Scotogenic generation of realistic neutrino mixing with D5

A mechanism of radiative generation of realistic neutrino mixing at one-loop level with $D5\times Z_2$ is presented in this paper. The process is demonstrated in two set-ups using $D5\times Z_2$ symmetry viz. Model 1 and Model 2. Two right-handed neutrinos are present in both the models. In both Model 1 and Model 2, when mixing between these two right-handed neutrinos are maximal, one can produce the form of the left-handed Majorana neutrino mass matrix corresponding to ${\theta }_{13}=0$, ${\theta }_{23}=\pi \mathrm{/}4$ and any value of ${\theta }_{12}^0$ associated with Tribimaximal (TBM), Bimaximal (BM), Golden Ratio (GR) or other mixings. Small shift from maximal mixing between the two right-handed neutrino states can generate non-zero ${\theta }_{13}$, deviation of ${\theta }_{23}$ from $\pi \mathrm{/}4$ and corrections to the solar mixing ${\theta }_{12}$ in one step for both Model 1 and Model 2. In both the models, two $Z_2$ odd inert $SU(2{)}_L$ doublet scalars are present. The lightest between these two scalars can be a viable dark matter candidate for both Model 1 and Model 2.