Analytical Description of the Earth Matter Effect on Neutrino Oscillations

J C DOLIVO; A D SUPANITSKY; G MEDINA-TANCO

Simposio; DISCRETE’08: Symposium on Prospects in the Physics of Discrete Symmetries; 2008

We present a formalism that provides a precise description of 2nu oscillations in a medium with a symmetric but otherwise arbitrary density profile. The analytical expressions, derived in terms of the first and second order Magnus approximations of the evolution operator, prove to be remarkably simple and can be used in a wide interval of the neutrino energies. They incorporate in accurate way the matter effects on the flavor amplitudes for neutrinos crossingtrough the Earth. When applied to calculations in the GeV regime characteristic of atmospheric and accelerator neutrinos, this accuracy is complemented by a good reproduction of the position of the maxima in the corresponding transition probabilities.