Probing the octant of $θ_{23}$ with very long baseline neutrino oscillation experiments: a global look

Abstract

We investigate the baseline range in which the $θ_{23}$ degeneracy in neutrino oscillation probabilities is absent for fixed values of $θ_{13}$ and CP violation phase $δ_{\rm CP}$. We begin by studying sensitivities of neutrino oscillation probabilities to $θ_{13}$, $θ_{23}$ and $δ_{\rm CP}$ for very-long-baseline neutrino oscillations. We show contour graphs of the muon-neutrino survival probability $P(ν_μ\to ν_μ)$ and the appearance probability $P(ν_e\to ν_μ)$ on the $\cos 2θ_{23}-\sin 2θ_{13}$ plane for baseline lengths $L=1000, 5000, \ 10000$, and 12000 km. For each baseline length, it is found that $P(ν_μ\to ν_μ)$ is more sensitive to $\sin 2θ_{13}$ at energies around its local maximum while it is more sensitive to $\cos 2θ_{23}$ at energies around its local minimum. On the other hand, the appearance probability $P(ν_e\to ν_μ)$ is sensitive to $\sin2θ_{13}$ and $\cos2θ_{23}$ only near its local maximum. We observe that the $θ_{23}$ degeneracy in $P(ν_μ\to ν_μ)$ is absent at energies around the local maximum of this probability, provided $θ_{13}$ is sufficiently large. The $θ_{23}$ degeneracy is also absent in general near the local maximum of $P(ν_e\to ν_μ)$. Using analytic approximations for neutrino oscillation probabilities, we demonstrate that the above observations for $L=1000, 5000, 10000, {\rm and} 12000$ km are in fact valid for all distances. The implications of these results on probing the octant of $θ_{23}$ are discussed in details.