Determining the sign of ${\Delta }_{31}$ at long baseline neutrino experiments

Abstract

Recently it is advocated that high intensity and low energy $(E_{\nu }\sim 2GeV)$ neutrino beams should be built to probe the $(13)$ mixing angle $\varphi$ 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 $\varphi$ is $ϵ$, then the same experiment is automatically sensitive to matter effects and the sign of ${\Delta }_{31}$ for values of $\varphi \ge 2ϵ$.

Comments: Title changed and paper rewritten. 4 pages, 1 figure, revtex