Renormalization of the Neutrino Mass Matrix

TL;DR

This paper derives simplified, symmetric renormalization group equations for Dirac neutrino parameters, providing invariants and solutions to understand how neutrino masses and mixing evolve with energy.

Contribution

It presents a rephasing invariant formulation of the RGEs for Dirac neutrinos, including exact and approximate invariants and solutions, highlighting flavor permutation symmetry.

Findings

Derived compact RGE equations with flavor permutation symmetry

Identified exact and approximate RGE invariants

Provided numerical examples illustrating parameter evolution

Abstract

In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations. We obtain both exact and approximate RGE invariants, in addition to some approximate solutions and examples of numerical solutions.