Neutrino oscillations at an entry-level neutrino factory and beyond

We consider the parameters of an entry-level neutrino factory designed to make the first observation of ${\nu }_e\to {\nu }_{\mu }$ oscillations, measure the corresponding amplitude ${\sin }^{2}2{\theta }_{13},$ and determine the sign of the atmospheric-scale $\delta m_{32}^2$ via matter effects. A 50 kt detector, a stored muon energy $E_{\mu }>~20\hspace{0.5em}\mathrm{GeV}$ and ${10}^{19}$ muon decays would enable these goals to be met provided ${\sin }^{2}2{\theta }_{13}>\mathrm{0.01.}\mathrm{}$ The determination of the sign of $\delta m_{32}^2$ also requires a baseline $L>~2000\hspace{0.5em}\mathrm{km}.$ An upgraded neutrino factory with $\mathrm{O}{(10\mathrm{}}^{20})$ decays would enable the first observation of ${\nu }_e\to {\nu }_{\tau }$ oscillations. With $\mathrm{O}{(10\mathrm{}}^{21})$ decays the effects of a large $\mathrm{CP}$ phase could be measured in the case of the large angle matter oscillation solution to the solar neutrino anomaly. Our analysis includes a family of three-neutrino models that can account for the atmospheric and solar neutrino oscillation indications.