Classification of simple heavy vector triplet models

Abstract: We investigate decay modes of spin-1 heavy vector bosons ($V'$) from the viewpoint of perturbative unitarity in a model-independent manner. Perturbative unitarity requires some relations among couplings. The relations are called unitarity sum rules. We derive the unitarity sum rules from processes that contain two fermions and two gauge bosons. We find the relations between $V'$ couplings to the SM fermions $(f)$ and $V'$ couplings to the SM gauge bosons ($V$). Using the coupling relations, we calculate partial decay widths for $V'$ decays into $VV$ and $ff$. We show that Br($W' \to WZ) \lesssim$ 2$\%$ in the system that contains $V'$ and CP-even scalars as well as the SM particles. This result is independent of the number of the CP-even scalars. We also show that contributions of CP-odd scalars help to make Br($W' \to WZ$) larger than Br($W' \to ff$) as long as the CP-odd scalars couple to both the SM fermions and the SM gauge bosons. The existence of the CP-odd scalar couplings is a useful guideline to construct models that predict Br($W' \to WZ) \gtrsim$ 2$\%$. Our analysis relies only on the perturbative unitarity of $f\bar{f} \to WW'$. Therefore our result can be applied to various models.