Vector particle scattering on the lattice

TL;DR

This paper develops a formalism for vector particle scattering on the lattice, deriving the Luescher equation and constructing operators for different irreducible representations, with applications to massive gauge bosons in scalar QED.

Contribution

It provides an explicit form of the Luescher equation for vector particles and constructs relevant operators, advancing lattice scattering analysis for massive gauge bosons.

Findings

Derived explicit Luescher equation for vector particles

Constructed operators in various irreducible representations

Applied formalism to scalar QED with massive gauge bosons

Abstract

In this work, we present an explicit form of the Luescher equation and consider the construction of the operators in different irreducible representations for the case of scattering of two vector particles. The formalism is applied to scalar QED in the Higgs Phase, where the $U(1)$ gauge boson acquires mass.