Confrontation of Different Relativistic Descriptions of Nuclear Matter

In this work we explore different relativistic descriptions of nuclear matter along the lines originally proposed in Refs.[1,2] where chiral symmetry is incorporated within the Walecka type Relativistic Mean Field (RMF) model as well as the effect of confinement through the nucleon response. The parameters of this model are controlled by fundamental properties, such as the chiral potential, the Lattice-QCD predictions, the quark structure, and two saturation properties (density and energy). The predictions of this chiral+confinement model is compared to two other models: another chiral model - but without confinement effect - and the original RMF model. For these three models, we additionally take care of parameter uncertainties and propagate them to our predictions for dense matter properties employing Bayesian statistics. We show that the combination of chiral potential with nucleon response represents a microscopically motivated and economical way to treat in-medium corrections to the scalar equation of motion, accurately reproducing the other two models which are directly fitted to the empirical properties of nuclear matter. In addition, the order hierarchy in power of the scalar field in the scalar potential is respected, which is not always the case for models where the scalar potential is fitted to empirical data. While these models are calibrated to the same properties at saturation density, they differ in their predictions as the density increases. Interestingly, we also show that, by fixing the $\rho$ coupling constant from the quark structure of the nucleon, these three models reproduce only half of the empirical symmetry energy.