Models with higher weak-isospin Higgs multiplets

In order for scale factors ${\kappa }_V(V=W,Z)$ of the 125-GeV Higgs boson couplings to have the possibilities of being greater than unity and ${\kappa }_W\ne {\kappa }_Z$ while keeping the electroweak ρ parameter unity at tree level, the Higgs sector must be extended with at least two exotic $SU{\left(2\right)}_L$ multiplets in addition to the doublet Higgs field in the Standard Model. By the requirements of perturbative unitarity, no Landau pole in gauge couplings, and no accidental global $U\left(1\right)$ symmetry, we exhaust all the possible combinations of two exotic Higgs fields and derive general formulas for ${\kappa }_V$. We find that the current central values ${\kappa }_W=1.12$ and ${\kappa }_Z=0.99$ reported by CMS can be accommodated in the model with a complex and a real Higgs triplets as the simplest example.