Oscillations of high energy neutrinos in matter: Precise formalism and parametric resonance
Abstract
We present a formalism for precise description of oscillation phenomena in high density medium, V > \Delta m^2/2E, where V is the matter-induced potential of neutrinos. By developing a perturbation theory in \xi\equiv\sin 2\theta_m, where \theta_m is the mixing angle in matter, we derive simple and physically transparent formulas for the oscillation probabilities in the lowest order in \xi, which are valid for arbitrary matter density profiles. The formulas can be applied to oscillations of high energy (E > 10 GeV) accelerator, atmospheric and cosmic neutrinos in the matter of the Earth, substantially simplifying numerical calculations. The effect of parametric enhancement of the oscillations of high energy neutrinos is discussed. Future high statistics experiments can provide an unambiguous evidence for this effect.Keywords
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