Quark production in heavy ion collisions I. Formalism and boost invariant fermionic light-cone mode functions

TL;DR

This paper develops a formalism for calculating quark production in high-energy heavy ion collisions using the color glass condensate framework, focusing on boost-invariant fermionic mode functions and their initial conditions.

Contribution

It introduces a new formalism expressing the quark spectrum via mode functions and provides an analytical initial value in a boost-invariant basis, along with a sampling algorithm.

Findings

Analytical initial mode functions in Fock-Schwinger gauge

Boost-invariant basis for fermionic modes

Statistical sampling algorithm for mode functions

Abstract

We revisit the problem of quark production in high energy heavy ion collisions, at leading order in $\alpha_s$ in the color glass condensate framework. In this first paper, we setup the formalism and express the quark spectrum in terms of a set of mode functions of the Dirac equation. We determine analytically their initial value in the Fock-Schwinger gauge on a proper time surface $Q_s\tau_0\ll 1$, in a basis which makes manifest the boost invariance properties of this problem. We also describe a statistical algorithm to perform the sampling of the mode functions.