Fluctuations of topological charge and chiral density in the early stage of high energy nuclear collisions

TL;DR

This paper investigates the early-stage topological charge and chiral density fluctuations in high-energy nuclear collisions using classical Yang-Mills simulations, revealing how these correlations evolve and relate to collision energy and saturation scales.

Contribution

It provides a systematic analysis of topological and chiral density correlations during the initial Glasma phase in heavy-ion collisions, connecting correlation lengths to energy scales and evolution time.

Findings

Correlation lengths are of the order of the inverse saturation scale.

Domains grow with proper time during the expansion.

Chiral density production slows down at a certain proper time.

Abstract

We study systematically the topological charge density and the chiral density correlations in the early stage of high energy nuclear collisions: the intial condition is given by the McLerran-Venugopalan model and the evolution of the gluon fields is studied via the Classical Yang-Mills equations up to proper time $\tau\approx 1$ fm/c for an $SU(2)$ evolving Glasma. Topological charge is related to the gauge invariant $\bm E \cdot \bm B$ where $\bm E$ and $\bm B$ denote the color-electric and color-magnetic fields, while the chiral density is produced via the chiral anomaly of Quantum Chromodynamics. We study how the correlation lengths are related to the collision energy, and how the correlated domains grow up with proper time in the transverse plane for a boost invariant longitudinal expansion. We estimate the correlation lengths of both quantities, that after a short transient results of the order of the typical energy scale of the model, namely the inverse of the saturation scale. We estimate the proper time for the formation of a steady state in which the production of the chiral density in the transverse plane per unit rapidity slows down, as well as the amount of chiral density that would be present at the switch time between the Classical Yang-Mills evolution and the relativistic transport or hydro for the quark-gluon plasma phase.