Energy-scale dependence of the lepton flavor-mixing matrix

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 Majorana masses of neutrinos. We analyze the renormalization group equations of the coefficients ($\kappa_{ij}$) of these effective operators under an approximation that neglects terms of order $\kappa^2$. We find that only $n_\mathrm{g}-1$ (where $n_\mathrm{g}$ is the generation number) real independent parameters in the lepton flavor-mixing matrix depend on the energy scale. In particular, all the phases in $\kappa$ are scale-independent.