Energy-Scale Dependence of the Lepton-Flavor-Mixing Matrix

TL;DR

This paper investigates how the lepton-flavor-mixing matrix evolves with energy scale within the minimal supersymmetric standard model, revealing that phases remain constant while certain parameters vary with energy.

Contribution

It provides an analysis of the renormalization group equations for the lepton-flavor-mixing matrix, showing phase invariance and parameter dependence on energy scale.

Findings

Phases in the effective neutrino mass operator are energy-scale independent.

Number of energy-dependent parameters in the mixing matrix is n_g - 1.

The analysis is performed under the approximation neglecting O(ppa^2) corrections.

Abstract

We study an energy-scale dependence of the lepton-flavor-mixing matrix in the minimal supersymmetric standard model with the effective dimension-five operators which give the masses of neutrinos. We analyze the renormalization group equations of kappa_{ij}s which are coefficients of these effective operators under the approximation to neglect the corrections of O(\kappa^2). As a consequence, we find that all phases in $\kappa$ do not depend on the energy-scale, and that only n_g-1 (n_g: generation number) real independent parameters in the lepton-flavor-mixing matrix depend on the energy-scale.