Absolute neutrino mass scale and dark matter stability from flavour symmetry

Abstract

We explore a simple but extremely predictive extension of the scotogenic model. We promote the scotogenic symmetry ${\mathbb{Z}}_2$ to the flavour non-Abelian symmetry $\Sigma (81)$, which can also automatically protect dark matter stability. In addition, $\Sigma (81)$ leads to striking predictions in the lepton sector: only Inverted Ordering is realised, the absolute neutrino mass scale is predicted to be $m_{\text{lightest}}\approx 7.5\times 10^{-4}$ eV and the Majorana phases are correlated in such a way that $|m_{ee}|\approx 0.018$ eV. The model also leads to a strong correlation between the solar mixing angle ${\theta }_{12}$ and ${\delta }_{CP}$, which may be falsified by the next generation of neutrino oscillation experiments. The setup is minimal in the sense that no additional symmetries or flavons are required.

Comments: 19 pages, 6 figures, 1 Table. v2: Additional comments about flavour symmetry breaking, FCNCs, and dark matter were added, also an Appendix concerning the scalar sector was included. This document matches the published version