CPviolation and matter effect in long baseline neutrino oscillation experiments

We show simple methods of how to separate pure $\mathrm{CP}$-violating effects from matter effects in long baseline neutrino oscillation experiments with three generations of neutrinos. We give compact formulas for neutrino oscillation probabilities assuming one of the three neutrino masses (presumably ${\nu }_{\tau }$ mass) to be much larger than the other masses and the effective mass due to the matter effect. Two methods are shown. One is to observe envelopes of the curves of oscillation probabilities as functions of neutrino energy; a merit of this method is that only a single detector is enough to determine the presence of $\mathrm{CP}$ violation. The other is to compare experiments with at least two different baseline lengths; this has the merit that it needs only a narrow energy range of oscillation data.