Freeze-In Dark Matter and Leptogenesis: a ${\psi }^{\mathrm{\prime }}$SM route

We investigate the possibility of \emph{freeze-in} dark matter production and baryogenesis via leptogenesis in a ${\psi }^{\mathrm{\prime }}$SM model, which is an $E_6$ extension of the Standard Model, featuring a residual $U(1{)}_{{\psi }^{\mathrm{\prime }}}$ gauge symmetry. This symmetry arises from a linear combination of $U(1{)}_{\chi }$ and $U(1{)}_{\psi }$, both of which are subgroups of the $E_6$. The spontaneous breaking of $U(1{)}_{{\psi }^{\mathrm{\prime }}}$ symmetry governs the dynamics of a singlet fermion, which serves as a freeze-in dark matter candidate. The dark matter mass arises from dimension-five operators, and a discrete symmetry ensures its stability. We show that freeze-in production from scalar decay can yield the correct relic abundance for dark matter masses between a few MeV to a few hundred GeV. Simultaneously, heavy right-handed neutrinos generate light neutrino masses via the type-I seesaw and produce the observed baryon asymmetry via leptogenesis.