Lepton Mixing Parameters from Discrete and CP Symmetries

TL;DR

This paper explores how combining discrete flavor symmetries with generalized CP transformations constrains lepton mixing parameters, leading to specific predictions for mixing angles and CP phases in neutrino physics.

Contribution

It derives conditions for consistent flavor and CP symmetry combinations and analyzes their implications for lepton mixing, especially within the S_4 symmetry group, revealing new predictive patterns.

Findings

Lepton mixing angles depend on a single parameter theta.

Certain symmetry patterns predict maximal atmospheric mixing and CP phases.

Some models predict trivial CP phases, others maximal phases.

Abstract

We consider a scenario with three Majorana neutrinos in which a discrete, finite flavour group G_f is combined with a generalized CP transformation. We derive conditions for consistently defining such a setup. We show that in general lepton mixing angles and CP phases (Dirac as well as Majorana) only depend on one single parameter theta which can take values between 0 and pi, if the residual symmetries are G_e contained in G_f in the charged lepton and G_nu=Z_2 x CP in the neutrino sector. We perform a comprehensive study for G_f=S_4 and find five cases which are phenomenologically interesting. They naturally lead to a non-zero reactor mixing angle and all mixing parameters are strongly correlated. Some of the patterns predict maximal atmospheric mixing and maximal Dirac phase, while others predict trivial Dirac and Majorana phases.