A Model for Large θ₁₃ Constructed using the Eigenvectors of the S₄ Rotation Matrices

Abstract

A procedure for using the eigenvectors of the elements of the representations of a discrete group in model building is introduced and is used to construct a model that produces a large reactor mixing angle, sin 2 θ13 = 2 3 sin 2 π 16 , in agreement with recent neutrino oscillation observations. The model fully constrains the neutrino mass ratios and predicts normal hierarchy with the light neutrino mass, m1 ≈ 25 meV. Motivated by the model, a new mixing ansatz is postulated which predicts all the mixing angles within 1σ errors.

Fully constrained Majorana neutrino mass matrices using $$\varvec{\varSigma (72\times 3)}$$ Σ ( 72 × 3 )

“…(22). No other coupling involving τ R , μ R or e R with eitherφ β orφ α is allowed, given the C 4 assignments in Table 3.…”

“…However, L † μ R andĀ βα , which transform as 3 × 1 and3 × 1, respectively, can couple, Eq. (22). Note thatĀ βα is a second-order product of φ β and φ α and it is antisymmetric.…”

“…δ = 0, π, and thus J = 0. Since the reactor angle was discovered to be non-zero at the Daya Bay reactor experiment in 2012 [15], there has been a resurgence of interest [16][17][18][19][20][21][22][23][24][25][26][27] in Tχ M and TφM and their equivalent forms. For any C P-conserving (δ = 0, π) mixing matrix with non-zero θ 13 and trimaximally mixed ν 2 column, we can have an equivalent parameterisation realised using the TφM matrix.…”

“…In 2012 [22], shortly after the discovery of the non-zero reactor mixing angle, it was shown that Tχ M ( …”

“…Unlike in Ref. [22] where the neutrino mass matrix was decomposed into a symmetric product of two matrices, here a single sextet representation of the flavour group is used to build the neutrino mass matrix. A brief discussion of the group Σ(72×3) and its representations is provided in Sect.…”