Does the Borexino experiment have enough resolution to detect the   neutrino flavor day-night asymmetry?
  The Earth's density distribution can be approximately considered piecewise continuous at the scale of two-flavor oscillations of neutrinos with energies about 1 MeV. This quite general assumption appears to be enough to analytically calculate the day-night asymmetry factor. Using the explicit time averaging procedure, we show that, within the leading-order approximation, this factor is determined by the electron density immediately before the detector, i.e. in the Earth's crust. Within the approximation chosen, the resulting asymmetry factor does not depend either on the properties of the inner Earth's layers or on the substance and the dimensions of the detector. For beryllium neutrinos, we arrive at the asymmetry factor estimation of about $-4 \times 10^{-4}$, which is at least one order of magnitude beyond the present experimental resolution, including that of the Borexino experiment. 
S. S. Aleshin, O. G. Kharlanov, and A. E. Lobanov
hep-ph