Time evolution of the chiral phase transition during a spherical expansion

TL;DR

This paper investigates the non-equilibrium evolution of a hadronic plasma during spherical expansion in heavy ion collisions, focusing on chiral phase transition dynamics, instabilities, and potential experimental signatures of disoriented chiral condensates.

Contribution

It provides a detailed analysis of the time evolution of chiral symmetry breaking and DCC formation during spherical expansion, highlighting differences from longitudinal expansion.

Findings

Instabilities occur for proper times less than 3 fm/c.

Low momentum pion spectrum increases due to domain growth.

Spherical expansion reaches the out regime faster with more particle production.

Abstract

We examine the non-equilibrium time evolution of the hadronic plasma produced in a relativistic heavy ion collision, assuming a spherical expansion into the vacuum. We study the $O(4)$ linear sigma model to leading order in a large-$N$ expansion. Starting at a temperature above the phase transition, the system expands and cools, finally settling into the broken symmetry vacuum state. We consider the proper time evolution of the effective pion mass, the order parameter $\langle \sigma \rangle$, and the particle number distribution. We examine several different initial conditions and look for instabilities (exponentially growing long wavelength modes) which can lead to the formation of disoriented chiral condensates (DCCs). We find that instabilities exist for proper times which are less than 3 fm/c. We also show that an experimental signature of domain growth is an increase in the low momentum spectrum of outgoing pions when compared to an expansion in thermal equilibrium. In comparison to particle production during a longitudinal expansion, we find that in a spherical expansion the system reaches the ``out'' regime much faster and more particles get produced. However the size of the unstable region, which is related to the domain size of DCCs, is not enhanced.