On colliding ultrarelativistic nuclei on a transverse lattice

TL;DR

This work develops a non-perturbative, real-time framework to study the early-time dynamics of small-x gluons in ultrarelativistic nucleus collisions by formulating a transverse lattice description. The approach reduces the problem to a Kogut–Susskind Hamiltonian in 2+1 dimensions with an adjoint scalar, using non-Abelian Weizsäcker–Williams fields as initial conditions and evolving them via lattice equations of motion. It enables the non-perturbative investigation of gluon radiation, energy density evolution, and potential thermalization, with observables that can feed into hydrodynamic models. While grounded in a classical approximation and boost-invariance, the method offers a bridge between initial-state physics and observable signatures, and sets the stage for relaxing key assumptions in future work.

Abstract

We argue that the classical evolution of small x modes in the collision of two ultrarelativistic nuclei is described on a transverse lattice by the Kogut--Susskind Hamiltonian in 2+1-dimensions coupled to an adjoint scalar field. The initial conditions for the evolution are provided by the non--Abelian Weizsäcker--Williams fields which constitute the classical parton distributions in each of the nuclei. We outline how lattice techniques developed for real time simulations of field theories in thermal equilibrium can be used to study non--perturbatively, thermalization and classical gluon radiation in ultrarelativistic nuclear collisions.