Leptonic Unitarity Triangle and CP-violation

Abstract

The area of the unitarity triangle is a measure of 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 non-oscillation experiments. A set of measurements is suggested which will, in principle, allow us to measure all sides of the triangle, and consequently to establish CP-violation. For different values of the CP-violating phase, $δ_D$, the required accuracy of measurements is estimated. The key elements of the method include determination of $|U_{e3}|$ and studies of the $ν_μ - ν_μ$ survival probability in oscillations driven by the solar mass splitting $Δm^2_{sun}$. 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 CP-asymmetry. It requires mainly studies of the {\it survival} probabilities and processes where oscillations are averaged or the coherence of the state is lost.