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Gluon Production from Non-Abelian Weizsäcker-Williams Fields in Nucleus-Nucleus Collisions

Alex Kovner, Larry McLerran, Heribert Weigert

TL;DR

This work extends the McLerran-Venugopalan framework to nucleus-nucleus collisions, showing that the early-time dynamics are governed by coherent non-abelian Weizsäcker-Williams fields described by classical Yang-Mills theory. It demonstrates a boost-invariant, tau-dependent evolution inside the forward light cone after the collision and provides a method to extract produced gluons from the asymptotic field, yielding initial conditions for subsequent parton cascades and hydrodynamics. The analysis identifies the saturation scale μ as the key parameter controlling nonlinear dynamics and gluon production, and highlights the need for numerical solutions to make quantitative predictions and enable experimental tests of the approach.

Abstract

We consider the collisions of large nuclei using the theory of McLerran and Venugopalan. The two nuclei are ultra-relativistic and sources of non-abelian Weizsäcker-Williams fields. These sources are in the end averaged over all color orientations locally with a Gaussian weight. We show that there is a solution of the equations of motion for the two nucleus scattering problem where the fields are time and rapidity independent before the collision. After the collision the solution depends on proper time, but is independent of rapidity. We show how to extract the produced gluons from the classical evolution of the fields.

Gluon Production from Non-Abelian Weizsäcker-Williams Fields in Nucleus-Nucleus Collisions

TL;DR

This work extends the McLerran-Venugopalan framework to nucleus-nucleus collisions, showing that the early-time dynamics are governed by coherent non-abelian Weizsäcker-Williams fields described by classical Yang-Mills theory. It demonstrates a boost-invariant, tau-dependent evolution inside the forward light cone after the collision and provides a method to extract produced gluons from the asymptotic field, yielding initial conditions for subsequent parton cascades and hydrodynamics. The analysis identifies the saturation scale μ as the key parameter controlling nonlinear dynamics and gluon production, and highlights the need for numerical solutions to make quantitative predictions and enable experimental tests of the approach.

Abstract

We consider the collisions of large nuclei using the theory of McLerran and Venugopalan. The two nuclei are ultra-relativistic and sources of non-abelian Weizsäcker-Williams fields. These sources are in the end averaged over all color orientations locally with a Gaussian weight. We show that there is a solution of the equations of motion for the two nucleus scattering problem where the fields are time and rapidity independent before the collision. After the collision the solution depends on proper time, but is independent of rapidity. We show how to extract the produced gluons from the classical evolution of the fields.

Paper Structure

This paper contains 4 sections, 31 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Review of the McLerran-Venugopalan Model
  3. The Two Nucleus Problem
  4. Summary and Conclusions

Figures (3)

  • Figure 1: Weizsäcker-Williams distribution for a single nucleus
  • Figure 2: Two nuclei Lorentz-contracted to infinitely thin sheets before the collision takes place
  • Figure 3: Regions with different structures of the gauge potential: In regions 1 and 2 we have the well known one nucleus solutions $\alpha_{1,2}$. While in the backward light cone there the gauge potential is vanishing we have a nontrivial solution in the forward lightcone, region 3