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.

Testing solar lepton mixing sum rules in neutrino oscillation experiments

“…In recent work, significant progress has been made in the categorisation of fully-specified mixing patterns subject to some weak model building assumptions. In subsection 2.2, we shall identify a set of leading-order predictions with θ ν 13 = 0 from arguments of symmetry by following two categorisation schemes from the literature [12,52]. As we shall explain, strictly speaking, one of these frameworks [12] is a subcase of the other [52]; however, its systematic exploration has not been presented before, and we shall show how this more restrictive scenario still finds all of the cases of the more comprehensive analysis, while shedding light on the group structure of the viable solutions.…”

“…[52]. In this work, it was assumed that neutrinos are Majorana particles, that a finite flavour group G is broken into the Klein group G ν = Z 2 × Z 2 in the neutrino sector, and G e = Z n , with n ∈ N, in the charged-lepton sector.…”

Direct and semi-direct approaches to lepton mixing with a massless neutrino

“…The main question around which the framework of residual symmetries in the fermion mass matrices [3,5,[11][12][13][14][15][16][17] has been constructed is the question: When do symmetries of a 3 × 3-matrix (partly) fix the matrix which diagonalises it?…”

“…Namely, if it did not contain such an 5 Throughout the paper we will use the SmallGroups ID to identify groups. This ID consists of two numbers in square brackets, i.e.…”

“…The advantage of the direct approach is that the prediction arises purely from symmetry and does not require any detailed knowledge of the model. However, the direct approach requires a rather large group [3][4][5][6], and the only viable mixing pattern is the trimaximal mixing, with δ being either zero or ±π.…”