Stability of the lepton-flavor mixing matrix against quantum corrections

Abstract

Recent neutrino experiments suggest strong evidence 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 the 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: $m_3^{} \sim m_2^{} \sim m_1^{}$ , where $m_i$ is the i-th generation neutrino mass. In this paper we study the stability of the lepton-flavor mixing matrix against quantum corrections for all three types of mass hierarchy in the minimal supersymmetric Standard Model with an effective dimension-five operator which gives the Majorana masses of neutrinos. The relative sign assignments of neutrino masses in each type play crucial role for the stability against quantum corrections. We find that 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 the definite unitary matrix according to the relative sign assignments of the neutrino mass eigenvalues as the effects of quantum corrections become large enough to neglect the squared mass differences of neutrinos.