Density matrix calculation of the dark matter abundance in the Higgs induced right-handed neutrino mixing model

We present new results on the calculation of the dark matter relic abundance within the Higgs induced right-handed neutrino mixing model, solving the associated density matrix equation. For a benchmark value of the dark matter mass $M_{DM}=220TeV$, we show the evolution of the abundance and how this depends on reheat temperature, dark matter lifetime and source right-handed neutrino mass $M_S$, with the assumption $M_S<M_{DM}$. We compare the results with those obtained within the Landau-Zener approximation, showing that the latter largely overestimates the final abundance giving some analytical insight. However, we also notice that since in the density matrix formalism the production is non-resonant, this allows source right-handed neutrino masses below the W boson mass, making dark matter more stable at large mass values. This opens an allowed region for initial vanishing source right-handed neutrino abundance. For example, for $M_S\gtrsim 1GeV$, we find $M_{DM}\gtrsim 20PeV$. Otherwise, for $M_S>M_W\sim 100GeV$, one has to assume a thermalisation of the source right-handed neutrinos prior to the freeze-in of the dark matter abundance. This results into a large allowed range for $M_{DM}$, depending on $M_S$. For example, imposing $M_S\gtrsim 300GeV$, allowing also successful leptogenesis, we find $0.5\lesssim M_{DM}/TeV\lesssim 500$. We also discuss in detail leptogenesis with two quasi-degenerate right-handed neutrinos, showing a case when observed dark matter abundance and matter-antimatter asymmetry are simultaneously reproduced. Finally, we comment on how an initial thermal source right-handed neutrino abundance can be justified and on how our results suggest that also the interesting case where $M_{DM}<M_S$, embeddable in usual high scale two right-handed neutrino seesaw models, might be viable.