Large-$N$ Pion Scattering, Finite-Temperature Effects and the Relationship of the $f_0(500)$ with Chiral Symmetry Restoration

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-$N$ $O(N+1)\mathrm{/}O(N)$ 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.