Parameter mapping between the microscopic nonlocal Nambu-Jona-Lasinio and constant-sound-speed models

Abstract

A covariant nonlocal Nambu-Jona-Lasinio (nlNJL) model, used to describe the color superconducting quark matter phase in hybrid neutron stars, is parametrized with two free parameters, the dimensionless vector and diquark coupling strengths $\eta_V$ and $\eta_D$. Changing the values of these parameters results in different equations of state (EoS) with varying stiffness. On the other hand, the constant-sound-speed (CSS) model is a frequently used, simple quark matter equation of state with three parameters: the slope parameter $A$, the speed of sound $c_s$ and the bag pressure $B$. We show that the CSS model EoS provides an excellent fit to that of the nlNJL model. This work provides a simple functional form for the mapping between the parameter spaces of these two models, i.e. the $\eta_D-\eta_V$ and $A-c_s^2-B$ parameter sets. These results allow for a simplified description of the quark matter phase in neutron stars and for an interpretation of hybrid neutron star phenomenology in terms of parameters of a Lagrangian quark matter model