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In the context of $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_\chi$,where $U(1)_\chi$ comes from $SO(10) \to SU(5) \times U(1)_\chi$, supplementedby the non-Abelian discrete $\Delta(27)$ symmetry for three lepton families,Dirac neutrino masses and their mixing are radiatively generated through darkmatter. The gauge $U(1)_\chi$ symmetry is broken spontaneously. The discrete$\Delta(27)$ symmetry is broken softly and spontaneously. Together, they resultin two residual symmetries, a global $U(1)_L$ lepton number and a darksymmetry, which may be $Z_2$, $Z_3$, or $U(1)_D$ depending on what scalarbreaks $U(1)_\chi$. Cobimaximal neutrino mixing, i.e. $\theta_{13} \neq 0$,$\theta_{23} = \pi/4$, and $\delta_{CP} = \pm \pi/2$, may also be obtained.

Scotogenic Cobimaximal Dirac Neutrino Mixing from $\Delta(27)$ and $U(1)_\chi$