Bayesian truncation errors in chiral effective field theory: nucleon-nucleon observables

Abstract

Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. In previous work, a Bayesian model for truncation errors of perturbative expansions was adapted to EFTs. The model yields posterior probability distribution functions (pdfs) for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. A first application was made to chiral EFT for neutron-proton scattering using the semi-local potentials of Epelbaum, Krebs, and Meißner (EKM). Here we extend this application to consider a larger set of regulator parameters, energies, and observables as a general example of a statistical approach to truncation errors. The Bayesian approach allows for statistical validations of the assumptions and enables the calculation of posterior pdfs for the EFT breakdown scale. The statistical model is validated for EKM potentials whose convergence behavior is not distorted by regulator artifacts. For these cases, the posterior for the breakdown scale is consistent with EKM assumptions.

24 pages. Corresponds to published version

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• Chiral effective field theory and nuclear forces
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including $\Delta$'s
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