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 singlet 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 $(eta^+,eta^0)$.
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