Correlations between $θ_{13}$ and $θ_{23}$ in a very long baseline neutrino oscillation experiment

Abstract

A very long baseline experiment, with $L/E$ of $1.6 \times 10^4$ m/MeV, has been proposed as the ideal means to measure $θ_{13}$, including its sign, for neutrino energies less than 50 MeV. Higher energies require consideration of the earth MSW effect. Approximating a constant density mantle, we examine the $ν_e$--$ν_μ$ and $ν_μ$--$ν_μ$ oscillation channels at very long baselines with particular focus upon the deviation of $θ_{23}$ from maximal mixing and the sign of $θ_{13}$. It is demonstrated that measurements of these oscillation channels in this region are sensitive to $θ_{13}$, including its sign, and to $θ_{23}$, including its octant, with a significant correlation between the value of $θ_{13}$ and the difference of $θ_{23}$ from maximal mixing.