CP- and T-Violation Effects in Long Baseline Neutrino Oscillation Experiments

We examine how large CP- and T-violation effects are allowed in long baseline neutrino experiments with three generations of neutrinos, considering both the solar neutrino deficit and the atmospheric neutrino anomaly. We considerd two cases: When we attribute only the atmospheric neutrino anomaly to neutrino oscillation and assume the constant transition probability of electron neutrino to explain the solar neutrino deficit, we may have large CP-violation effect. When we attribute both the atmospheric neutrino anomaly and the solar neutrino deficit to neutrino oscillation, we can see sizable T-violation effects. In this case, however, we cannot ignore the matter effect and we will not see the pure CP-violation effect. We also show simple methods how to separate pure CP violating effect from the matter effect. We give compact formulae for neutrino oscillation probabilities assuming one of the three neutrino masses (presumably tau neutrino mass) to be much larger than the other masses and the effective mass due to 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 CP violation. The other is to compare experiments with at least two different baseline lengths; this has a merit that it needs only narrow energy range of oscillation data.