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 muon- and 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 μ-->eγ is calculated for a general SU(2) × U(1) gauge model. From this and a similar study of the decay μ-->eeē we derive a set of conditions which guarantees that the violation of muon- and 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 SU(2) × U(1) gauge theory. We then focus on the phenomenological predictions of a particular gauge model with three left-handed doublets of leptons and quarks. These include the existence of charged and neutral heavy leptons and of small violations of μ-e universality and the relation GβFθC = GμF. Other muon- and electron-number-violating effects include nonvanishing rates for the decays K+/--->π+/-eμ̄ and KL-->eμ̄ and for the reactions μ + N-->e + N and νμ + N-->e- + X.