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Determination of θ<inf>23</inf> in long-baseline neutrino oscillation experiments with three-flavor mixing effects

Abstract:

We examine the accuracy of θ23 determination in future long-baseline (LBL) νμ disappearance experiments in the three-flavor mixing scheme of neutrinos. Despite that the error of sin 22θ23 is indeed a few percent level at around the maximal mixing, we show that the error of physics variable s232 is large, δ(s232)/s232 ≃ 10-20%, depending upon regions of θ23. The errors are severely affected by the octant degeneracy of θ23, and δ(s232) is largely amplified by the Jacobian factor relating these two variables in a region near the maximal mixing. The errors are also affected by the uncertainty due to the unknown value of θ13; δ(s232) is doubled at off maximal in the second octant of θ23 where the effect is largest. To overcome this problem, we discuss combined analysis with νe appearance measurement in LBL experiments, or with reactor measurement of θ13. For possible relevance of subleading 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 132 and Δm312/Δm 312.