Determining the sign of Delta₃₁ at long baseline neutrino experiments

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