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

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 (\`a la "bottom-up"), we calculate the non-equilibrium evolution of the local background energy-momentum tensor as well as the non-equilibrium 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, e.g. IP-Glasma, 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 $\sqrt{s_{NN}}=2.76\,\text{TeV}$ central Pb-Pb collisions, the typical time scale when viscous hydrodynamics with shear viscosity over entropy ratio $\eta/s=0.16$ becomes applicable is $\tau_\text{hydro}\sim 1\,\text{fm/c}$ after the collision.