Analytical treatment of long-term observations of the day-night asymmetry for solar neutrinos

Abstract

The Earth's density distribution can be approximately considered piecewise continuous at the scale of two-flavor oscillations of typical solar neutrinos, such as the beryllium-7 and boron-8 neutrinos. This quite general assumption appears to be enough to analytically calculate the day-night asymmetry factor for such neutrinos. Using the explicit time averaging procedure, we show that, within the leading-order approximation, this factor is determined by the electron density within about one oscillation length under the detector, namely, in the Earth's crust (and upper mantle for high-energy neutrinos). We also evaluate the effect of the inner Earth's structure on the observed asymmetry and show that it is suppressed and mainly comes from the neutrinos observed near the winter and summer solstices. As a result, we arrive at the strict interval constraint on the asymmetry, which is valid within quite a wide class of Earth models.