Classification of lepton mixing matrices from finite residual symmetries

Abstract

Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is based on the assumption that the residual symmetries originate from a finite flavour symmetry group. The mathematical tools which allow us to accomplish this classification are theorems on sums of roots of unity. We find 17 sporadic cases plus one infinite series of mixing matrices associated with three-flavour mixing, all of which have already been discussed in the literature. Only the infinite series contains mixing matrices which are compatible with the data at the 3 sigma level.

Correction of a wrong identification (there are consequently 17 sporadic lepton mixing cases); change in the title to include the word "finite"; newer neutrino data used; minor corrections and clarifications; version matches publication in JHEP

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