Asymmetric long-lived dark matter and leptogenesis from type-III seesaw framework

Abstract: We propose a simple model in the type-III seesaw framework to explain the neutrino mass, asymmetric dark matter (ADM), and baryon asymmetry of the Universe. We extend the standard model with a vector-like singlet lepton ($\chi$) and a hypercharge zero scalar triplet ($\Delta$) in addition to three hypercharge zero triplet fermions($\Sigma_i~,i=1,2,3$). A $Z_2$ symmetry is imposed under which $\chi$ and $\Delta$ are odd, while all other particles are even. As a result, the lightest $Z_2$ odd particle $\chi$ behaves as a candidate of DM. In the early Universe, the $CP$-violating out-of-equilibrium decay of heavy triplet fermions to the Standard Model lepton ($L$) and Higgs ($H$) generate a net lepton asymmetry, while that of triplet fermions to $\chi$ and $\Delta$ generate a net asymmetric DM. The lepton asymmetry is converted to the required baryon asymmetry of the Universe via the electroweak sphalerons, while the asymmetry in $\chi$ remains as a DM relic that we observe today. We introduce a singlet scalar $\Phi$, with mass $M_\phi < M_\chi$, which not only assists to deplete the symmetric component of $\chi$ through the annihilation process: $\bar{\chi} \chi \to \Phi \Phi$ but also paves a path to detect DM $\chi$ at direct search experiments through $\Phi-H$ mixing. The electro-weak symmetry breaking induces a non-zero vacuum expectation value to $\Delta$, which leads to an unstable asymmetric DM ranging from a few MeV to hundreds of GeV. We then explore the displaced vertex signatures of the charged components of the scalar triplet $\Delta$ at colliders.