Medium induced Lorentz symmetry breaking effects in nonlocal PNJL models

TL;DR

This paper investigates how medium-induced Lorentz symmetry breaking affects the thermodynamics and meson properties in nonlocal PNJL models, revealing distinct behaviors depending on the interaction regulator choice.

Contribution

It introduces a model extension allowing Lorentz-violating terms in the quark selfenergy and analyzes their impact on phase transitions and meson dynamics.

Findings

Meson widths exhibit similar temperature dependence across various regulators.

Instanton liquid model regulator causes markedly different meson behavior.

The model provides insights into the Mott effect and meson spectral functions.

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 selfenergy which violate Lorentz invariance due to the presence of the medium. We examine the critical properties, the phase diagram as well as 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 and 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 where the nonlocal interactions are introduced via the instanton liquid model singles out with a drastically different behavior.