A new parametrization of the neutrino mixing matrix for neutrino oscillations

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, $V=\cos \theta I+i\sin \theta U$. There are only three real parameters in $V$ including the parameter $\theta$. It is interesting to find that experimental data on atmospheric neutrino dictates the angle $\theta$ to be $\pi \mathrm{/}4$ such that the ${\nu }_{\mu }$ and ${\nu }_{\tau }$ 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 ($\theta$ and $ϵ$) predicts that the oscillating probabilities for ${\nu }_e\to {\nu }_{\mu }$ and ${\nu }_e\to {\nu }_{\tau }$ to be equal and of the order $2\epsilon^2 = (0.25\sim 2.5)\times 10^{-3}$. The measurement of CP asymmetries at the proposed Neutrino Factories would also provide a test of our parametrization.