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Majorana CP phases in bi-pair neutrino mixing and leptogenesis

We estimate Majorana CP phases for a given flavor neutrino mass matrix (M_ν) consistent with the bi-pair neutrino mixing, which is recently proposed to describe neutrino mixings given by \sinθ_{13}=0 for the reactor neutrino mixing, \sin^2θ_{12} = 1-1/\sqrt{2} for the solar neutrino mixing and either \sin^2θ_{23} = \tan^2θ_{12} or \sin^2θ_{23}=1-\tan^2θ_{12} for the atmospheric neutrino mixing. Sizes of Majorana CP phases are evaluated so as to generate the observed baryon asymmetry in the universe via a leptogenesis scenario within the framework of the minimal seesaw model, where M_νsatisfies det(M_ν)=0 and one active Majorana CP phase (ϕ) is present. Assuming the normal mass hierarchy for light neutrinos and one zero texture for a 3X2 Dirac neutrino mass matrix, we find that ϕlies in the region of 0.69<|ϕ|<0.92 [rad], which is converted into allowed regions of α=arg(M_{eμ}) and β=arg(M_{eτ}), where M_{ij} (i,j=e,μ,τ) denote the i-j matrix element of M_ν. The phases αand βturn out to satisfy 0.31<|α|<0.40 [rad] and -1.25<β<-0.32 [rad]. The approximate numerical equality of |ϕ|\approx 2|α| is consistent with our theoretical estimation of ϕ=ϕ_2-ϕ_3 for ϕ_2=-(α+β) and ϕ_3\approx α-βvalid for the normal mass hierarchy. We also find the following scaling property: (M'^{μμ}-M'^{ee}/t^2_{12})/M'^{μτ}=M'^{μτ}/(M'^{ττ}-M'^{ee}/t^2_{12})=-M'^{eτ}/M'^{eμ} (t^2_{12}=\tan^2θ_{12}=\sqrt{2}-1), where M'^{ij} stands for M_{ij} evaluated on the basis of the Particle Data Group's phase convention.