Mechanism for Nonconservation of Muon Number

We consider the possibility that muon-number conservation is not a fundamental symmetry of nature. In simple SU(2) ⊗ U(1) gauge theories with several scalar boson doublets, muon number will still atuomatically be conserved by the intermediate-vector-boson interactions, but not by effects of virtual scalar bosons. The branching ratio for $\mu \to e+\gamma$ is estimated to be of order ${\left(\frac{\alpha }{\pi }\right)}^3$. Other $\mu -e$ transition processes are also discussed.