Electromagnetic Properties of a Charged Vector Meson

Abstract

A systematic study is made of the electromagnetic properties of charged vector mesons. The various formalisms used to describe charged particles of spin 1 are compared, and a new first-order formulation of the St\uckelberg theory is developed. For the most general first-order Proca Lagrangian, subject to the usual symmetry requirements we eliminate the redundant components to obtain a Hamiltonian formulation. The theory is interpreted in the nonrelativistic limit, and the terms corresponding to spin-orbit coupling and electric quadrupole-moment interaction are identified. The analogy to spin-\textonehalf{} theory has led us to consider spin equations of motion which agree with the quantum-mechanical equations to order ${m}^{\ensuremath{-}2}$.This general form for the electromagnetic interaction is applied to a recalculation of the $\ensuremath{\mu}\ensuremath{\rightarrow}e+\ensuremath{\gamma}$ decay rate through a vector-meson intermediary. We conclude, that the absence of this process is not necessarily an argument against the existence of an intermediary meson in weak interactions.