Leptonic unitarity triangle and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>violation

Abstract

The area of the unitarity triangle is a measure of CP-violation. We introduce\nthe leptonic unitarity triangles and study their properties. We consider the\npossibility of reconstructing the unitarity triangle in future oscillation and\nnon-oscillation experiments. A set of measurements is suggested which will, in\nprinciple, allow us to measure all sides of the triangle, and consequently to\nestablish CP-violation. For different values of the CP-violating phase,\n$\\delta_D$, the required accuracy of measurements is estimated. The key\nelements of the method include determination of $|U_{e3}|$ and studies of the\n$\\nu_{\\mu} - \\nu_{\\mu}$ survival probability in oscillations driven by the\nsolar mass splitting $\\Delta m^2_{sun}$. We suggest additional astrophysical\nmeasurements which may help to reconstruct the triangle. The method of the\nunitarity triangle is complementary to the direct measurements of CP-asymmetry.\nIt requires mainly studies of the {\\it survival} probabilities and processes\nwhere oscillations are averaged or the coherence of the state is lost.\n