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

TL;DR

This paper investigates how the properties of the $f_{0}(500)$ resonance change with temperature below the chiral transition, using a large-$N$ Non-Linear Sigma Model to connect these changes with chiral symmetry restoration.

Contribution

It provides a theoretical analysis of the $f_{0}(500)$ resonance's thermal behavior within a large-$N$ framework, linking resonance dynamics to chiral symmetry restoration.

Findings

The $f_{0}(500)$ mass and width vary with temperature below the critical point.

Thermal effects influence the dynamical generation of the $f_{0}(500)$ resonance.

The study connects resonance behavior with the chiral phase transition.

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.