Golden measurements at a neutrino factory

The precision and discovery potential of a neutrino factory based on muonstorage rings is studied. For three-family neutrino oscillations, we analysehow to measure or severely constraint the angle $\theta_{13}$, CP violation,MSW effects and the sign of the atmospheric mass difference $\Delta m^2_{23}$.We present a simple analytical formula for the oscillation probabilities inmatter, with all neutrino mass differences non-vanishing, which clarifies thesubtleties involved in disentangling the unknown parameters. The appearance of``wrong-sign muons'' at three reference baselines is considered: 732 km, 3500km, and 7332 km. We exploit the dependence of the signal on the neutrinoenergy, and include as well realistic background estimations and detectionefficiencies. The optimal baseline turns out to be ${\cal O}(3000$ km).Analyses combining the information from different baselines are also presented.