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

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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.
© 2016 American Physical Society. Work partially supported by research Contracts No. FPA2011-27853-C02-02 (Spanish “Ministerio de Ciencia e Innovación”), No. FPA2014-53375-C2-2-P (Spanish “Ministerio de Economía y Competitividad”). We also acknowledge the support of the EU FP7 HadronPhysics3 project, the Spanish Hadron Excellence Network (Spanish “Ministerio de Economía y Competitividad” Contract No. FIS2014-57026-REDT) and the UCM-Banco de Santander Contract No. GR3/14 910309. S. C. thanks Professor José Rolando Roldán and the High Energy Physics group of Universidad de los Andes. In particular, he acknowledges financial support from that University to perform a research stay at Universidad Complutense during which this work was partially accomplished. We are also grateful to José Ramón Peláez and Jacobo Ruiz de Elvira for useful comments and for providing us with their parametrization values for the phase shift.
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