Bayesian statistics in low-energy nuclear physics using effective field theory

Precision calculations of low- and medium-mass nuclei are now possible due to recent developments in many-body calculations. However, these predictions are limited by the availability of a reliable input nuclear interaction, and the uncertainty of such a calculation has yet to be fully quantified for comparison with experiment. Potentials derived using chiral effective field theory (EFT), which describes the dynamics of the nucleus at low energies in terms of nucleons and pions, are now the most widely used input for many-body calculations. However, chiral interactions suffer from a range of issues from not being fully renormalized to a lack of knowledge of the precise energy scales where they should be used. Using Bayesian statistical approaches, we are exploring different facets of EFT interactions. In particular, we have developed a novel framework for the estimation of EFT low-energy constants (LECs) that explicitly incorporates theoretical uncertainty and expectations into the fitting process. We have also built a statistical model using Gaussian Processes to estimate EFT truncation errors and explore correlations between EFT calculations of nucleon-nucleon scattering observables. A major value-added of a statistical model for theoretical errors in EFT is that we have developed validation tools that can be used to detect physics issue with EFT interactions. These efforts are aimed at two major goals: Estimating a full theoretical uncertainty for nuclear structure and reaction calculations; and using data and statistics to detect physics issues and to provide additional guidance for theory practitioners.