Classification of lepton mixing patterns from finite flavour symmetries

TL;DR

This paper systematically classifies lepton mixing patterns derived from finite flavour symmetries, revealing a limited set mostly incompatible with current neutrino oscillation data.

Contribution

It provides a complete list of achievable lepton mixing patterns from finite symmetries and identifies their associated groups, advancing understanding of flavour symmetry constraints.

Findings

Most mixing patterns are 3-sigma excluded by data.

The list of possible patterns is limited.

Finite symmetries can fully determine lepton mixing angles.

Abstract

Flavour symmetries have been used to constrain both quark and lepton mixing parameters. In particular, they can be used to completely fix the mixing angles. For the lepton sector, assuming that neutrinos are Majorana particles, we have derived the complete list of mixing patterns achievable in this way, as well as the symmetry groups associated to each case. Partial computer scans done in the past have hinted that such list is limited, and this does indeed turn out to be the case. In addition, most mixing patterns are already 3-sigma excluded by neutrino oscillation data.