Large-N pion scattering at finite temperature: The f_0(500) and chiral restoration

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 f_0(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 f_0(500) pole at finite T, which is consistent with chiral symmetry restoration when the scalar susceptibility is saturated by the f_0(500) state, in a second-order transition scenario and in accordance with lattice and theoretical analysis