Lepton mixing patterns from combinations of elementary correlations

TL;DR

This paper systematically explores all possible leptonic mixing patterns derived from elementary correlations, classifies them into two groups, and discusses their implications for neutrino physics and flavor models.

Contribution

It provides a comprehensive classification of 62 viable leptonic mixing patterns based on elementary correlations, including their CP phase predictions and model implications.

Findings

62 viable mixing patterns identified at 3σ level

Patterns can be grouped into perturbative and non-perturbative types

Small changes in 3 can significantly impact flavor model alignments

Abstract

Recent data of reactor neutrino experiments set more stringent constraint on leptonic mixing patterns. We examine all possible patterns on the basis of combinations of elementary correlations of elements of leptonic mixing matrix. we obtain 62 viable mixing patters at 3$\sigma$ level of mixing parameters. Most of these patterns can be paired via the {\mu}- interchange which changes the octant of $\theta_{23}$ and the sign of $\cos{\delta}$. All viable patterns can be classified into two groups: the perturbative patterns and non-perturbative patterns. The former can be obtained from perturbing TBM. The latter cannot be obtained from perturbing any mixing pattern whose $\theta_{13}$ is zero. Different predictions of Dirac CP phase $\delta$ of these two types of mixing patterns are discussed. Evolutions of mass matrices of neutrinos with small mixing parameters are discussed via special mixing patterns on the basis of flavor groups. In general cases, a small variation of $\sin\theta_{13}$ may bring about large modifications to alignment of vacuum expectation values in a mixing model. Therefore, small but nonzero $\sin\theta_{13}$ brings a severer challenge to leptonic mixing models on the basis of flavor groups than usual views.