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 i j ( i , j = e , μ , τ ) as flavor neutrino masses, that induces maximal CP violation as well as maximal atmospheric neutrino mixing. The masses of M μ μ , M τ τ and M μ τ + σ M e e ( σ = ± 1 ) turn out to be completely determined by M e μ and M e τ for given mixing angles. The appearance of CP violation is found to originate from the interference between the μ– τ symmetric part of M and its breaking part. If | M e μ | = | M e τ | , giving either M e μ = − σ e i θ M e τ or M e μ = − σ e i θ M e τ * with a phase parameter θ, is further imposed, we find that | M μ μ | = | M τ τ | is also satisfied. These two constraints can be regarded as an extended version of the constraints in the μ– τ symmetric texture given by M e μ = − σ M e τ and M μ μ = M τ τ . Majorana CP violation becomes active if arg ( M μ τ ) ≠ arg ( M e μ ) + θ / 2 for M e μ = − σ e i θ M e τ and if arg ( M μ τ ) ≠ θ / 2 for M e μ = − σ e i θ M e τ * .