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 = 220 TeV, 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 ≳ 1 GeV, we find M_DM≳ 20 PeV. Otherwise, for M_S > M_W∼ 100 GeV, 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 ≳ 300 GeV, allowing also successful leptogenesis, we find 00.5 ≲ M_DM/TeV ≲ 50. 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.