Scotogenic model for co-bimaximal mixing

We present a scotogenic model, i.e. a one-loop neutrino mass model with dark right-handed neutrino gauge singlets and one inert dark scalar gauge doublet $\eta$, which has symmetries that lead to co-bimaximal mixing, i.e. to an atmospheric mixing angle $\theta_{23} = 45^\circ$ and to a $CP$-violating phase $\delta = \pm \pi/2$, while the mixing angle $\theta_{13}$ remains arbitrary. The symmetries consist of softly broken lepton numbers $L_\alpha$ ($\alpha = e,\mu,\tau$), a non-standard $CP$ symmetry, and three $Z_2$ symmetries. We indicate two possibilities for extending the model to the quark sector. Since the model has, besides $\eta$, three scalar gauge doublets, we perform a thorough discussion of its scalar sector. We demonstrate that it can accommodate a Standard Model-like scalar with mass $125\, \mathrm{GeV}$, with all the other charged and neutral scalars having much higher masses.