Direct test of the MSW effect by the solar appearance term in beam experiments

We discuss if one can verify the MSW effect in neutrino oscillations at a high confidence level in long-baseline experiments. We demonstrate that for long enough baselines at neutrino factories, the matter effect sensitivity is, as opposed to the mass hierarchy sensitivity, not suppressed by $\sin^2 2 \theta_{13}$ because it is driven by the solar oscillations in the appearance probability. Furthermore, we show that for the parameter independent direct verification of the MSW effect at long-baseline experiments, a neutrino factory with a baseline of at least 6000 km is needed. For superbeams, we do not find a $5\sigma$ discovery potential of the MSW effect independent of $\sin^2 2 \theta_{13}$. We finally summarize different methods to test the MSW effect.