Properties of the Neutrino Mixing Matrix

Abstract

For neutrino mixing we propose to use the parameter set $X_i$ $(=|V_{ei}{|}^2)$ and ${\Omega }_i$ $(={ϵ}_{ijk}|V_{\mu j}{|}^2|V_{\tau k}{|}^2)$, 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.

Comments: 14 pages, 5 figures