Implications of the Daya Bay observation of \theta_{13} on the leptonic flavor mixing structure and CP violation

TL;DR

The paper explores the implications of the Daya Bay measurement of heta_{13} for the structure of lepton flavor mixing and CP violation, proposing models and analyzing their compatibility with experimental data.

Contribution

It introduces phenomenological strategies for understanding lepton mixing, examines patterns of the mixing matrix, and discusses CP violation geometrically and through parametrizations.

Findings

heta_{13} is approximately 8.8°, significantly non-zero.

Lepton mixing matrix may have an approximate ermi- auermi symmetry.

Multiple parametrizations of the mixing matrix are summarized.

Abstract

The Daya Bay Collaboration has recently reported its first \bar{\nu}_e \to \bar{\nu}_e oscillation result which points to \theta_{13} \simeq 8.8^\circ \pm 0.8^\circ (best-fit \pm 1\sigma range) or \theta_{13} \neq 0^\circ at the 5.2\sigma level. The fact that this smallest neutrino mixing angle is not strongly suppressed motivates us to look into the underlying structure of lepton flavor mixing and CP violation. Two phenomenological strategies are outlined: (1) the lepton flavor mixing matrix U consists of a constant leading term U_0 and a small perturbation term \Delta U; and (2) the mixing angles of U are associated with the lepton mass ratios. Some typical patterns of U_0 are reexamined by constraining their respective perturbations with current experimental data. We illustrate a few possible ways to minimally correct U_0 in order to fit the observed values of three mixing angles. We point out that the structure of U may exhibit an approximate \mu-\tau permutation symmetry in modulus, and reiterate the geometrical description of CP violation in terms of the leptonic unitarity triangles. The salient features of nine distinct parametrizations of U are summarized, and its Wolfenstein-like expansion is presented by taking U_0 to be the democratic mixing pattern.