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

## TL;DR

This paper proposes a model where Dirac neutrino masses and their cobimaximal mixing are generated radiatively through dark matter within a framework combining $U(1)_ ext{chi}$ and $ ext{Delta}(27)$ symmetries, leading to specific residual symmetries.

## Contribution

It introduces a novel radiative mechanism for Dirac neutrino masses using discrete and gauge symmetries, resulting in cobimaximal mixing consistent with experimental data.

## Key findings

- Neutrino masses are generated radiatively via dark matter.
- The model achieves cobimaximal mixing with $ heta_{13}
eq 0$, $ heta_{23} = rac{ ext{pi}}{4}$, and $ ext{delta}_{CP} = ext{pm} rac{ ext{pi}}{2}.
- Residual symmetries include a global lepton number and a dark symmetry.

## 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. $\theta_{13} \neq 0$, $\theta_{23} = \pi/4$, and $\delta_{CP} = \pm \pi/2$, may also be obtained.