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

We sample the posterior probability distributions of the low-energy constants (LECs) in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="normal">Δ</a:mi></a:math>-full chiral effective field theory <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mo>(</c:mo><c:mi>χ</c:mi><c:mi>EFT</c:mi><c:mo>)</c:mo></c:mrow></c:math> 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 (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>n</d:mi><d:mi>p</d:mi></d:mrow></d:math>) cross sections and polarizations. We use priors grounded in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>χ</e:mi><e:mi>EFT</e:mi></e:mrow></e:math> 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>n</f:mi><f:mi>p</f:mi></f:mrow></f:math> scattering energies and angles in the ranges 45–83 MeV and 24–39 degrees, respectively. These correlations yield a nondiagonal covariance matrix and reduce the number of independent scattering data with factors of 8 and 4 at the second and third chiral orders, respectively. The relatively small difference between the second- and third-order predictions in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi mathvariant="normal">Δ</g:mi></g:math>-full <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>χ</i:mi><i:mi>EFT</i:mi></i:mrow></i:math> 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 nuclear theory.