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We present quantum Monte Carlo calculations of light nuclei, neutron-$\alpha$scattering, and neutron matter using local two- and three-nucleon ($3N$)interactions derived from chiral effective field theory up tonext-to-next-to-leading order (N$^2$LO). The two undetermined $3N$ low-energycouplings are fit to the $^4$He binding energy and, for the first time, to thespin-orbit splitting in the neutron-$\alpha$ $P$-wave phase shifts.Furthermore, we investigate different choices of local $3N$-operator structuresand find that chiral interactions at N$^2$LO are able to simultaneouslyreproduce the properties of $A=3,4,5$ systems and of neutron matter, incontrast to commonly used phenomenological $3N$ interactions.

Chiral Three-Nucleon Interactions in Light Nuclei, Neutron-$\alpha$ Scattering, and Neutron Matter