A triplet gauge boson with hypercharge one

Abstract

A vector boson $W_1^{\mu }$ with the quantum numbers $\left(3,1\right)$ under $SU{\left(2\right)}_L\times U(1{)}_Y$ could in principle couple with the Higgs field via the renormalizable term $W_1^{\mu \ast }H{D}_{\mu }H$. 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 $W_1$ gauge boson is non-trivial. In this work I will describe two variations of a minimal setup containing this field; they are based on an extended $SO(5)\times SU\left(2\right)\times U(1)$ electroweak group. I will nevertheless show that interactions such as $W_1^{\mu \ast }H{\partial }_{\mu }H$ are never generated in a Yang-Mills theory. A coupling between $W_1$, $H$ and another Higgs doublet $H^{\prime }$ 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; depending on the quantum numbers, they may couple to pairs of Standard Model fermions, or to a Standard Model fermion and an exotic one.

Comments: 16 pages