Two-Loop $Z_4$ Dirac Neutrino Masses and Mixing, with 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. ${\theta }_{13}\ne 0$, ${\theta }_{23}=\pi /4$, ${\delta }_{CP}=\pm \pi /2$, 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).

Comments: 15 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1905.01535