Resonance Scattering Phase Shifts on a Non – Rest Frame Lattice

Many low energy hadrons, such as the rho, can observed as resonances in scattering experiments. A proposal by Lüscher enables one to determine infinite volume elastic scattering phases from the two-particle energy spectrum measured from finite periodic lattices. In this work, we generalize the formalism to the case where the total momentum of the particles is non-zero; i.e.,the lattice frame is not the center-of-mass frame of the scattering particles. There are several advantages to this procedure including making a wider variety of center of mass energies accessible with a fixed lattice volume, and making the avoided level crossing in a P-wave decay occur with a smaller volume. The formalism is tested with a simple lattice model of two fields with different masses and a 3-point coupling in 3 + 1 dimensions. We find remarkable agreement between the rest-frame and non-rest-frame scattering.