Time-Dependent Observables in Heavy Ion Collisions II: in Search of Pressure Isotropization in the $\varphi^4$ Theory

TL;DR

This paper investigates the early-time dynamics of heavy ion collisions using a scalar field model, revealing discrepancies with kinetic theory predictions and finding no evidence of pressure isotropization after a single scattering event.

Contribution

It provides an exact diagrammatic calculation of late-time observables in a scalar theory, challenging kinetic theory assumptions about pressure buildup in heavy ion collisions.

Findings

Exact calculations align with free streaming scenario.

Disagreement with kinetic theory on pressure development.

No evidence of isotropization after one scattering event.

Abstract

To understand the dynamics of thermalization in heavy ion collisions in the perturbative framework it is essential to first find corrections to the free-streaming classical gluon fields of the McLerran-Venugopalan model. The corrections that lead to deviations from free streaming (and that dominate at late proper time) would provide evidence for the onset of isotropization (and, possibly, thermalization) of the produced medium. To find such corrections we calculate the late-time two-point Green function and the energy-momentum tensor due to a single $2 \to 2$ scattering process involving two classical fields. To make the calculation tractable we employ the scalar $\varphi^4$ theory instead of QCD. We compare our exact diagrammatic results for these quantities to those in kinetic theory and find disagreement between the two. The disagreement is in the dependence on the proper time $\tau$ and, for the case of the two-point function, is also in the dependence on the space-time rapidity $\eta$: the exact diagrammatic calculation is, in fact, consistent with the free streaming scenario. Kinetic theory predicts a build-up of longitudinal pressure, which, however, is not observed in the exact calculation. We conclude that we find no evidence for the beginning of the transition from the free-streaming classical fields to the kinetic theory description of the produced matter after a single $2 \to 2$ rescattering.