On self-complementarity relations of neutrino mixing

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.