Regression analysis of the nuclear symmetry energy for relativistic mean-field models

Regression analysis for the symmetry energy within a sample of relativistic mean-field models of nuclear matter is performed. The selected models consistently meet the experimentally obtained limitations. A proposed measure of the importance of adding the fourth-order term to the symmetry energy is analyzed. As a result of the research, it became possible to arrange the models and perform two-dimensional and one-dimensional linear regression analyses. The one-dimensional regression analysis between the input parameters confirms the appropriateness of introducing the division of the sample of considered models into four separate classes representing four statistically different fits. An additional result is the formulation of constraints on the function, which describes the energy density of the system. The performed two-dimensional regression analysis refers to an alternative method of parametrizing the symmetry energy using the power law. It was found that the Akaike information criterion of model selection involving the gamma exponent is sensitive to splitting the symmetry energy into the kinetic and potential parts. The analysis indicates that the more appropriate way of splitting is the one that does not consider the interaction with the sigma meson in the kinetic part.