In the Standard Model, the Higgs field is a doublet of SU(2) and hypercharge $Y=1/2$. We have four real scalar degrees of freedom (since $H$ is a complex doublet); three of these get "eaten" to form the longitudinal polarizations of the $W^±_\mu$ and $Z_\mu$. One scalar remains: the Higgs boson.
What would happen if we modified the Standard Model to have a Higgs triplet with hypercharge $Y=1$? (With the $\tau^a$ being the 3x3 Pauli matrices). Do we have 3 Higgs bosons?
