Enhancement of the $H^\pm W^\mp Z$ vertex in the three scalar doublet model

Understand

We compute one-loop induced trilinear vertices with physical charged Higgs bosons $H^\pm$ and ordinary gauge bosons, i.e., $H^\pm W^\mp Z$ and $H^\pm W^\mp \gamma$, in the model with two active plus one inert scalar doublet fields under a $Z_2(\text{unbroken})\times \tilde{Z}_2(\text{softly-broken})$ symmetry.

• The $Z_2$ and $\tilde{Z}_2$ symmetries are introduced to guarantee the stability of a dark matter candidate and to forbid the flavour changing neutral current at the tree level, respectively.
• The dominant form factor $F_Z$ of the $H^\pm W^\mp Z$ vertex can be enhanced by non-decoupling effects of extra scalar boson loop contributions.
• We find that, in such a model, $|F_Z|^2$ can be one order of magnitude larger than that predicted in two Higgs doublet models under the constraints from vacuum stability, perturbative unitarity and the electroweak precision observables.