Leptonic CP violation: zero, maximal or between the two extremes

Abstract

Discovery of the CP-violation in the lepton sector is one of the challenges of the particle physics. We search for possible principles, symmetries and phenomenological relations that can lead to particular values of the CP-violating Dirac phase, $\delta$. In this connection we discuss two extreme cases: the zero phase, $\delta = 0$, and the maximal CP-violation, $\delta = \pm \pi/2$, and relate them to the peculiar pattern of the neutrino mixing. The maximal CP-violation can be related to the $\nu_\mu - \nu_\tau$ reflection symmetry. We study various aspects of this symmetry and introduce a generalized reflection symmetry that can lead to an arbitrary phase that depends on the parameter of the symmetry transformation. The generalized reflection symmetry predicts a simple relation between the Dirac and Majorana phases. We also consider the possibility of certain relations between the CP-violating phases in the quark and lepton sectors.