Neutrino factories and the “magic” baseline

We show that for a neutrino factory baseline of L~7300--7600km a ``clean'' measurement of sin²2θ₁₃ becomes possible, which is almost unaffected by parameter degeneracies. We call this baseline the ``magic'' baseline, because its length depends only on the matter density profile. For a complete analysis, we demonstrate that the combination of the magic baseline with a baseline of 3 000 km is the ideal solution to perform equally well for sin²2θ₁₃, the sign of Δm₃₁², and CP violation sensitivities. In particular, this combination can very successfully resolve parameter degeneracies even below sin²2θ₁₃<10^-4.