Abstract
In this work we present an extension of the LüScher formalism to include the interaction of particles with spin, focusing on the scattering of two vector particles. The derived formalism will be applied to Scalar QED in the Higgs Phase, where the U(1) gauge boson acquires mass.
Highlights
The study of scattering in Lattice Field Theory starts with the original work of Lüscher [1]
We will focus on the case of two identical vector particles and we will make use of the spatial symmetries of the lattice to factorize the Lüscher equation
By means of operators that transform under a certain irreducible representation of the spatial symmetry group, we gain access to the different phase shifts of the theory
Summary
The study of scattering in Lattice Field Theory starts with the original work of Lüscher [1]. In this first work, he derived equations for the scattering length and phase shift of spinless particles in the rest frame. We derive a general Lüscher equation for scattering of particles with arbitrary spin through the matching to a non-relativistic effective theory. The results obtained here are in agreement with Ref. By means of operators that transform under a certain irreducible representation of the spatial symmetry group, we gain access to the different phase shifts of the theory. The equations will be tested in Scalar QED, for which first numerical results will be shown
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