Large Matter Effects in ${ν_μ\to ν_τ}$ Oscillations

Abstract

We show that matter effects change the ${\rm {ν_μ\to ν_τ}}$ oscillation probability by as much as 70% for certain ranges of energies and pathlengths. Consequently, the ${\rm {ν_μ\to ν_μ}}$ survival probability also undergoes large changes. A proper understanding of $ν_μ$ survival rates must consider matter effects in $P_{μτ}$ as well as $P_{μe}$. We comment on a) how these matter effects may be observed and the sign of $Δ_{31}$ determined in atmospheric neutrino measurements and at neutrino factories and b) how they lead to heightened sensitivity for small $θ_{13}$.