Neutrino mixing, interval matrices and singular values

TL;DR

This paper investigates the properties of singular values of neutrino mixing matrices within interval matrices, proposing a contraction condition to identify physically admissible and potentially nonunitary mixings, with implications for new physics and quark sector applications.

Contribution

It introduces a contraction-based criterion for physical neutrino mixing matrices within interval matrices and develops a convex hull approach for the mixing space, including nonunitary cases via matrix dilations.

Findings

Identifies contraction property as necessary for physical mixings.

Develops a convex hull model for the mixing space.

Constructs unitary extensions for nonunitary mixings.

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 three through the theory of unitary matrix dilations. We discuss further applications to the quark sector.