Properties of the Neutrino Mixing Matrix

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