Stability of the Lepton-Flavor Mixing Matrix Against Quantum Corrections

TL;DR

This paper investigates how quantum corrections affect the stability of the lepton-flavor mixing matrix across different neutrino mass hierarchies within the minimal supersymmetric Standard Model, highlighting the importance of mass sign assignments.

Contribution

It provides a comprehensive analysis of the stability of the lepton-flavor mixing matrix against quantum corrections for all neutrino mass hierarchy types, emphasizing the role of neutrino mass signs.

Findings

Type A mixing matrix is stable against quantum corrections.

Type B with same signs of m_1 and m_2 is unstable, opposite signs are stable.

Type C approaches a fixed unitary matrix as quantum effects grow.

Abstract

Recent neutrino experiments suggest the strong evidences of tiny neutrino masses and the lepton-flavor mixing. Neutrino-oscillation solutions for the atmospheric neutrino anomaly and the solar neutrino deficit can determine the texture of neutrino mass matrix according to the neutrino mass hierarchies as Type A: m_3 \gg m_2 \sim m_1, Type B: m_3 \ll m_2 \sim m_1, and Type C: m_3 \sim m_2 \sim m_1. In this paper we study the stability of the lepton-flavor mixing matrix against quantum corrections for all types of mass hierarchy in the minimal supersymmetric Standard Model with the effective dimension-five operator which gives Majorana masses of neutrinos. The relative sign assignments of neutrino masses in each type play the crucial roles for the stability against quantum corrections. We find the lepton-flavor mixing matrix of Type A is stable against quantum corrections, and that of Type B with the same (opposite) signs of m_1 and m_2 are unstable (stable). For Type C, the lepton-flavor-mixing matrix approaches to the definite unitary matrix according to the relative sign assignments of neutrino mass eigenvalues, as the effects of quantum corrections become large enough to neglect squared mass differences of neutrinos.