The geometric correlations of leptonic mixing parameters

TL;DR

This paper introduces a novel geometric approach to analyze correlations among leptonic mixing parameters, revealing specific regions of parameter space and their implications for astrophysical neutrino observations.

Contribution

It presents an alternative geometric method for studying leptonic mixing correlations, diverging from traditional group or algebraic structure approaches.

Findings

Scatter points concentrate on special regions in parameter space

Correlations between mixing angles and CP phase are identified

Predicted flavor ratios of high-energy astrophysical neutrinos are derived

Abstract

Leptonic mixing patterns are usually extracted on the basis of groups or algebraic structures. In this paper, we introduce an alternative geometric method to study the correlations between the leptonic mixing parameters. At the 3$\sigma$ level of the recent global fit data of neutrino oscillations, the distribution of the scattered points of the angles between the vectors, which are constructed by the element of the leptonic mixing matrix, is analysed. We find that the scattered points are concentrated on several special regions. Using the data in these regions, correlations of the leptonic mixing angles and the Dirac CP violating phase are obtained. The implications of the correlations are shown through the predicted flavor ratio of high-energy astrophysical neutrinos (HANs) at Earth.