Extracting Matter Effects, Masses and Mixings at a Neutrino Factory

We discuss and quantify different possibilities to determine matter effects, the value and the sign of $Delta m^2_{31}$, as well as the magnitude of $\sin^2 2\theta_{13}$ in very long baseline neutrino oscillation experiments. We study neutrino oscillation at a neutrino factory in the $\nu_\mu\to\nu_\mu$ disappearance and $\nu_e\to\nu_\mu$ appearance channels with and without muon charge identification. One possibility is to analyze the $\nu_e\to\nu_\mu$ appearance channels leading to wrong sign muon events, which requires however very good muon charge identification. Without charge identification it is still possible to operate the neutrino factory both with $\mu^-$ and $\mu^+$ beams and to analyze the differences in the total neutrino event rate spectra. We show that this leads already to a quite good sensitivity, which may be important if right sign charge rejection capabilities are insufficient. With muon charge identification one can study the $\nu_\mu\to\nu_\mu$ disappearance and the $\nu_e\to\nu_\mu$ appearance channels independently. The best method is finally achieved by combining all available information of the $\nu_\mu\to\nu_\mu$ disappearance and $\nu_e\to\nu_\mu$ appearance channels with charge identification and we show the sensitivity which can be achieved.