On self-complementarity relations of neutrino mixing

Abstract

With the latest results of a large mixing angle ${\theta }_{13}$ for neutrinos by the T2K, MINOS and Double Chooz experiments, we find that the self-complementarity (SC) relations agree with the data in some angle-phase parametrizations of the lepton mixing matrix. There are three kinds of self-complementarity relations: (1) ${\vartheta }_i+{\vartheta }_j={\vartheta }_k=45^{\circ }$; (2) ${\vartheta }_i+{\vartheta }_j={\vartheta }_k$; (3) ${\vartheta }_i+{\vartheta }_j=45^{\circ }$ (where $i$, $j$, $k$ denote the mixing angles in the angle-phase parametrizations). We present a detailed study on the self-complementarity relations in nine different angle-phase parametrizations, and also examine the explicit expressions in reparametrization-invariant form, as well as their deviations from global fit. These self-complementarity relations may lead to new perspective on the mixing pattern of neutrinos.

Comments: 11 pages, no figure, 3 tables. Version for publication in PLB