Long-baseline neutrino oscillation experiments and $\mathrm{CP}$ violation in the lepton sector

We discuss possibilities to investigate the effects of $\mathrm{CP}$ (and $T)$ violation in the lepton sector in neutrino oscillation experiments. We consider the effects of $\mathrm{CP}$ violation in the framework of two schemes of mixing of four massive neutrinos that can accommodate the results of all neutrino oscillation experiments. Using the constraints on the mixing parameters that follow from the results of short-baseline neutrino oscillation experiments, we derive rather strong upper bounds on the effects of $\mathrm{CP}$ violation in ${\stackrel{\mathrm{(-)}}{\nu }}_{\mu }\leftrightarrows {\stackrel{\mathrm{(-)}}{\nu }}_e$ transitions in long-baseline neutrino oscillation experiments. We show that the effects of $\mathrm{CP}$ violation in ${\stackrel{\mathrm{(-)}}{\nu }}_{\mu }\leftrightarrows {\stackrel{\mathrm{(-)}}{\nu }}_{\tau }$ transitions in long-baseline oscillation experiments can be as large as is allowed by the unitarity of the mixing matrix. The matter effects, which complicate the problem of searching for $\mathrm{CP}$ violation in long-baseline experiments, are discussed in detail. We consider the $T$-odd asymmetries whose measurement could allow to reveal $T$ and $\mathrm{CP}$ violation in the lepton sector independently from matter effects.