CP Nonconservation in Three-Neutrino Oscillations

Direct $\mathrm{CP}$ tests in neutrino oscillations require comparison of off-diagonal channels ${\ensuremath{\nu}}_{\ensuremath{\alpha}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\beta}}$ with $\mathrm{CP}$-conjugate channels ${\overline{\ensuremath{\nu}}}_{\ensuremath{\alpha}}\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{\ensuremath{\beta}}$ (or with ${\ensuremath{\nu}}_{\ensuremath{\beta}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\alpha}}$ by assuming $\mathrm{CPT}$ invariance). For the three-neutrino case, it is shown that $\mathrm{CP}$-nonconservation effects are identical in all three available channels ${\ensuremath{\nu}}_{e}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}$, ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, and ${\ensuremath{\nu}}_{\ensuremath{\tau}}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{e}$, and argued that they could be large and measurable in meson factory experiments. Indirect $\mathrm{CP}$ tests include the correlation of average probabilities.