Neutrino oscillations: what is magic about the "magic" baseline?

Abstract

Physics interpretation of the ``magic'' baseline, $L_{magic}$, that can play important role in future oscillation experiments is given. The ``magic'' baseline coincides with the refraction length, $l_0$. The latter, in turn, approximately equals the oscillation length in matter at high energies. Therefore at the baseline $L = l_0$ the oscillation phase is $2\pi$, and consequently, the ``solar'' amplitude of oscillations driven by $\theta_{12}$ and $\Delta m^2_{21}$ vanishes. As a result, in the lowest order (i) the interference of amplitudes in the $\nu_e - \nu_\mu$ $(\nu_\tau)$ transition probability is absent; (ii) dependence of the probability on the CP-phase, $\delta$, as well as on $\theta_{12}$ and $\Delta m^2_{21}$ disappears. Corrections to the equality $L_{magic} = l_0$ are estimated. Effect of changing density is considered and two new magic trajectories are identified for neutrinos that cross the core of the Earth. Other magic baselines associated with zeros of the atmospheric amplitude are discussed.