$Z_4$ scotogenic model with a Higgs portal

We propose a new Scotogenic type model based on a global $Z_4$ symmetry involving dark matter candidates. After the symmetry breaking as $Z_4$ to $Z_2$ via the singlet scalar vacuum expectation value (VEV), the lightest Majorana fermion works as a viable thermal freeze-out dark matter (DM) candidate, and the mass terms for active neutrinos are generated as a finite quantum correction at the 1-loop level. A key point of realising our Scotogenic structure is to introduce two types of Majorana fermions (heavy right-handed neutrinos) and inert Higgs doublets with opposite $Z_4$ parities. Since a large VEV for the singlet scalar is not so harmful in an appropriate realisation of the Higgs mechanism for the SM gauge symmetry, we can naturally realise a TeV-scale fermionic DM candidate, where constraints via direct detection experiments are less than those for sub-TeV DM. Our scenario involves the Higgs-portal DM interactions, which help the realisation of the correct DM relic abundance. Relying on the structure of the model, it is possible to find a natural partner for coannihilation. Our scenario can be investigated via the measurement of the Higgs trilinear self-coupling at the Large Hadron Collider. The simplest way to evade the domain-wall problem by adding a tiny soft $Z_2$ breaking term works, keeping a sufficient longevity of the decaying DM lifetime.