### Speaker

### Description

The nature of neutrinos, whether Dirac or Majorana, is hitherto not known. Assuming that the neutrinos are Dirac, which needs $B-L$ to be an exact symmetry, we attempt to explain the observed proportionality between the relic densities of dark matter (DM) and baryonic matter in the present Universe ${\it i.e.,}\,\, \Omega_{\rm DM} \approx 5\, \Omega_{\rm B}$. We extend the Standard Model (SM) by introducing heavy scalar doublets $X_i, i=1,2$ and $\eta$, two singlet scalars $\Phi$ and $\Phi'$, a vector-like Dirac fermion $\chi$ representing the DM and three right-handed neutrinos $\nu_{R_i}, i=1,2,3$. Assuming $B-L$ is an exact symmetry of the early Universe, the CP-violating out-of-equilibrium decay of heavy scalar doublets: $X_i, i=1,2$ to the SM lepton doublet $L$ and the right-handed neutrino $\nu_R$, generate equal and opposite $B-L$ asymmetry among left ($\nu_L$) and right ($\nu_R$)-handed neutrinos. We ensure that $\nu_L-\nu_R$ equilibration does not occur until below the electroweak (EW) phase transition during which a part of the lepton asymmetry gets converted to dark matter asymmetry through a dimension eight operator, which conserves $B-L$ symmetry and remains in thermal equilibrium above sphaleron decoupling temperature. A part of the remaining $B-L$ asymmetry then gets converted to a net B-asymmetry through EW-sphalerons which are active at a temperature above 100 GeV. To alleviate the small-scale anomalies of $\Lambda$CDM, we assume the DM ($\chi$) to be self-interacting via a light mediator $\Phi$, which not only depletes the symmetric component of the DM, but also paves a way to detect the DM at terrestrial laboratories through $\Phi-H$ mixing, where $H$ is the SM Higgs doublet.