Wolfenstein-like Parametrization of the Neutrino Mixing Matrix

Abstract

We show that the $3\times 3$ lepton flavor mixing matrix $V$ can be expanded in powers of a Wolfenstein-like parameter $\Lambda \equiv |V_{\mu 3}| \sim 1/\sqrt{2}$, which measures the strength of flavor conversion in atmospheric neutrino oscillations. The term of ${\cal O}(\Lambda^2)$ is associated with the large mixing angle in solar neutrino oscillations. The Dirac phase of CP violation enters at or below ${\cal O}(\Lambda^8)$, and the Majorana phases of CP violation are not subject to the $\Lambda$-expansion. Terrestrial matter effects on this new parametrization in realistic long-baseline neutrino oscillation experiments are briefly discussed. Some comments are also given on the possible relation between $\Lambda$ and a relatively weak hierarchy of neutrino masses.