Leptonic unitarity triangle andCPviolation

Abstract

The area of the unitarity triangle is a measure of $\mathrm{CP}$ violation. We introduce the leptonic unitarity triangles and study their properties. We consider the possibility of reconstructing the unitarity triangle in future oscillation and nonoscillation experiments. A set of measurements is suggested which will, in principle, allow us to measure all sides of the triangle, and consequently to establish $\mathrm{CP}$ violation. For different values of the $\mathrm{CP}$-violating phase ${\ensuremath{\delta}}_{D},$ the required accuracy of measurements is estimated. The key elements of the method are the determination of $|{U}_{e3}|$ and studying the ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ survival probability in the oscillations driven by the solar mass splitting $\ensuremath{\Delta}{m}_{\mathrm{sun}}^{2}.$ We suggest additional astrophysical measurements which may help to reconstruct the triangle. The method of the unitarity triangle is complementary to the direct measurements of $\mathrm{CP}$ asymmetry. It requires mainly studies of the survival probabilities and processes where oscillations are averaged or the coherence of the state is lost.