Matter effects on neutrino oscillations in long baseline experiments

We calculate matter effects on neutrino oscillations relevant for long baseline experiments. In particular, we compare the results obtained with constant density along the neutrino path versus results obtained by incorporating the actual density profiles in the Earth. We study the dependence of the oscillation signal on both $E/\Delta m_{\mathrm{atm}}^2$ and on the angles in the leptonic mixing matrix. We also comment on the influence of $\Delta m_{\mathrm{sol}}^2$ and CP violation on the oscillations. The results show quantitatively how, as a function of these input parameters, matter effects can cause significant (25%) changes in the oscillation probabilities. An important conclusion is that matter effects can be useful in amplifying certain neutrino oscillation signals and helping one to obtain measurements of mixing parameters and the magnitude and sign of $\Delta m_{\mathrm{atm}}^2.$