Two-baryon systems with twisted boundary conditions

We explore the use of twisted boundary conditions in extracting the nucleon mass and the binding energy of two-baryon systems, such as the deuteron, from lattice QCD calculations. Averaging the results of calculations performed with periodic and antiperiodic boundary conditions imposed upon the light-quark fields, or other pairwise averages, improves the volume dependence of the deuteron binding energy from similar to e(-kL)/L to similar to e(-root 2kL)/L. However, a twist angle of pi/2 in each of the spatial directions improves the volume dependence from similar to e(-kL)/L to similar to e(-2kL)/L. Twist averaging the binding energy with a random sampling of twist angles improves the volume dependence from similar to e(-kL)/L to similar to e(-2kL)/L, but with a standard deviation of similar to e(-kL)/L, introducing a signal-to-noise issue in modest lattice volumes. Using the experimentally determined phase shifts and mixing angles, we determine the expected energies of the deuteron states over a range of cubic lattice volumes for a selection of twisted boundary conditions.