Collisions
• Gluon production in current-nucleus and nucleon-nucleus collisions in a quasi-classical approximation
• Gluon Production at High Transverse Momentum in the McLerran-Venugopalan Model of Nuclear Structure Functions
• Triumvirate of Running Couplings in Small-x Evolution
• Production of gluons in the classical field model for heavy ion collisions
• Transverse flow and hadro-chemistry in Au+Au collisions at \sqrt{s_{NN}}=200 GeV
• Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies
• Nuclear Stopping in Au+Au Collisions at sqrt(sNN) = 200 GeV
• The initial gluon multiplicity in heavy ion collisions
• Pressure isotropization in high energy heavy ion collisions
• How Protons Shatter Colored Glass
• Flow Vorticity in Peripheral High Energy Heavy Ion Collisions
• Classical Gluodynamics of High Energy Nuclear Collisions: an Erratum and an Update
• Energy density of the Glasma
• High energy factorization in nucleus-nucleus collisions
• Universal Flow in the First Stage of Relativistic Heavy Ion Collisions
• Universality of the saturation scale and the initial eccentricity in heavy ion collisions
• The initial state of ultra-relativistic heavy ion collision
• Effective String Rope Model for the initial stages of Ultra-Relativistic Heavy Ion Collisions
• Initial energy density and gluon distribution from the Glasma in heavy-ion collisions
• Light projectile scattering off the Color Glass Condensate
• From Color Fields to Quark Gluon Plasma
• Collinear Singularities and Running Coupling Corrections to Gluon Production in CGC
• Global Flow of Glasma in High Energy Nuclear Collisions
• Decoherence and Entropy Production in Relativistic Nuclear Collisions
• Rapidity Profile of the Initial Energy Density in Heavy-Ion Collisions
• Wilson lines - color charge densities correlators and the production of eta' in the CGC for pp and pA collisions

Cited by in corpus (51)

• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution
• 3-D Glasma initial state for relativistic heavy ion collisions
• High Gluon Densities in Heavy Ions Collisions
• Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions
• Linearly polarized gluons and axial charge fluctuations in the Glasma
• ${}^{16}{\mathrm{O}}^{16}\mathrm{O}$ at RHIC and the LHC comparing $\alpha$ clustering vs substructure
• Transport of hard probes through glasma
• Setting the string shoving picture in a new frame
• Heavy Quarks Embedded in Glasma
• The cathode tube effect: heavy quarks probing the Glasma in p-Pb collisions
• Heavy Quarks in Turbulent QCD Plasmas
• Exploring non-equilibrium quark-gluon plasma effects on charm transport coefficients
• Initial state of Heavy-Ion Collisions: Isotropization and thermalization
• Simulating collisions of thick nuclei in the color glass condensate framework
• Possible octupole deformation of ${}^{208}$Pb and the ultracentral $v_2$ to $v_3$ puzzle
• Ballistic diffusion of heavy quarks in the early stage of relativistic heavy ion collisions at RHIC and LHC
• Diffusion of heavy quarks in the early stage of high-energy nuclear collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider
• Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach
• New paradigm for fluctuations in heavy-ion collisions
• Spin polarization and correlation of quarks from glasma
• Large Baryon Densities Achievable in High Energy Heavy Ion Collisions Outside the Central Rapidity Region
• 3-D structure of the Glasma initial state -- Breaking boost-invariance by collisions of extended shock waves in classical Yang-Mills theory
• Initial correlations of the Glasma energy-momentum tensor
• Physical characteristics of glasma from the earliest stage of relativistic heavy ion collisions
• Hot spots and gluon field fluctuations as causes of eccentricity in small systems
• Space-time structure of 3+1D color fields in high energy nuclear collisions
• A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions
• The energy-momentum tensor at the earliest stage of relativistic heavy ion collisions
• High Baryon Densities in Heavy Ion Collisions at Energies Attainable at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider
• Broad excitations in a 2+1D overoccupied gluon plasma
• Particle distribution in intense fields in a light-front Hamiltonian approach
• Evolution of pressures and correlations in the Glasma produced in high energy nuclear collisions
• Pressure Anisotropy in Heavy Ion Collisions from Color Glass Condensate
• Initial Angular Momentum and Flow in High Energy Nuclear Collisions
• First Saturation Correction in High Energy Proton-Nucleus Collisions: I. Time evolution of classical Yang-Mills fields beyond leading order
• Classical model for diffusion and thermalization of heavy quarks in a hot medium: memory and out-of-equilibrium effects
• Evolution of initial stage fluctuations in the glasma
• First Saturation Correction in High Energy Proton-Nucleus Collisions: II. Single Inclusive Semi-Hard Gluon Production
• Stability of Classical Chromodynamic Fields
• High Baryon Densities Achieveable at RHIC and LHC
• Evolution of eccentricities induced by geometrical and quantum fluctuations in proton-nucleus collisions
• Impact of Multiplicity Fluctuations on Entropy Scaling Across System Size
• An Initial State with Shear in Peripheral Heavy Ion Collisions
• Topological charge fluctuations in the Glasma
• Revisiting the Gluon Spectrum in the Boost-Invariant Glasma from a Semi-Analytic Approach
• Initial conditions in AA and pA collisions
• Event-By-Event Initial Conditions for Heavy Ion Collisions
• Achieving high baryon densities in the fragmentation regions in heavy ion collisions at top RHIC energy
• Fluctuations in ultra-relativistic heavy ion collisions
• Gauge invariant momentum broadening of hard probes in glasma