The energy-momentum tensor at the earliest stage of relativistic heavy ion collisions

TL;DR

This paper derives an analytic expression for the gluon energy-momentum tensor at early times in high-energy nuclear collisions using the Colour Glass Condensate theory, providing insights into initial conditions for subsequent evolution.

Contribution

It presents a sixth-order proper time expansion of the energy-momentum tensor within the CGC framework, addressing technical challenges and regularization issues.

Findings

Results are physically meaningful up to near hydrodynamic initialization times.

The calculation captures early-time evolution of energy density and pressures.

Highlights the importance of regularization and parameter choices in CGC calculations.

Abstract

Nuclear collisions at high energies produce a gluon field that can be described using the Colour Glass Condensate (CGC) effective theory at proper times $\tau \lesssim 1$ fm/c. The theory can be used to calculate the gluon energy-momentum tensor, which provides information about the early time evolution of the chromo-electric and chromo-magnetic fields, energy density, longitudinal and transverse pressures, and other quantities. We obtain an analytic expression for the energy-momentum tensor using an expansion in the proper time, and working to sixth order. The calculation is technically difficult, in part because the number of terms involved grows rapidly with the order of the $\tau$ expansion, but also because of several subtle issues related to the definition of event-averaged correlators, the method chosen to regulate these correlators, and the dependence of results on the parameters introduced by the regularization and nuclear density profile functions. All of these issues are crucially related to the important question of the extent to which we expect a CGC approach to be able to accurately describe the early stages of a heavy ion collision. We present some results for the evolution of the energy density and the longitudinal and transverse pressures. We show that our calculation gives physically meaningful results up to values of the proper time which are close to the regime at which hydrodynamic simulations are initialized. In a companion paper [1] we give a detailed analysis of several other experimentally relevant quantities that can be calculated from the energy-momentum tensor.