Radiative neutrino masses from order-4 CP symmetry

TL;DR

This paper develops two minimal models for neutrino masses using order-4 CP symmetry, extending the scalar and quark sector framework to neutrinos, and introduces mechanisms for neutrino mass suppression and hierarchy.

Contribution

It constructs novel CP4-symmetric Majorana neutrino models with three Higgs doublets and right-handed neutrinos, demonstrating new mass generation and suppression mechanisms.

Findings

Models produce three non-zero light neutrino masses.

Built-in phase alignment suppresses neutrino masses.

Natural hierarchy of two neutrino mass scales.

Abstract

Generalized CP symmetry of order 4 (CP4) is surprisingly powerful in shaping scalar and quark sectors of multi-Higgs models. Here, we extend this framework to the neutrino sector. We build two simple Majorana neutrino mass models with unbroken CP4, which are analogous to Ma's scotogenic model. Both models use three Higgs doublets and two or three right-handed (RH) neutrinos. The minimal CP4 symmetric scotogenic model uses only two RH neutrinos, leads to three non-zero light neutrino masses, and contains a built-in mechanism to further suppress them via phase alignment. With three RH neutrinos, one generates a type I seesaw mass matrix of rank 1, which is then corrected by the same scotogenic mechanism, naturally leading to two neutrino mass scales with mild hierarchy. These minimal CP4-based constructions emerge as a primer for introducing additional symmetry structures and exploring their phenomenological consequences.