Heavy Pseudo-Dirac Doublet Dark Matter and Non-Thermal Leptogenesis in Light of the LZ Event

Motivated by the recent LZ candidate nuclear-recoil event, we study pseudo-Dirac electroweak doublet dark matter in the mass range ${10}^2$–${10}^4\mathrm{T}\mathrm{e}\mathrm{V}$, where bounds from searches for neutrinos produced by dark matter annihilation in the Sun can be evaded. To suppress the excessive thermal relic abundance, we consider freeze-out during inflaton domination followed by entropy production during reheating. We examine whether this cosmological history can also accommodate non-thermal leptogenesis. Our analysis includes dark matter production through the emission of virtual electroweak gauge bosons in right-handed-neutrino decays and through thermalization cascades. Our estimates suggest that the two scenarios can be reconciled if dark matter pair emission in right-handed-neutrino decays is kinematically forbidden and cascade production is sufficiently suppressed. Such a realization, however, requires enhanced CP violation, typically involving fine-tuning in the seesaw mechanism or the right-handed-neutrino mass spectrum.