Chiral symmetry breaking and chemical equilibrium in heavy-ion collisions

Sourendu Gupta,Jajati K Nayak,Sushant K Singh

doi:10.1103/physrevd.103.054023

Abstract

We examine the thermalization of an ensemble of the octet of pseudoscalar mesons, in the isospin symmetric limit, whose interactions are constrained through chiral symmetry, unitarity, and measurements. The reaction amplitudes generate all resonances up to masses of about 2 GeV, with twelve input parameters, namely f_pi, three masses, and eight low energy constants (LECs) of chiral perturbation theory. In linear response theory, we find that matter takes an extremely long time to thermalize. These long relaxation times are directly related to the fact that these mesons are pseudo-Goldstone bosons of chiral symmetry breaking. This result indicates that fireballs created with zero baryon number in heavy-ion collisions will drop out of chemical equilibrium once they enter the chiral symmetry broken phase.

Highlights

In heavy-ion collisions, as in all collider experiments, the main observables are the particles in the final state and their momenta
We are able to avoid this due to advances in QCD, which allows us to proceed with a small number of low-energy constants (LECs) in chiral perturbation theory (ChPT), which may be determined by measurements of other hadron properties, and to write unitary amplitudes for the transport theory without any ad hoc UV cutoff
We examined the chemical relaxation time in a gas of the SU(3) octet of pseudoscalar mesons in the linear response approximation

Summary

INTRODUCTION

In heavy-ion collisions, as in all collider experiments, the main observables are the particles in the final state and their momenta. Right from the early days of heavy-ion collisions there have been efforts to build a complete dynamical description of the whole history of the fireball in terms of known particle physics [5,6,7,8,9] These transport computations assume that the fireball is made up of an interacting system of quarks and gluons in the very initial stages; trace their interactions; and usually find that the system approaches equilibrium, cools, and turns into an interacting system of hadrons. Even though it is approximate, chiral symmetry is predictive because it strongly constrains the low-energy interactions of the pseudoscalar mesons which are the pseudo-Goldstone bosons of this symmetry breaking [12,13,14] Such a theory is known to be very good at predicting many properties of the lightest pseudoscalar mesons including decay constants and reaction cross sections [14,15,16].

Chemical rate equations and relaxation times

Expansion timescale and freeze-out

Hadron cross sections from chiral perturbation theory

RESULTS

CONCLUSIONS