# Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions

Kurkela, Aleksi (Theoretical Physics Department, CERN, Geneva, Switzerland and Faculty of Science and Technology, University of Stavanger, 4036 Stavanger, Norway) ; Mazeliauskas, Aleksas (Institut für Theoretische Physik, Universität Heidelberg, 69120 Heidelberg, Germany and Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA) ; Paquet, Jean-François (Department of Physics, Duke University, Durham, North Carolina 27708, USA and Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA) ; Schlichting, Sören (Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany and Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA) ; Teaney, Derek (Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA)

27 March 2019

Abstract: We develop a macroscopic description of the space-time evolution of the energy-momentum tensor during the pre-equilibrium stage of a high-energy heavy-ion collision. Based on a weak coupling effective kinetic description of the microscopic equilibration process (à la “bottom-up”), we calculate the nonequilibrium evolution of the local background energy-momentum tensor as well as the nonequilibrium linear response to transverse energy and momentum perturbations for realistic boost-invariant initial conditions for heavy-ion collisions. We demonstrate how this framework can be used on an event-by-event basis to propagate the energy-momentum tensor from far-from-equilibrium initial-state models to the time ${\tau }_{\text{hydro}}$ when the system is well described by relativistic viscous hydrodynamics. The subsequent hydrodynamic evolution becomes essentially independent of the hydrodynamic initialization time ${\tau }_{\text{hydro}}$ as long as ${\tau }_{\text{hydro}}$ is chosen in an appropriate range where both kinetic and hydrodynamic descriptions overlap. We find that for $\sqrt{{s}_{NN}}=2.76\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\text{TeV}$ central Pb-Pb collisions, the typical timescale when viscous hydrodynamics with shear viscosity over entropy ratio $\eta /s=0.16$ becomes applicable is ${\tau }_{\text{hydro}}\sim 1\phantom{\rule{0.16em}{0ex}}\mathrm{fm}/c$ after the collision.

Published in: Physical Review C 99 (2019)