SU(4) × U(1) gauge theory. I. Muon-number nonconservation

This is the first in a series of three papers in which we study a unified gauge theory based on the group SU(4) × U(1). In this paper we present the general group-theoretical structure of SU(4) × U(1) and study in particular the muon-number-nonconserving processes which occur in the model. In the subsequent papers we shall study $\mathrm{CP}$ violation and present a new approach to understanding the Cabibbo angle. The central theme of our work is that all of the phenomena discussed in this series can be understood through the spontaneous-breakdown mechanism. In this paper we construct an explicit Higgs potential which breaks SU(4) × U(1) down to the usual SU(2) × U(1) theory of Weinberg and Salam. Of particular interest in this paper are rare muon-number-nonconserving processes, such as $\mu \to e\gamma$, which are forced to take place in our model once the symmetry has been broken. Our model possesses 12 new heavy intermediate vector bosons, and the available experimental constraints on their masses are presented.