Lattice chiral effective field theory with three-body interactions at next-to-next-to-leading order

We consider low-energy nucleons at next-to-next-to-leading order in lattice chiral effective field theory. Three-body interactions first appear at this order, and we discuss several methods for determining three-body interaction coefficients on the lattice. We compute the energy of the triton and low-energy neutron-deuteron scattering phase shifts in the spin-doublet and spin-quartet channels using Lüscher’s finite-volume method. In the four-nucleon system we calculate the energy of the $ \alpha$ -particle using auxiliary fields and projection Monte Carlo