Fluctuations of the initial color fields in high energy heavy ion collisions

TL;DR

This paper derives explicit formulas for initial color field fluctuations in high energy heavy ion collisions within the Color Glass Condensate framework, crucial for accurate numerical simulations of the early collision stages.

Contribution

It provides the first-principles derivation of fluctuation spectra in the Fock-Schwinger gauge by solving linearized Yang-Mills equations with plane wave initial conditions.

Findings

Explicit formulas for fluctuation modes in Fock-Schwinger gauge

Method to incorporate fluctuations in numerical simulations

Enhanced understanding of early-time dynamics in heavy ion collisions

Abstract

In the Color Glass Condensate approach to the description of high energy heavy ion collisions, one needs to superimpose small random Gaussian distributed fluctuations to the classical background field, in order to resum the leading secular terms that result from the Weibel instability, that would otherwise lead to pathological results beyond leading order. In practical numerical simulations, one needs to know this spectrum of fluctuations at a proper time $\tau \ll Q_s^{-1}$ shortly after the collision, in the Fock-Schwinger gauge $A^\tau=0$. In this paper, we derive these fluctuations from first principles, by solving the Yang-Mills equations linearized around the classical background, with plane wave initial conditions in the remote past. We perform the intermediate steps in light-cone gauge, and we convert the results to the Fock-Schwinger gauge at the end. We obtain simple and explicit formulas for the fluctuation modes.