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

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(κ^2). As a consequence, we find that all phases in $κ$ 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.

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