$Z_p$ scalar dark matter from multi-Higgs-doublet models

In many models, stability of dark-matter particles is protected by a conserved ${\mathbb{Z}}_2$ quantum number. However, dark matter can be stabilized by other discrete symmetry groups, and examples of such models with custom-tailored field content have been proposed. Here, we show that electroweak symmetry-breaking models with $N$ Higgs doublets can readily accommodate scalar dark matter candidates stabilized by groups ${\mathbb{Z}}_p$ with any $p\le 2^{N-1}$, leading to a variety of kinds of microscopic dynamics in the dark sector. We give examples in which semiannihilation or multiple semiannihilation processes are allowed or forbidden, which can be especially interesting in the case of asymmetric dark matter.