Inference of the low-energy constants in delta-full chiral effective field theory including a correlated truncation error

We sample the posterior probability distributions of the low-energy constants (LECs) in delta-full chiral effective field theory ($\chi$EFT) up to third order. We use eigenvector continuation for fast and accurate emulation of the likelihood and Hamiltonian Monte Carlo to draw effectively independent samples from the posteriors. Our Bayesian inference is conditioned on the Granada database of neutron-proton ($np$) cross sections and polarizations. We use priors grounded in $\chi$EFT assumptions and a Roy-Steiner analysis of pion-nucleon scattering data. We model correlated EFT truncation errors using a two-feature Gaussian process, and find correlation lengths for $np$ scattering energies and angles in the ranges 40--120 MeV and 25--45 degrees, respectively. These correlations yield a non-diagonal covariance matrix and reduce the number of independent scattering data with a factor of eight and four at the second and third chiral orders, respectively. The relatively small difference between the second and third order predictions in delta-full $\chi$EFT suppresses the marginal variance of the truncation error and the effects of its correlation structure. Our results are particularly important for analyzing the predictive capabilities in \textit{ab initio} nuclear theory.