The Earth Regeneration Effect of Solar Neutrinos: a Numerical Treatment with Three Active Neutrino Flavors

Abstract

We introduce an integrated algorithm for full scale investigation of the earth regeneration effect of solar neutrinos with all three active neutrinos. We illustrate that the earth effect on low energy solar neutrinos ($E_ν< 20$ MeV) causes large variations in the survival probabilities for large values of the mixing angle $θ_{12}$ for a given value of $θ_{13}$. But it is maximal for small values of $θ_{13}$ and diminishes for large values at a given value of $θ_{12}$. The nadir angle dependence is sensitive to the value of $E'\equiv E/Δ_{12}$. As far as low energy solar neutrinos are concerned we notice that the earth effect is more pronounced for core penetration. We confirm that the earth effect leaves the SMA region almost intact regardless of $θ_{13}$ and that it is significant for high energy $^8$B and $hep$ neutrinos in the LMA region. We also show that for large values of $θ_{13}$, the earth effect is significant for high energy neutrinos ($E'\gtrsim 10^9$) and it can be large at any nadir angle.