A new Wolfenstein-like expansion of lepton flavor mixing towards understanding its fine structure

Abstract

Taking the tri-bimaximal flavor mixing pattern as a particular basis, we propose a new way to expand the $3\times 3$ unitary Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton flavor mixing matrix $U$ in powers of the magnitude of its smallest element $\xi \equiv \left|U^{}_{e 3}\right| \simeq 0.149$. Such a Wolfenstein-like parametrization of $U$ allows us to easily describe the salient features and fine structures of flavor mixing and CP violation, both in vacuum and in matter.