Determination of Neutrino Mass Texture for Maximal CP Violation

Abstract

We show a general form of neutrino mass matrix (M), whose matrix elements are denoted by M_{ij} (i.j=e, mu, tau) as flavor neutrino masses, that induces maximal CP violation as well as maximal atmospheric neutrino mixing. The masses of M_{mu mu}, M_{tau tau} and M_{mu tau}+sigma M_{ee} (sigma =\pm 1) turn out to be completely determined by M_{e mu} and M_{e tau} for given mixing angles. The appearance of CP violation is found to originate from the interference between the mu-tau symmetric part of M and its breaking part. If |M_{e mu}|=|M_{e tau}|, giving either M_{e mu}=-sigma e^{i theta} M_{e tau} or M_{e mu}=-sigma e^{i theta}M*_{e tau} with a phase parameter theta, is further imposed, we find that |M_{mu mu}|=|M_{tau tau}|is also satisfied. These two constraints can be regarded as an extended version of the constraints in the mu-tau symmetric texture given by M_{e mu}=-sigma M_{e tau} and M_{mu mu}=M_{tau tau}. Majorana CP violation becomes active if arg(M_{mu tau})\neq arg(M_{e mu})+theta/2 for M_{e mu}=-sigma e^{i theta} M_{e tau} and if arg(M_{mu tau})\neq theta/2 for M_{e mu}=-sigma e^{i theta} M*_{e tau}.