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We explore the constraints on the three-nucleon force (3NF) of chiraleffective field theory ($\chi$EFT) that are provided by bound-state observablesin the $A=3$ and $A=4$ sectors. Our statistically rigorous analysisincorporates experimental error, computational method uncertainty, and theuncertainty due to truncation of the $\chi$EFT expansion atnext-to-next-to-leading order. A consistent solution for the ${}^3$H bindingenergy, the ${}^4$He binding energy and radius, and the ${}^3$H $\beta$-decayrate can only be obtained if $\chi$EFT truncation errors are included in theanalysis. All of these except the $\beta$-decay rate give essentiallydegenerate constraints on the 3NF low-energy constants, so it is crucial forestimating these parameters. We use eigenvector continuation for fast andaccurate emulation of No-Core Shell Model calculations of the consideredfew-nucleon observables. This facilitates sampling of the posterior probabilitydistribution, allowing us to also determine the distributions of thehyperparameters that quantify the truncation error. We find a $\chi$EFTexpansion parameter of $Q=0.33 \pm 0.06$ for these observables.

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