Fingerprinting the Type-Z three Higgs doublet models

There has been great interest in a model with three Higgs doublets in which fermions with a particular charge couple to a single and distinct Higgs field. We study the phenomenological differences between the two common incarnations of this so-called Type-Z 3HDM. We point out that the differences between the two models arise from the scalar potential only. Thus we focus on observables that involve the scalar self-couplings. We find it difficult to uncover features that can uniquely set apart the $Z_3$ variant of the model. However, by studying the dependence of the trilinear Higgs couplings on the nonstandard masses, we have been able to isolate some of the exclusive indicators for the $Z_2\times Z_2$ version of the Type-Z 3HDM. This highlights the importance of precision measurements of the trilinear Higgs couplings.