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

Abstract

We present new results on the calculation of the dark matter relic abundance within the Higgs induced right-handed neutrino mixing model, solving 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 right-handed 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 dark matter abundance. 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 values of its mass and this still allows an allowed region in the case of initial vanishing source right-handed 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 right-handed neutrinos prior to the freeze-in of the dark matter abundance. In this case one has a large allowed range for the dark matter mass, depending on \(M_{\rm S}\). For example, imposing \(M_{\rm S} \gtrsim 300\,{\rm GeV}\), allowing also successful leptogenesis from decays, we find \(500 \,{\rm GeV }\lesssim M_{\rm DM} \lesssim 0.5 \,{\rm PeV}\). We also comment on how an initial thermal source right-handed neutrino abundance can be justified and notice that our results suggest that also the interesting case \(M_{\rm DM} < M_{\rm S}\), embaddable in usual high scale two right-handed neutrino seesaw models, might be viable.