# Two-Loop $Z_4$ Dirac Neutrino Masses and Mixing, with Self-Interacting Dark Matter

## TL;DR

This paper proposes a two-loop mechanism within a specific gauge and family symmetry framework to generate Dirac neutrino masses and mixing, while also addressing self-interacting dark matter and preserving cosmological constraints.

## Contribution

It introduces a novel two-loop model linking Dirac neutrino masses with self-interacting dark matter, ensuring cobimaximal mixing and CMB compatibility.

## Key findings

- Realizes cobimaximal neutrino mixing with non-zero $ heta_{13}$
- Ensures dark-matter scalar mediators decay only to neutrinos
- Provides a consistent framework for Dirac neutrinos and self-interacting dark matter

## Abstract

Choosing how gauge $U(1)_\chi$ breaks in the context of $SO(10) \to SU(5) \times U(1)_\chi$, $Z_4$ lepton number may be obtained which maintains neutrinos as Dirac fermions. Choosing $\Delta(27)$ as the family symmetry of leptons, tree-level Dirac neutrino masses may be forbidden. Choosing a specific set of self-interacting dark-matter particles, Dirac neutrino masses and mixing may then be generated in two loops. This framework allows the realization of cobimaximal neutrino mixing, i.e. $\theta_{13} \neq 0$, $\theta_{23} = \pi/4$, $\delta_{CP} = \pm \pi/2$, as well as the desirable feature that the light scalar mediator of dark-matter interactions decays only to neutrinos, thereby not disrupting the cosmic microwave background (CMB).