Explaining the 3.5 keV X-ray line in a L_μ−L_τ extension of the inert doublet model

We explain the existence of neutrino masses and their flavour structure, dark matter relic abundance and the observed 3.5 keV X-ray line within the framework of a gauged U(1)_{Lμ − Lτ} extension of the "scotogenic" model. In the U(1)_{Lμ − Lτ} symmetric limit, two of the RH neutrinos are degenerate in mass, while the third is heavier. The U(1)_{Lμ − Lτ} symmetry is broken spontaneously. Firstly, this breaks the μ−τ symmetry in the light neutrino sector. Secondly, this results in mild splitting of the two degenerate RH neutrinos, with their mass difference given in terms of the U(1)_{Lμ − Lτ} breaking parameter. Finally, we get a massive Z_μτ gauge boson. Due to the added Z₂ symmetry under which the RH neutrinos and the inert doublet are odd, the canonical Type-I seesaw is forbidden and the tiny neutrino masses are generated radiatively at one loop. The same Z₂ symmetry also ensures that the lightest RH neutrino is stable and the other two can only decay into the lightest one. This makes the two nearly-degenerate lighter neutrinos a two-component dark matter, which in our model are produced by the freeze-in mechanism via the decay of the Z_μτ gauge boson in the early universe. We show that the next-to-lightest RH neutrino has a very long lifetime and decays into the lightest one at the present epoch explaining the observed 3.5 keV line.