Quantifying uncertainties and correlations in the nuclear-matter equation of state

TLDR: In this paper, the size and smoothness properties of the correlated EFT truncation error were extracted from high-order many-body perturbation theory calculations with nucleon-nucleon and three-Nucleon interactions up to fourth order in the chiral effective field theory.

Abstract: We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $\ensuremath{\chi}\mathrm{EFT}$ expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $\ensuremath{\chi}\mathrm{EFT}$ breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.