A precise analytical description of the Earth matter effect on oscillations of low energy neutrinos

Details A precise analytical description of the Earth matter effect on oscillations of low energy neutrinos A precise analytical description of the Earth matter effect on oscillations of low energy neutrinos

2004-07-12

arxiv.org/abs/hep-ph/0407138v2

Phys.Rev. D71 (2005) 033006

Physics

High Energy Physics

High Energy Physics - Phenomenology

REVTeX 4, 6 pages, 1 figure, several clarifications added, typos corrected

Scientific paper

10.1103/PhysRevD.71.033006

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 $\epsilon(x) \equiv 2V(x)E/\Delta m^2$ where $V(x)$ is the neutrino potential at position $x$. We show the absence of large undamped phases which makes the expansion in $\epsilon$ 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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