A Parametrization for the Neutrino Mixing Matrix

Abstract

We propose a flexible and model independent parametrization of the neutrino mixing matrix, which takes advantage of the fact that there are up to three small quantities in neutrino mixing phenomenology: (i) the deviation from maximal mixing of solar neutrinos, (ii) the mixing matrix element U_{e3} and (iii) the deviation from maximal mixing of atmospheric neutrinos. It is possible to quantify those three observations with a parameter \lambda \sim 0.2, which appears at least linearly in all elements of the mixing matrix. The limit \lambda -> 0 corresponds to exact bimaximal mixing. Present and future experiments can be used to pin down the power of \lambda required to usefully describe the observed phenomenology. Observing that the ratio of the two measured mass squared differences is roughly \lambda^2 allows to further study the structure of the Majorana mass matrix. We comment on the implications of this parametrization for neutrinoless double beta decay and on the oscillation probabilities in long-baseline experiments.