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Flavor Neutrino Masses giving sinθ_{13}=0

Among neutrino mixings, the reactor mixing angle, θ_{13}, is observed to be almost vanishing and is consistent with θ_{13}=0. We discuss how the condition of θ_{13}=0 constrains models of neutrino mixings and show that, for flavor neutrino masses given by M_{ij} (i,j=e,μ,τ), two conditions of M_{eτ}=-e^{2iγ}tan(θ_{23})M_{eμ} and M_{ττ}=e^{4iγ}M_{μμ}+e^{2iγ}[2/tan(2θ_{23})]M_{μτ} lead to θ_{13}=0, where θ_{23} is the atmospheric neutrino mixing angle and γis its associated phase. The rephasing invariance can select two phases provided by α=arg(M_{eμ}) and β=arg(M_{eτ}), giving γ=(β-α)/2.