Analytic Solutions to the RG Equations of the Neutrino Physical Parameters

TL;DR

This paper derives analytic solutions for the energy-scale dependence of neutrino parameters, including mixing angles and Majorana phases, revealing their stability properties under quantum corrections.

Contribution

It provides the first analytic solutions to RG equations for neutrino parameters with Majorana phases, clarifying their scale dependence and stability.

Findings

Majorana phase instability coincides with mixing angle instability

Analytic solutions describe the evolution of neutrino parameters with energy scale

The ratio r governs the RG evolution of neutrino mixing and phases

Abstract

In the case of two generation neutrinos, the energy-scale dependence of the lepton-flavor mixing matrix with Majorana phase can be governed by only one parameter r, which is the ratio between the diagonal elements of neutrino mass matrix. By using this parameter r, we derive the analytic solutions to the renormalization group equations of the physical parameters, which are the mixing angle, Majorana phase, and the ratio of the mass-squared difference to the mass squared of the heaviest neutrino. The energy-scale dependence of the Majorana phase is clarified by using these analytic solutions. The instability of the Majorana phase causes in the same parameter region in which the mixing angle is unstable against quantum corrections.