Long-baseline study of the leading neutrino oscillation at a neutrino factory

Within the framework of three-flavor neutrino oscillations, we consider the physics potential of ${\nu }_e\to {\nu }_{\mu }$ appearance and ${\nu }_{\mu }\to {\nu }_{\mu }$ survival measurements at a neutrino factory for a leading oscillation scale $\delta m^2\sim 3.5\times {10}^{-3}\hspace{0.5em}{\mathrm{eV}}^2.$ Event rates are evaluated versus baseline and stored muon energy, and optimal values discussed. Over a sizable region of oscillation parameter space, matter effects would enable the sign of $\delta m^2$ to be determined from a comparison of ${\nu }_e\to {\nu }_{\mu }$ with ${\overline{\nu }}_e\to {\overline{\nu }}_{\mu }$ event rates and energy distributions. It is important, therefore, that both positive and negative muons can be stored in the ring. Measurements of the ${\nu }_{\mu }\to {\nu }_{\mu }$ survival spectrum could determine the magnitude of $\delta m^2$ and the leading oscillation amplitude with a precision of $\mathcal{O}\hspace{0.5em}(1\%-2\%).$