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

Abstract

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 $SO(10)\to SU(5)\times U(1{)}_{\chi }$, supplemented by the non-Abelian discrete $\Delta (27)$ symmetry for three lepton families, Dirac neutrino masses and their mixing are radiatively generated through dark matter. The gauge $U(1{)}_{\chi }$ symmetry is broken spontaneously. The discrete $\Delta (27)$ symmetry is broken softly and spontaneously. Together, they result in two residual symmetries, a global $U(1{)}_L$ lepton number and a dark symmetry, which may be $Z_2$, $Z_3$, or $U(1{)}_D$ depending on what scalar breaks $U(1{)}_{\chi }$. Cobimaximal neutrino mixing, i.e. ${\theta }_{13}\ne 0$, ${\theta }_{23}=\pi /4$, and ${\delta }_{CP}=\pm \pi /2$, may also be obtained.

Comments: 11 pages, 1 figure, ref. added