Properties of the Neutrino Mixing Matrix

TL;DR

This paper introduces a new parameterization of the neutrino mixing matrix using directly measurable quantities, providing insights into mu-tau asymmetry and simplifying the analysis of neutrino oscillation data in matter.

Contribution

It proposes a novel parameter set for neutrino mixing, including measurable parameters and a measure of mu-tau asymmetry, with implications for analyzing long baseline experiments.

Findings

All $\Omega_{i}$ are small with large uncertainties.

Behavior of $\Omega_{i}$ in matter is simple and predictable.

Parameters are directly measurable from oscillation probabilities.

Abstract

For neutrino mixing we propose to use the parameter set $X_{i}$ $(=|V_{ei}|^{2})$ and $\Omega_{i}$ $(=\epsilon_{ijk}|V_{\mu j}|^{2}|V_{\tau k}|^{2})$, with two constraints. These parameters are directly measurable since the neutrino oscillation probabilities are quadratic functions of them. Physically, the set $\Omega_{i}$ signifies a quantitative measure of $\mu-\tau$ asymmetry. Available neutrino data indicate that all the $\Omega_{i}$'s are small $(\lesssim O(10^{-1}))$, but with large uncertainties. The behavior of $\Omega_{i}$ as functions of the induced neutrino mass in matter are found to be simple, which should facilitate the analyses of long baseline experiments.