EPJ

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EPJ C - Particles and Fields
Particles and Fields

Eur. Phys. J. C 10, 677-680
DOI 10.1007/s100529900152

Energy-scale dependence of the lepton flavor-mixing matrix

N. Haba1,2 - Y. Matsui3 - N. Okamura4 - M. Sugiura3

1 Department of Physics, The Ohio State University, Columbus, OH 43210, USA (e-mail: haba@pacific.mps.ohio-state.edu)
2 Faculty of Engineering, Mie University, Tsu Mie 514-8507, Japan
3 Department of Physics, Nagoya University, Nagoya, 464-8602, Japan (e-mail: matsui,sugiura@eken.phys.nagoya-u.ac.jp) 4 Theory Group, KEK, Tsukuba Ibaraki 305-0801, Japan (e-mail: naotoshi.okamura@kek.jp)

Received: 10 April 1999 / Revised version: 23 May 1999 / Published online: 28 September 1999

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.

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