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

Abstract

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 $T$ and 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.

24 pages, 12 figures. Funding agency added in the Acknowledgments

References in corpus (5)

• The QCD transition temperature: results with physical masses in the continuum limit II.
• The QCD phase transition with physical-mass, chiral quarks
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Role of the tetraquark in the chiral phase transition
• Electromagnetic effects in the pion dispersion relation at finite temperature

Cited by in corpus (6)

• Thermal behaviors of light scalar resonances at low temperatures
• The role of the thermal $f_0(500)$ in chiral symmetry restoration
• Chiral Symmetry Restoration for the large-$N$ pion gas
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures
• Light Meson Masses using AdS/QCD modified Soft Wall Model
• Chiral Symmetry restoration from the hadronic regime