A new idea for neutrino mass was proposed recently, where its smallness is not due to the seesaw mechanism, i.e. not inversely proportional to some large mass scale. It comes from a one-loop mechanism with dark matter in the loop consisting of single
t Majorana fermions $N_i$ with masses of order 10 keV and neutrino masses are scaled down from them by factors of about $10^{-5}$. We discuss how this model may be implemented with the non-Abelian discrete symmetry $A_4$ for neutrino mixing, and consider the phenomenology of $N_i$ as well as the extra scalar doublet $(eta^+,eta^0)$.
The non-Abelian discrete symmetry D(7) of the heptagon is successfully applied to both quark and lepton mass matrices, including CP violation.
Assuming that neutrinos acquire radiative seesaw Majorana masses through their interactions with dark matter, i.e. scotogenic from the Greek scotos meaning darkness, and using the non-Abelian discrete symmetry $A_4$, we propose a model of neutrino ma
sses and mixing with nonzero $theta_{13}$ and necessarily large leptonic CP violation, allowing both the normal and inverted hierarchies of neutrino masses, as well as quasi-degenerate solutions.