Radiative neutrino masses from order-4 CP symmetry

Igor P Ivanov

doi:10.1007/jhep02(2018)025

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.

Highlights

The intrinsic weakness of Z2 or ZN family symmetries in multi-scalar models is that they still allow for many free parameters
These results naturally lead to the question of whether CP symmetry of order 4 (CP4) can be extended to the neutrino sector and, remaining unbroken, can produce a new, CP4-based version of the scotogenic model
We aim to apply this scotogenic idea not to the inert doublet model but to the CP4 3HDM, three-Higgs-doublet model equipped with the generalized CP symmetry of order 4 (CP4) and no other accidental symmetries

Summary

Ma’s scotogenic model

The model postulates a new global symmetry Z2, under which the SM fields are even, and adds a second electroweak Higgs doublet Φ2 and three RH neutrinos Ni, all of which are odd. In this way the charged leptons are coupled only to the SM-like doublet Φ1, but the Yukawa neutrino interactions mediated by Φ2 as well as the Majorana mass term for N ’s are allowed:. Due to Φ2 = 0, no Dirac mass term appears, and the LH neutrinos remain massless at the tree level These masses are generated at the 1-loop level via loop diagrams mediated by the inert neutral scalars H and A, figure 1. It can provide tiny neutrino masses for reasonably large Mk, it cannot predict patterns in the mass matrix Mν, since the Yukawa couplings Yαk can be arbitrary

CP4 3HDM

CP4 symmetric neutrino sector

Two RH neutrinos: the minimal CP4 scotogenic model

Three neutrino case: two mass scales with mild hierarchy

Conclusions