Inspired by a new relation ${\theta }_{13}^{\mathrm{PMNS}}={\theta }_C/\sqrt{2}$ observed from the relatively large ${\theta }_{13}^{\mathrm{PMNS}}$, we find that the combination of this relation with the quark-lepton complementarity and the self-complementarity results in correlations of the lepton mixing angles with the quark mixing angles. We find that the three mixing angles in the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix are all related to the Wolfenstein parameter $\lambda$ in the quark mixing, so they are also correlated. Consequently, the PMNS matrix can be parameterized by $\lambda$, A, and a Dirac $CP$-violating phase $\delta$. Such parametrizations for the PMNS matrix have the same explicitly hierarchical structure as the Wolfenstein parametrization for the Cabibbo-Kobayashi-Maskawa matrix in the quark mixing, and the bimaximal mixing pattern is deduced at the leading order. We also discuss implications of these phenomenological relations in parametrizations.

• Received 4 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.093002