Correlations between ${\theta }_{13}$ and ${\theta }_{23}$ 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 ${\theta }_{13}$, 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 ${\nu }_e$--${\nu }_{\mu }$ and ${\nu }_{\mu }$--${\nu }_{\mu }$ oscillation channels at very long baselines with particular focus upon the deviation of ${\theta }_{23}$ from maximal mixing and the sign of ${\theta }_{13}$. It is demonstrated that measurements of these oscillation channels in this region are sensitive to ${\theta }_{13}$, including its sign, and to ${\theta }_{23}$, including its octant, with a significant correlation between the value of ${\theta }_{13}$ and the difference of ${\theta }_{23}$ from maximal mixing.

8 pages, 3 figures