Analytic and Parameter-Free Formula for the Neutrino Mixing Matrix

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.