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 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.

Thermodynamics of an exactly solvable confining quark model

“…Besides the pressure, two other relevant observables that can be calculated are the quark density (42), and the quark number susceptibility (43), as shown in Figs. (5a) and (5b).…”

“…A possible way to extend the NJL model is to include a nonlocal current-current interaction kernel [40][41][42][43]. As a result, complex quark masses may appear, indicating confinement in the sense we discussed before.…”

“…However, due to its four-fermion interaction, the nonlocal NJL model is not renormalizable, similarly to its local version. Besides, it also leads to unstable thermodynamic behavior [42][43][44].…”

Crossover Transition to Quark Matter in Heavy Hybrid Stars

“…The hybrid EoS is constructed from a non-local Nambu-Jona-Lasinio model (nl-NJL) [7,8,9] with appreciable vector interaction strength [10], while for the nuclear matter we use the DD2 EoS [11,12].…”

Astrophysics Constraints on the EOS

“…For the former we employ standard nuclear matter EoS like APR [21] and DD2 [14] (see also [22,23]) which we modify at high densities by adopting an excluded volume with a nonlinear dependence on the chemical potential [24] For the quark phase, we use the nonlocal PNJL model EoS of Refs. [7,25] where the 4-momentum dependence of the formfactors is adjusted to describe the dynamical mass function and wave function renormalization of the T = 0 quark propagator from lattice QCD simulations [26,27] and the vector meson coupling η v is adjusted to obtain the slope of the chemical potential dependence of the pseudocritical temperature T c (µ) in accordance with lattice QCD [5]. In addition, we follow the procedure suggested in [13] to implement a µ dependence of η v by interpolating between zero temperature pressures P < = P Q (µ; η < ) and P > = P Q (µ; η > ) in β − equilibrium which are calculated at different, but fixed values η < = η v (µ ≤ µ c ) and η > = η v (µ > µ c ).…”