Classical Gluon Radiation in Ultrarelativistic Nucleus-Nucleus Collisions

TL;DR

The paper analyzes gluon production in ultrarelativistic nucleus–nucleus collisions by solving the classical Yang–Mills equations in covariant gauge with nuclei modeled as ensembles of color charges on eikonal trajectories. It constructs the classical field to order $g^3$, demonstrates its exact correspondence with covariant-gauge Feynman diagrams, and derives explicit coordinate-space expressions for the radiated field along with energy, number, and multiplicity distributions, including nucleon form factors that regulate infrared behavior. The results reproduce earlier findings (Gunion–Bertsch; Kovner–McLerran–Weigert) while clarifying the regime of validity of the classical description and showing that quantum effects emerge at order $g^5$. Together, these findings illuminate the initial, pre-thermal dynamics of heavy-ion collisions and provide boost-invariant observables relevant for early-time evolution and potential thermalization studies.

Abstract

The classical Yang-Mills equations are solved perturbatively in covariant gauge for a collision of two ultrarelativistic nuclei. The nuclei are taken as ensembles of classical color charges on eikonal trajectories. The classical gluon field is computed in coordinate space up to cubic order in the coupling constant g. We construct the Feynman diagrams corresponding to this field and show the equivalence of the classical and diagrammatic approaches. An argument is given which demonstrates that at higher orders in g the classical description of the process breaks down. As an application, we calculate the energy, number, and multiplicity distributions of produced soft gluons and reproduce earlier results by Gunion and Bertsch and by Kovner, McLerran, and Weigert.

Figures (3)

• Figure 1: The nuclear collision as envisaged here (for details, see text).
• Figure 2: Diagrams contributing to the gluon field at order $g^3$.
• Figure 3: Graphs contributing to the gluon production at order $g^5$.