We study the three-nucleon system at next-to-next-to-next-to-leading order ($\mathrm{N^3LO}$) in the framework of chiral effective field theory (EFT) on the lattice.
Our calculations do not rely on a perturbative treatment of subleading contributions to the nuclear forces.
For the two-nucleon potential, we apply the previously developed $\mathrm{N^3LO}$ lattice interaction.
For the leading contribution to the three-nucleon force, we determine the two low-energy constants (LECs) in the contact interactions by adjusting the ground state energy and half-life of triton, where the latter employs the nuclear axial current at $\mathrm{N^2LO}$ in chiral EFT.
Additionally, the ground state energy of helion and the charge radii of the two considered nuclei are computed. No effect of the smearing regularization in the three-nucleon contact interaction is observed here.
We compare our results with recent lattice-EFT calculations that are based on a potential tuned to light and medium-mass nuclei using the wave-function-matching technique to circumvent the Monte-Carlo sign problem.