Quark and Gluon Production from a Boost-invariantly Expanding Color Electric Field

TL;DR

This paper develops a formalism to compute quark and gluon particle spectra in an expanding classical color electric field, revealing finite lifetime effects, differences between quark and gluon production, and quark mass dependencies relevant to heavy ion collisions.

Contribution

It introduces a one-loop canonical quantization method in expanding coordinates to analyze particle production in a boost-invariant color electric field, including finite lifetime effects.

Findings

Finite lifetime significantly alters particle spectra.

Distinct production rates for quarks and gluons.

Quark mass influences the production spectra.

Abstract

Particle production from an expanding classical color electromagnetic field is extensively studied, motivated by the early stage dynamics of ultra-relativistic heavy ion collisions. We develop a formalism at one-loop order to compute the particle spectra by canonically quantizing quark, gluon and ghost fluctuations under the presence of such an expanding classical color background field; the canonical quantization is done in the $\tau$-$\eta$ coordinates in order to take into account manifestly the expanding geometry. As a demonstration, we model the expanding classical color background field by a boost-invariantly expanding homogeneous color electric field with lifetime $T$, for which we obtain analytically the quark and gluon production spectra by solving the equations of motion of QCD non-perturbatively with respect to the color electric field. In this paper we study (i) finite lifetime effect which is found to modify significantly the particle spectra from those expected from the Schwinger formula; (ii) the difference between the quark and gluon production; and (iii) the quark mass dependence of the production spectra. Implications of these results to ultra-relativistic heavy ion collisions are also discussed.