Natural suppression of symmetry violation in gauge theories: Muon- and electron-lepton-number nonconservation

We analyze the circumstances under which the violations of an approximate symmetry in a unified gauge theory of weak interactions are naturally suppressed; in particular, we investigate approximate muonand electron-type lepton-number conservation as an example of such a symmetry. Extending earlier work, we propose a unified treatment of this symmetry together with strangeness conservation by the weak neutral current and CP invariance. The rate for the decay p, ~ ey is calculated for a general SU(2) )& U(1) gauge model. From this and a similar study of the decay p, ~eee we derive a set of conditions which guarantees that the violation of muonand electron-type lepton-number conservation is naturally strongly suppressed. As part of this, we compute the nondiagonal electromagnetic vertex to one-loop order for an arbitrary