Neutrino factories and the “magic” baseline

We show that for a neutrino factory baseline of $L\sim 7300–7600\mathrm{km}$ a “clean” measurement of ${\sin }^{2}2{\theta }_{13}$ 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 ${\sin }^{2}2{\theta }_{13},$ the sign of $\Delta m_{31}^2,$ and CP violation sensitivities. In particular, this combination can very successfully resolve parameter degeneracies even below ${\sin }^{2}2{\theta }_{13}<{10}^{-4}.$