Resonant phase shift from finite volume interactions

Abstract

A scattering process can be modelled by a finite volume lattice with appropriate boundary conditions. Such lattices have intermediate states with discretized energy spectrum. With Lüscher’s formula we can obtain the phase shifts of these states. We constructed a three dimensional, non-relativistic model for the scattering of two scalar mesons on a lattice. The resonant energy spectra at different lattice sizes were obtained. Using Lüscher’s formula, the corresponded phase shifts were calculated. Then, we compared the infinite volume phase shifts with the finite volume phase shifts acquired by Lüscher’s formula.