Earth matter density uncertainty in atmospheric neutrino oscillations

Abstract

That muon neutrinos $ν_μ$ oscillating into the mixture of tau neutrinos $ν_τ$ and sterile neutrinos $ν_{s}$ has been studied to explain the atmospheric $ν_μ$ disappearance. In this scenario, the effect of Earth matter is a key to determine the fraction of $ν_{s}$. Considering that the Earth matter density has uncertainty and this uncertainty has significant effects in some neutrino oscillation cases, such as the CP violation in very long baseline neutrino oscillations and the day-night asymmetry for solar neutrinos, we study the effects caused by this uncertainty in the above atmospheric $ν_μ$ oscillation scenario. We find that this uncertainty seems to have no significant effects and that the previous fitting results need not to be modified fortunately.