Chiral Effective Field Theory Parameter Estimation Using Markov Chain Monte Carlo

Effective field theories (EFTs) offer a rigorous connection of quantum chromodynamics to the low energy regime of nuclear structure and interactions. While high-quality effective interactions have been produced that can successfully replicate experimental data, they suffer from the same shortcoming that plagues much of theoretical nuclear physics: a lack of error estimation. While rough estimates have been used to quantify uncertainties in the models, rigorous and systematic uncertainty quantifications are currently still missing. To remedy this, we introduce an implementation of Markov Chain Monte Carlo (MCMC) to sample from the EFT parameter space. This allows for the quantification of uncertainties on the parameters of the EFT through their probability distributions. We further show that the uncertainty in the EFT parameters can be used to estimate the error in observable calculations through the samples produced.