An S matrix description of state mixing: Part I: General formalism, with Rho-Omega mixing as an Illustration

Abstract

The notion of state mixing is formulated in terms of S matrix language alone. The object is to work with quantities which are closely related to experiment, while avoiding the particularities of Hamiltonian theory or field theory. The scheme applies to particles of any spin, it is explicitly unitary, and useful in phenomenology as well as in dynamical S matrix models. Unlike the mass matrix method, it avoids the assumption that the states to be mixed evolve from discrete eigenstates of an unperturbed Hamiltonian. The main ingredient is a perturbation method by which the inverse of the K matrix is related to a corresponding unperturbed matrix. In some cases the latter can be defined directly from physical scattering matrices, without the device of turning off interactions. In this and following papers the method is applied to ϱ - ω, ϕ - ω, and K 0 - K 0 mixing. The results amount to more than a simple rephrasing of earlier treatments. As the discussion of ϱ - ω mixing in this paper illustrates, the physical arguments take quite a different form, and some new aspects of mixing questions are brought out.