Large- N pion scattering at finite temperature: The f0 (500) and chiral restoration

Abstract

We consider the O(N+1)/O(N) nonlinear sigma model for large N as an effective theory for low-energy QCD at finite temperature T, in the chiral limit. At T=0 this formulation provides a good description of scattering data in the scalar channel and dynamically generates the f0(500) pole, the pole position lying within experimental determinations. Previous T=0 results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite T and show that it exactly satisfies thermal unitarity, which had been assumed but not formally proven in previous works. We discuss the main differences with the T=0 result, and we show that one can define a proper renormalization scheme with T=0 counterterms such that the renormalized amplitude can be chosen to depend only on a few parameters. Next, we analyze the behavior of the f0(500) pole at finite T, which is consistent with chiral symmetry restoration when the scalar susceptibility is saturated by the f0(500) state, in a second-order transition scenario and in accordance with lattice and theoretical analysis.