Comparison of different relativistic models applied to dense nuclear matter

TL;DR

This paper compares three relativistic models of dense nuclear matter, analyzing their predictions and uncertainties, and highlights differences in their behavior at high densities and their ability to reproduce empirical data.

Contribution

It introduces and compares three relativistic models incorporating chiral and confinement effects, using Bayesian methods to assess uncertainties and differences at high densities.

Findings

RMF and RMF-C models share features at high density

RMF-CC predicts a significantly lower scalar field at high density

All models reproduce only half of the empirical symmetry energy when fixing the $ ho$ coupling

Abstract

We explore three different classes of relativistic approaches applied to the description of dense nuclear matter: a Walecka-type relativistic mean field model (RMF), an extension including an effective chiral potential (RMF-C) and a further extension with a chiral potential and confinement effects (RMF-CC). The parameters of the latter are controlled by fundamental properties such as the chiral potential, Lattice-QCD predictions, the quark sub-structure, as well as empirical properties at nuclear matter saturation. While these models are calibrated to the same properties at saturation density, they differ in their predictions as the density increases. We take care of parameter uncertainties and propagate them to our predictions for symmetric nuclear matter by employing Bayesian statistics. We show that RMF and RMF-C share common features as the density increases, while RMF-CC behaves differently. For instance, the scalar field at $6n_\textrm{sat}$ reaches $\sim 20$ MeV for RMF-CC while it is larger than $\sim 70$ MeV for RMF and RMF-C. 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.