Effect of the smaller mass-squared difference for the long base-line neutrino experiments

Usually, neutrino oscillation experiments are analyzed within the two-flavor framework, which is governed by one mass-squared difference and one mixing angle. But there are six parameters, two mass-squared differences, three mixing angles, and one CP phase, within the three-flavor framework. In this paper, we estimate the effect from the smaller mass-squared difference, the other mixing angles, and the CP phase, which we call the three-flavor effect, for the determination of the mass-squared difference and the mixing angle from the νμ's survival and transition probabilities with the two-flavor analysis. It is found that the mass-squared difference from the two-flavor analysis is slightly shifted from the larger mass-squared difference by the three-flavor effect. The order of magnitude of the three-flavor effect for the mass-squared difference is comparable with that of the expected error in the mass-squared difference from the two-flavor analysis of future long base-line neutrino oscillation experiments. The CP phase dependence of the νμ → νe transition probability is also shown. (author)