The triton in a finite volume

Understanding the volume dependence of the triton binding energy is an important step towards lattice simulations of light nuclei. We calculate the triton binding energy in a finite cubic box with periodic boundary conditions to leading order in the pionless effective field theory. Higher order corrections are estimated and the proper renormalization of our results is verified explicitly. We present results for the physical triton as well as for the pion-mass dependence of the triton spectrum near the “critical” pion mass, Mπcrit≈197 MeV, where chiral effective field theory suggests that the nucleon-nucleon scattering lengths in the 1S0- and 3S1-channels diverge simultaneously. An extension of the Lüscher formula to the three-body system is implicit in our results.