A rephasing invariant study of neutrino mixing

TL;DR

This paper develops rephasing invariant renormalization group equations for Dirac neutrinos, revealing symmetries and invariants that help understand neutrino mixing evolution despite the lack of complete analytical solutions.

Contribution

It introduces a rephasing invariant parametrization for neutrino RGEs and identifies exact and approximate invariants, advancing the theoretical understanding of neutrino mixing.

Findings

Derived symmetric RGE equations for Dirac neutrinos

Identified exact and approximate RGE invariants

Provided numerical examples illustrating parameter evolution

Abstract

We derive a set of renormalization group equations (RGE) for Dirac neutrinos using a rephasing invariant parametrization. The symmetric properties of these equations under flavor permutation facilitate the derivation of some exact and approximate RGE invariants. Even though the complete analytical solutions for the RGE are unavailable, we provide a numerical example that illustrate the evolution of the neutrino mixing parameters.