Medium induced Lorentz symmetry breaking effects in nonlocal Polyakov-Nambu-Jona-Lasinio models

Abstract

In this paper, we detail the thermodynamics of two-flavor nonlocal Polyakov-Nambu-Jona-Lasinio models for different parametrizations of the quark interaction regulators. The structure of the model is upgraded in order to allow for terms in the quark self-energy that violate Lorentz invariance due to the presence of the medium. We examine the critical properties, the phase diagram, and the equation of state. Furthermore, some aspects of the Mott effect for pions and sigma mesons are discussed explicitly within a nonlocal Polyakov-Nambu-Jona-Lasinio model. In particular, we continued the meson polarization function in the complex energy plane. Under certain approximations we were able to extract the imaginary part as a function of the meson energy. We were not able to calculate the dynamical meson mass and therefore resorted to a technical study of the temperature dependence of the meson width by replacing the meson energy with the temperature-dependent spatial meson mass. Our results show that, while the temperature behavior of the meson widths is qualitatively the same for a wide class of covariant regulators, the special case in which the nonlocal interactions are introduced via the instanton liquid model singles out with a drastically different behavior.