Analytic and Parameter-Free Formula for the Neutrino Mixing Matrix

TL;DR

This paper derives a parameter-free analytic formula for the neutrino mixing matrix that accurately fits experimental data and can be extended to quark mixing, providing insights into leptonic CP violation.

Contribution

It introduces a universal, parameter-free analytic expression for the PMNS matrix, validated against measurements and applicable to quark mixing.

Findings

Fits all measured PMNS matrix components at 99.7% confidence

Predicts the leptonic Jarlskog invariant

Preliminary CKM matrix estimates show promise but have large errors

Abstract

A parameter-free analytic expression for the PMNS matrix is derived which fits numerically all the measured matrix components at 99.7$\%$ confidence. Results are proven within the microscopic model and include a prediction of the leptonic Jarlskog invariant. The approach is universal in the sense that it can be applied to the quark sector as well. Preliminary numbers obtained for the CKM matrix elements look promising, but are plagued with large theoretical errors.