https://doi.org/10.1140/epja/s10050-021-00600-x
Regular Article - Theoretical Physics
The energy-momentum tensor at the earliest stage of relativistic heavy-ion collisions
1
Department of Physics, Brandon University, R7A 6A9, Brandon, MB, Canada
2
Winnipeg Institute for Theoretical Physics, Winnipeg, MB, Canada
3
National Centre for Nuclear Research, ul. Pasteura 7, 02-093, Warsaw, Poland
4
Institute of Physics, Jan Kochanowski University, ul. Uniwersytecka 7, 25-406, Kielce, Poland
Received:
21
May
2021
Accepted:
1
October
2021
Published online:
15
January
2022
Nuclear collisions at high energies produce a gluon field that can be described using the Colour Glass Condensate (CGC) effective theory at proper times 
fm. 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 
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.
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