Deviations from tri-bimaximal mixing

TL;DR

This paper explores possible deviations from the tri-bimaximal lepton mixing pattern, analyzing perturbations, parametrizations, and mechanisms to generate non-zero U_{e3} consistent with recent experimental hints.

Contribution

It provides a comprehensive discussion of perturbations to tri-bimaximal mixing, including a new parametrization of the PMNS matrix and methods to produce non-zero U_{e3}.

Findings

Deviations can arise from soft breaking, RG running, and charged lepton corrections.

A convenient parametrization of the PMNS matrix is proposed.

Mechanisms to generate non-zero U_{e3} are discussed.

Abstract

Current data indicates that lepton mixing is very close to the tri-bimaximal mixing scenario. In general, however, one expects deviations from any mixing scenario. We discuss several examples to perturb tri-bimaximal mixing, namely soft breaking, renormalization group running and charged lepton corrections. We also present a convenient parametrization of the PMNS matrix which takes advantage of the apparently close to tri-bimaximal mixing pattern. Finally, it is discussed how to generate values of U_{e3} which correspond to the recently found hint for non-zero U_{e3}.