Large-$N$ Pion Scattering, Finite-Temperature Effects and the Relationship of the $f_{0}(500)$ with Chiral Symmetry Restoration

Abstract

In this work, we review how the mass and the width of the $f_{0}(500)$ pole behave in a regime where temperature is below the critical chiral transition value. This is attained by considering a large-$N$ $O(N + 1)/O(N)$ invariant Non-Linear Sigma Model (NLSM) such that we can study the dynamical generation of a $f_{0}(500)$ resonance. Introducing thermal effects via the imaginary time formalism allows us to study the behavior of the pole and relate it to chiral restoration.