Phenomenology of a gauge boson triplet with hypercharge one

A vector boson W mu 1 with the quantum numbers (3; 1) under SU(2)L x U(1)Y could in principle couple with the Higgs field via the renormalizable term W mu*1 HD mu H. This interaction is known to affect the T parameter and, in so doing, it could potentially explain the recent CDF measurement of the W-boson mass. As it is often the case with vectors, building a viable model with a W1 gauge boson is nontrivial. In this work I will describe two variations of a minimal setup containing this field; they are based on an extended SO(5) x SU(2) x U(1) electroweak group. I will nevertheless show that interactions such as W mu* 1 H partial differential mu H are not generated in a Yang-Mills theory. A coupling between W1, H and another Higgs doublet H' is possible though. Finally, I will provide an explicit recipe for the construction of viable models with gauge bosons in arbitrary representations of the Standard Model group which may couple to a Standard Model fermion and an exotic one.