Year: 2012
Type: article
Abstract: Inspired by a new relation ${\ensuremath{\theta}}_{13}^{\mathrm{PMNS}}={\ensuremath{\theta}}_{C}/\sqrt{2}$ observed from the relatively large ${\ensuremath{\theta}}_{13}^{\mathrm{PMNS}}$, 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 $\ensuremath{\lambda}$ in the quark mixing, so they are also correlated. Consequently, the PMNS matrix can be parameterized by $\ensuremath{\lambda}$, A, and a Dirac $CP$-violating phase $\ensuremath{\delta}$. 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.
Authors: Xinyi Zhang, Bo-Qiang Ma
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2046122004