Determination of theta_{23} in Long-Baseline Neutrino Oscillation Experiments with Three-Flavor Mixing Effects

Abstract

We examine accuracy of theta_{23} determination in future long-baseline (LBL) nu_{mu} disappearance experiments in the three-flavor mixing scheme of neutrinos. Despite that the error of sin^2{2theta_{23}} is indeed a few % level at around the maximal mixing, we show that the error of physics variable s^2_{23} is large, delta(s^2_{23})/s^2_{23} \simeq 10-20%, depending upon regions of theta_{23}. The errors are severely affected by the octant degeneracy of theta_{23}, and delta(s^2_{23}) is largely amplified by the Jacobian factor relating these two variables in a region near to the maximal mixing. The errors are also affected by the uncertainty due to unknown value of theta_{13}; delta(s^2_{23}) is doubled at off maximal in the second octant of theta_{23} where the effect is largest. To overcome this problem, we discuss combined analysis with nu_e appearance measurement in LBL experiments, or with reactor measurement of theta_{13}. For possible relevance of sub-leading effects even in the next-generation LBL experiments, we give a self-contained derivation of the survival probability to the next to leading order in s^2_{13} and Delta m^2_{21} / Delta m^2_{31}.