Bayesian Discrepancy Models for Full Uncertainty Propagation in Effective Field Theories

A full accounting of the uncertainties inherent in chiral effective field theory (χEFT) is a requirement for rigorous uncertainty quantification across the nuclear chart. We propose a Bayesian discrepancy model that is informed by the convergence of χEFT to quantify the size of its higher-order contributions. Based in Gaussian processes, the discrepancy due to χEFT truncation can then be used for two important goals: (1) to obtain better estimates of the χEFT parameters when fit to data and (2) to quantify uncertainties in predictions from χEFTs that have already been fit. We show how the discrepancy model arises naturally from the physics of χEFT, how the discrepancy term appears in fitting and prediction equations, and discuss the application of these techniques to the search for neutrinoless double beta decay.