Multicomponent dark matter in extended $U(1)_{B-L}$: neutrino mass and high scale validity

Standard Model with right handed neutrinos charged under additional $U(1)_{B-L}$ gauge symmetry offer solutions to both dark matter (DM) problem and neutrino mass generation, although constrained severely from relic density, direct search and Higgs vacuum stability. We therefore investigate a multicomponent DM scenario augmented by an extra inert scalar doublet, that is neutral under $U(1)_{B-L}$, which aids to enlarge parameter space allowed by DM constraints and Higgs vacuum stability. The lightest right-handed neutrino and the $CP$-even inert scalar are taken as the dark matter candidates and constitute a two component dark matter framework as they are rendered stable by an unbroken $\mathbb{Z}_2 \times \mathbb{Z}_2^\prime$ symmetry. DM-DM conversion processes turn out crucial to render requisite relic abundance in mass regions of the RH neutrino that do not appear in the stand-alone $U(1)_{B-L}$ scenario. In addition, the one-loop renormalisation group (RG) equations in this model demonstrate that the electroweak (EW) vacuum can be stabilised till $\sim 10^{9}$ GeV in a parameter region compatible with the observed relic, the direct detection bound and other relevant constraints.