Evolution of pressures and correlations in the Glasma produced in high energy nuclear collisions

TL;DR

This study numerically investigates the early-time evolution of the SU(2) Glasma in high-energy nuclear collisions, focusing on pressure anisotropy and field correlations, revealing limited impact of initial fluctuations unless they carry significant energy.

Contribution

It provides the first detailed numerical analysis of pressure evolution and field correlations in the Glasma without longitudinal expansion, highlighting the effects of initial fluctuations.

Findings

Pressure ratio P_L/P_T remains largely unaffected unless fluctuations are energetically substantial.

Transverse field correlations evolve from anticorrelation to increased correlation length.

Longitudinal correlations decrease at small separations, indicating partial loss of longitudinal coherence.

Abstract

We consider the SU(2) Glasma with gaussian fluctuations and study its evolution by means of classical Yang-Mills equations solved numerically on a lattice. Neglecting in this first study the longitudinal expansion we follow the evolution of the pressures of the system and compute the effect of the fluctuations in the early stage up to $t\approx 2$ fm/c, that is the time range in which the Glasma is relevant for high energy collisions. We measure the ratio of the longitudinal over the transverse pressure, $P_L/P_T$, and we find that unless the fluctuations carry a substantial amount of the energy density at the initial time, they do not change significantly the evolution of $P_L/P_T$ in the early stage, and that the system remains quite anisotropic. We also measure the longitudinal fields correlators both in the transverse plane and along the longitudinal direction: while at initial time fields appear to be anticorrelated in the transverse plane, this anticorrelation disappears in the very early stage and the correlation length in the transverse plane increases; on the other hand, we find that the longitudinal correlator decreases for a small longitudinal separation while being approximately constant for larger separation, which we interpret as a partial loss of longitudinal correlation induced by the dynamics.