The neutrino mixing matrix could (almost) be diagonal with entries {\pm}1

TL;DR

This paper proposes that the neutrino mixing matrix could be nearly diagonal with entries ±1, offering a simple, falsifiable ansatz that aligns with experimental data and provides a new way to organize and interpret neutrino mixing observations.

Contribution

It introduces a novel, phenomenological ansatz that the neutrino mixing matrix is almost hermitian and close to diag(+1,-1,-1), which has not been previously studied.

Findings

The ansatz is consistent with current heta_13 measurements.

A parametrization of deviations from the leading order relation is provided.

The group-invariant angle between matrices is used as a data comparison tool.

Abstract

It is consistent with the measurement of \theta_13 ~ 0.15 by Daya Bay to suppose that, in addition to being unitary, the neutrino mixing matrix is also almost hermitian, and thereby only a small perturbation from diag(+1,-1,-1) in a suitable basis. We suggest this possibility simply as an easily falsifiable ansatz that has not already been studied, as well as to offer a potentially useful means of organizing the experimental data. We explore the phenomenological implications of this ansatz and parametrize one type of deviation from the leading order relation |V_e3| \approx |V_\tau 1|. We also emphasize the group-invariant angle between orthogonal matrices as a means of comparing to data. The discussion is purely phenomenological, without any attempt to derive the condition V{\dag} \approx V from a fundamental theory.