On the effect of high order empirical parameters on the nuclear equation of state

A quantitative knowledge of the nuclear Equation of State (EoS) requires an accurate estimation of the uncertainties on the EoS parameters and their mutual correlations. Such correlations are empirically observed in a large set of EoS models by different authors, but they are not always fully understood. We show that some of these correlations can be interpreted from basic physical constraints imposed on a simple Taylor expansion of the binding energy around saturation density. In particular, we investigate the correlations among the following empirical parameters: the symmetry energy $E_{sym}$, the slope and curvature of the symmetry energy $L_{sym}$ and $K_{sym}$, and the curvature and skewness of the binding energy in symmetric matter $K_{sat}$ and $Q_{sat}$. The uncertainties on these correlations is estimated through analytical modelling as well as a meta-modelling analysis of the EoS subject to physical constraints. We show that a huge dispersion of the correlations among low order empirical parameters is induced by the unknown higher order empirical parameters, such as $K_{sym}$ (second order) and $Q_{sat}$ and $Q_{sym}$ (third order). We also propose an explanation of the reason why $Q_{sat}$ is weakly constrained by present experimental data. We conclude that selective observables on high order parameters, such as $K_{sym}$ and $Q_{sat}$, should be better determined before the present uncertainties on the EoS can be further reduced.