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We present a family of nucleon-nucleon (NN) plus three-nucleon (3N)interactions up to N3LO in the chiral expansion that provides an accurate abinitio description of ground-state energies and charge radii up to themedium-mass regime with quantified theory uncertainties. Starting from the NNinteractions proposed by Entem, Machleidt and Nosyk, we construct 3Ninteractions with consistent chiral order, non-local regulator, and cutoffvalue and explore the dependence of nuclear observables over a range of massnumbers on the 3N low-energy constants. By fixing these constants using the 3-Hand 16-O ground-state energies, we obtain interactions that robustly reproduceexperimental energies and radii for large range from p-shell nuclei to thenickel isotopic chain and resolve many of the deficiencies of previousinteractions. Based on the order-by-order convergence and the cutoff dependenceof nuclear observables, we assess the uncertainties due the interaction, whichyield a significant contribution to the total theory uncertainty.

Family of Chiral Two- plus Three-Nucleon Interactions for Accurate Nuclear Structure Studies