Search for all renormalizable interactions

This paper is a continuation of a systematic search for all renormalizable interactions of heavy vector bosons. It is argued that in any renormalizable theory the $S$ matrix must satisfy high-energy unitarity bounds in the tree approximation. In an earlier work it was shown that any massive vector interaction, containing four or fewer boson fields and derivatives in each term, is unitarily bounded at high energy if and only if it is equivalent to a spontaneously broken gauge theory (modulo Abelian vector mass terms). In this paper unitarity bounds are imposed on a general Lagrangian which contains any number of fields (vector and scalar) and derivatives. We show that such an interaction is unitarily bounded only if it is canonically equivalent to an interaction with three-field vertices of mass dimension less than or equal to 4. This result lends further support to the notion that gauge theories are the only renormalizable theories of vector particles and that the appearance of Lie groups of internal symmetries in particle physics can be traced to the requirement of renormalizability.