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 (RH) neutrino mixing model, solving the associated density matrix equation. For a benchmark value of the dark matter mass $M_{\rm DM} = 220\,{\rm TeV}$, we show the evolution of the abundance and how this depends on reheat temperature, dark matter lifetime and source RH neutrino mass $M_{\rm S}$, with the assumption $M_{\rm S} < M_{\rm DM}$. 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 RH 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 RH neutrino abundance. For example, for $M_{\rm S} \gtrsim 1\,{\rm GeV}$, we find $M_{\rm DM}\gtrsim 20\,{\rm PeV}$. Otherwise, for $M_{\rm S} > M_W\sim 100\,{\rm GeV}$, one has to assume a thermalisation of the source RH neutrinos prior to the freeze-in of the dark matter abundance. This results into a large allowed range for $M_{\rm DM}$, depending on $M_{\rm S}$. For example, imposing $M_{\rm S} \gtrsim 300\,{\rm GeV}$, allowing also successful leptogenesis, we find $0.5 \lesssim M_{\rm DM}/{\rm TeV} \lesssim 500$. We also discuss in detail leptogenesis with two quasi-degenerate RH 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 RH neutrino abundance can be justified and on how our results suggest that also the interesting case where $M_{\rm DM} < M_{\rm S}$, embeddable in usual high scale two RH neutrino seesaw models, might be viable.