Search for CP Violation at a Neutrino Factory in a Four-Neutrino Model

The CP violation effects in long baseline neutrino oscillations are studied in the framework of a four-neutrino model (three active neutrinos and one sterile neutrino). It is assumed that neutrino masses are devided into two nearly degenerate pairs, as indicated by the oscillation data. Approximative analytic expressions are derived for the probability differences $\Delta P_{\a\b} \equiv P(\nu_\alpha \to \nu_\beta)- P(\bar\nu_\alpha \to \bar\nu_\beta)$ taking into account the CP violation effect of the Earth's crust. The matter effect is found to be small compared with the genuine CP violation term, in contrast with the three-neutrino model.