Effect of the Smaller Mass-Squared Difference for the Long Base-Line Neutrino Experiments

Usually, neutrino oscillation experiments are analyzed within the two-flavorframework which is governed by 1 mass-squared difference and 1 mixing angle.But there are 6 parameters,2 mass-squared differences, 3 mixing angles, and 1CP phase within the three-flavor framework.In this article,we estimate theeffect from the smaller mass-squared difference,the other mixing angles, andthe CP phase, which we call three-flavor effect, for the determination of themass-squared difference and the mixing angle from the nu_mu's survival andtransition probability with the two-flavor analysis.It is found that themass-squared difference from the two-flavor analysis is slightly shifted fromthe larger mass-squared difference by the three-flavor effect.The order ofmagnitude of the three-flavor effect for the mass-squared difference iscomparable with that of the expected error for the mass-squared difference ofthe two-flavor analysis in the future long base-line neutrino oscillationexperiments.The CP phase dependence of the nu_mu to nu_etransition probabilityis also shown.Comment: 13 pages, no figure new reference added, correct typos, Accepted by Progress of Theoretical Physic