Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables

Abstract

We explore the constraints on the three-nucleon force (3NF) of chiral effective field theory $(\ensuremath{\chi}\mathrm{EFT})$ that are provided by bound-state observables in the $A=3$ and $A=4$ sectors. Our statistically rigorous analysis incorporates experimental error, computational method uncertainty, and the uncertainty due to truncation of the $\ensuremath{\chi}\mathrm{EFT}$ expansion at next-to-next-to-leading order. A consistent solution for the $^{3}\mathrm{H}$ binding energy, the $^{4}\mathrm{He}$ binding energy and radius, and the $^{3}\mathrm{H}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay rate can only be obtained if $\ensuremath{\chi}\mathrm{EFT}$ truncation errors are included in the analysis. The $\ensuremath{\beta}$-decay rate is the only one of these that yields a nondegenerate constraint on the 3NF low-energy constants, which makes it crucial for the parameter estimation. We use eigenvector continuation for fast and accurate emulation of no-core shell model calculations of the few-nucleon observables. This facilitates sampling of the posterior probability distribution, allowing us to also determine the distributions of the parameters that quantify the truncation error. We find a $\ensuremath{\chi}\mathrm{EFT}$ expansion parameter of $Q=0.33\ifmmode\pm\else\textpm\fi{}0.06$ for these observables.