Dark matter to baryon ratio from scalar triplets decay in type-II seesaw

We propose a minimal model for the cosmic coincidence problem $\Omega_{\rm DM}/\Omega_B \sim 5$ and neutrino mass in a type-II seesaw scenario. We extend the standard model of particle physics with a $\rm SU(2)$ singlet leptonic Dirac fermion $\chi$, which represents the candidate of dark matter (DM), and two triplet scalars $\Delta_{1,2}$ with hierarchical masses. In the early Universe, the CP violating out-of-equilibrium decay of lightest $\Delta$ generates a net $B-L$ asymmetry in the visible sector (comprising of SM fields), where $B$ and $L$ represents the total baryon and lepton number respectively. A part of this asymmetry gets transferred to the dark sector (comprising of DM $\chi$) through a dimension eight operator which conserves $B-L$. Above the electroweak phase transition, the $B-L$ asymmetry of the visible sector gets converted to a net $B$-asymmetry by the $B+L$ violating sphalerons, while the $B-L$ asymmetry of the dark sector remains untouched which we see today as relics of DM. We show that the observed DM abundance can be explained for a DM mass about 8 GeV. We then introduce an additional singlet scalar field $\phi$ which mixes with the SM-Higgs to annihilate the symmetric component of the DM resonantly which requires the singlet scalar mass to be twice the DM mass, {\it i.e.} around 16 GeV, which can be searched at collider experiments. In our model, the active neutrinos also get small masses by the induced vacuum expectation value (vev) of the triplet scalars $\Delta_{1,2}$. In the later part of the paper we discuss all the constraints on model parameters coming from invisible Higgs decay, Higgs signal strength, DM direct detection and relic density of DM.