Correlations between θ₁₃ and θ₂₃ in a very long baseline neutrino oscillation experiment

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A very long baseline experiment, with L/E of 1.6 × 10⁴ m/MeV, has been proposed as the ideal means to measure θ₁₃, 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 νₑ--νμ and νμ--νμ oscillation channels at very long baselines with particular focus upon the deviation of θ₂₃ from maximal mixing and the sign of θ₁₃. It is demonstrated that measurements of these oscillation channels in this region are sensitive to θ₁₃, including its sign, and to θ₂₃, including its octant, with a significant correlation between the value of θ₁₃ and the difference of θ₂₃ from maximal mixing.