Neutrino oscillations in low density medium

Details Neutrino oscillations in low density medium Neutrino oscillations in low density medium

2004-04-06

arxiv.org/abs/hep-ph/0404060v3

Phys.Rev.Lett. 93 (2004) 241801

Physics

High Energy Physics

High Energy Physics - Phenomenology

discussion simplified, clarifications added

Scientific paper

10.1103/PhysRevLett.93.241801

For the case of small matter effects: $V \ll \Delta m^2/2E$, where $V$ is the matter potential, we develop the perturbation theory using $\epsilon \equiv 2VE/\Delta m^2$ as the expansion parameter. We derive simple and physically transparent formulas for the oscillation probabilities in the lowest order in $\epsilon$ which are valid for arbitrary density profile. The formulas can be applied for propagation of the solar and supernova neutrinos in matter of the Earth, substantially simplifying numerical calculations. Using these formulas we study sensitivity of the oscillation effects to structures of the density profile situated at different distances from the detector $d$. We show that for the mass-to-flavor state transitions, {\it e.g.}, $\nu_2 \to \nu_e$, the sensitivity is suppressed for remote structures: $d > l_{\nu} E/\Delta E$, where $l_{\nu}$ is the oscillation length and $\Delta E/E$ is the energy resolution of detector.

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