Accurate calibration of relativistic mean-field models: correlating observables and providing meaningful theoretical uncertainties

TL;DR

This paper introduces a covariance analysis method for relativistic mean-field models, enabling estimation of theoretical uncertainties and revealing correlations between physical observables, with implications for constraining nuclear matter properties.

Contribution

It applies covariance analysis to relativistic mean-field models to quantify uncertainties and uncover correlations, enhancing model calibration and predictive power.

Findings

Covariance analysis provides meaningful uncertainties for model parameters and observables.

Strong correlation between symmetry energy slope and neutron-skin thickness of Lead.

A 1% measurement of Lead's neutron radius constrains the symmetry energy slope to about 30%.

Abstract

Theoretical uncertainties in the predictions of relativistic mean-field models are estimated using a chi-square minimization procedure that is implemented by studying the small oscillations around the chi-square minimum. By diagonalizing the matrix of second derivatives, one gains access to a wealth of information---in the form of powerful correlations---that would normally remain hidden. We illustrate the power of the {\sl covariance analysis} by using two relativistic mean-field models: (a) the original linear Walecka model and (b) the accurately calibrated FSUGold parametrization. In addition to providing meaningful theoretical uncertainties for both model parameters and predicted observables, the covariance analysis establishes robust correlations between physical observables. In particular, we show that whereas the correlation coefficient between the slope of the symmetry energy and the neutron-skin thickness of Lead is indeed very large, a 1% measurement of the neutron radius of Lead may only be able to constrain the slope of the symmetry energy to about 30%.