Early Time Dynamics of Gluon Fields in High Energy Nuclear Collisions

TL;DR

This paper analytically studies the early evolution of gluon fields in high-energy nuclear collisions, revealing pressure ratios, energy flow patterns, and angular momentum generation, with implications for understanding initial conditions in heavy ion experiments.

Contribution

It provides a formal recursive analytical solution for the initial gluon field dynamics, including energy-momentum tensor and flow characteristics, at very high energies.

Findings

Derived analytic expressions for initial chromo-electric and chromo-magnetic fields.

Identified hydrodynamic-like transverse energy flow contributions.

Showed emergence of angular momentum from non-abelian effects.

Abstract

Nuclei colliding at very high energy create a strong, quasi-classical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromo-electric and chromo-magnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. For example, we find that the ratio of longitudinal to transverse pressure very early in the system behaves as $p_L/p_T = -[1-\frac{3}{2a}(Q\tau)^2]/[1-\frac{1}{a}(Q\tau)^2]+\mathcal{O}(Q\tau)^4$ where $\tau$ is the longitudinal proper time, $Q$ is related to the saturation scales $Q_s$ of the two nuclei, and $a = \ln (Q^2/\hat{m}^2)$ with $\hat m$ a scale to be defined later. Our results are generally applicable if $\tau \lesssim 1/Q$. As already discussed in a previous paper, the transverse energy flow $S^i$ of the gluon field exhibits hydrodynamic-like contributions that follow transverse gradients of the energy density $\nabla^i \varepsilon$. In addition, a rapidity-odd energy flow also emerges from the non-abelian analog of Gauss' Law and generates non-vanishing angular momentum of the field. We will discuss the space-time picture that emerges from our analysis and its implications for observables in heavy ion collisions.