Determining the sign of $Δ_{31}$ at long baseline neutrino experiments

Abstract

Recently it is advocated that high intensity and low energy $(E_ν\sim 2 GeV)$ neutrino beams should be built to probe the $(13)$ mixing angle $ϕ$ to a level of a few parts in $10^4$. Experiments using such beams will have better signal to background ratio in searches for $ν_μ\to ν_e$ oscillations. We propose that such experiments can also determine the sign of $Δ_{31}$ even if the beam consists of {\it neutrinos} only. By measuring the $ν_μ\to ν_e$ transitions in two different energy ranges, the effects due to propagation of neutrinos through earth's crust can be isolated and the sign of $Δ_{31}$ can be determined. If the sensitivity of an experiment to $ϕ$ is $ε$, then the same experiment is automatically sensitive to matter effects and the sign of $Δ_{31}$ for values of $ϕ\geq 2 ε$.