Two-sector leptogenesis in a two-Higgs-doublet model with spontaneous CP violation

Abstract: The extension of the Standard Model (SM) field content with one inert Higgs doublet (IHD) and three right-handed neutrinos (RHNs) is a well-motivated approach. The key advantages of the model include the appearance of a weakly interacting massive particle (WIMP) like dark matter (DM) candidate from the neutral component of the IHD, along with the plausible explanation of the sub-eV mass range of SM neutrinos via the radiative seesaw mechanism. Additionally, the decay of RHNs can contextualize the baryon asymmetry of the universe via leptogenesis and is intricately connected to CP violation. Also, given the ongoing searches for light scalars at various experimental facilities, the extended Higgs sector of the model continues to be at the forefront. However, this scotogenic framework encounters a deficiency in providing the observed amount of relic density for a particular mass range $\sim (80 - 500) $ GeV of its DM candidate, hence requiring further augmentation. Also, the WIMP scenarios have not yet resulted in conclusive hints at the direct detection experiments. In this context, our work is based on further extension of the above Scotogenic model by a dark sector. Additionally, considering the cosmic coincidence aspect, we operate within the framework of two-sector leptogenesis. To have a predictive flavor structure in the visible sector, we impose $A_4$ symmetry. Also, we adhere to spontaneous CP violation via complex vacuum expectation value of the falvon field, leading to a situation where there is only one CP-violating phase as a common connection between the visible and dark sectors. In our analysis, we find for the lightest RHN mass $\sim 10^{10}$ GeV, our results are in good agreement with the observational ratio of relic densities, i.e., $\Omega_{\rm DM}/\Omega_{\rm b} \sim 5$ for a few GeV range of mass of the dark sector DM candidate.