arXiv · hep-ph/0407138
A precise analytical description of the Earth matter effect on oscillations of low energy neutrinos
Abstract
We present a formalism for the matter effects in the Earth on low energy neutrino fluxes which is both accurate and has all advantages of a full analytic treatment. The oscillation probabilities are calculated up to second order term in $ε(x) \equiv 2V(x)E/Δm^2$ where $V(x)$ is the neutrino potential at position $x$. We show the absence of large undamped phases which makes the expansion in $ε$ well behaved. An improved expansion is presented in terms of the variation of $V(x)$ around a suitable mean value which allows to treat energies up to those relevant for Supernova neutrinos. We discuss also the case of three-neutrino mixing.
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A. N. Ioannisian, N. A. Kazarian, A. Yu. Smirnov, D. Wyler. 2004-10-19. A precise analytical description of the Earth matter effect on oscillations of low energy neutrinos. https://doi.org/10.1103/physrevd.71.033006
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