Probing matter effects with neutrino long baseline experiments

We consider ${\nu }_{\mu }\to {\nu }_e$ oscillations in long baseline experiments within a three flavor oscillation framework. A non-zero measurement of this oscillation probability implies that the $\mathrm{}\left(13\right)\mathrm{}$ mixing angle $\phi$ is non-zero. We consider the effect of neutrino propagation through the matter of Earth’s crust and show that, given the constraints from solar neutrino and CHOOZ data, matter effects enhance the mixing for neutrinos rather than for anti-neutrinos. We need data from two different experiments with different baseline lengths (such as K2K and MINOS) to discern the effect of the matter term.