Forbidden Transitions in Pole Models with Unitary Symmetry

Abstract

Two selection rules are derived which explain vanishing transition matrix elements found for many processes. A decay is forbidden in a pole model having a momentum-independent symmetry-breaking vertex and a symmetry-conserving vertex with arbitrary form factors if either (1) all propagators are equal in magnitude and the matrix elements of the symmetry-breaking vertex are proportional to those of a generator of the symmetry group, or (2) the propagators involve only known mass differences described by the Gell-Mann-Okubo mass formula and the matrix elements of the symmetry-breaking vertex are described by the $D$ coupling of three unitary octets. Applications to $K$ decays and nonleptonic $\Sigma$ decays are discussed.