Neutrino mixing, interval matrices and singular values

Abstract

We study the properties of singular values of mixing matrices embedded within an experimentally determined interval matrix.We argue that any physically admissible mixing matrix needs to have the property of being a contraction. This condition constrains the interval matrix, by imposing correlations on its elements and leaving behind only physical mixings that may unveil signs of new physics in terms of extra neutrino species. We propose a description of the admissible three-dimensional mixing space as a convex hull over experimentally determined unitary mixing matrices parametrized by Euler angles, which allows us to select either unitary or nonunitary mixing matrices. The unitarity-breaking cases are found through singular values and we construct unitary extensions, yielding a complete theory of minimal dimensionality larger than 3 through the theory of unitary matrix dilations. We discuss further applications to the quark sector.