Large-Npion scattering at finite temperature: Thef0(500)and chiral restoration

Santiago Cortés, A. Gómez Nicola, John Morales
2016 Physical Review D  
We consider the O(N+1)/O(N) Non-Linear 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 generates dynamically 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
more » ... nd show that it satisfies exactly 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 behaviour 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.
doi:10.1103/physrevd.93.036001 fatcat:tlmzecpif5dx7fmrmhlnhvcehq