The triton in a finite volume

TL;DR

This paper investigates how the binding energy of the triton nucleus depends on the finite volume in lattice simulations, using pionless effective field theory, and extends the understanding of three-body systems in finite volumes.

Contribution

It provides leading order calculations of the triton binding energy in finite volume and extends the Luescher formula to three-body systems, including pion-mass dependence.

Findings

Results for physical triton binding energy in finite volume.

Analysis of pion-mass dependence near critical mass.

Verification of proper renormalization in the calculations.

Abstract

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, Mpi_c ~ 197 MeV, where chiral effective field theory suggests that the nucleon-nucleon scattering lengths in the singlet- and triplet-channels diverge simultaneously. An extension of the Luescher formula to the three-body system is implicit in our results.