A new parametrization of the neutrino mixing matrix for neutrino oscillations

Abstract

In this paper we study three active neutrino oscillations, favored by recent data from SuperK and SNO, using a new parametrization of the lepton mixing matrix $V$ constructed from a linear combination of the unit matrix $I$, and a hermitian unitary matrix $U$, that is, $V = \cosθI + i\sin θU$. There are only three real parameters in $V$ including the parameter $θ$. It is interesting to find that experimental data on atmospheric neutrino dictates the angle $θ$ to be $π/4$ such that the $ν_μ$ and $ν_τ$ mixing is maximal. The solar neutrino problem is solved via the MSW effect with a small mixing angle, with $U$ depending on one small parameter $ε$. The resulting mixing matrix with just two parameters ($θ$ and $ε$) predicts that the oscillating probabilities for $ν_e\to ν_μ$ and $ν_e \to ν_τ$ to be equal and of the order $2ε^2 = (0.25\sim 2.5)\times 10^{-3}$. The measurement of CP asymmetries at the proposed Neutrino Factories would also provide a test of our parametrization.