Flavor neutrino masses giving sinθ13=0

Among neutrino mixings, the reactor mixing angle, θ13, is observed to be almost vanishing and is consistent with θ13=0. We discuss how the condition of θ13=0 constrains models of neutrino mixings and show that, for flavor neutrino masses given by Mij(i,j=e,μ,τ), two conditions of Meτ=−e2iγtanθ23Meμ and Mττ=e4iγMμμ+e2iγ(2/tan2θ23)Mμτ lead to θ13=0, where θ23 is the atmospheric neutrino mixing angle and γ is its associated phase. The rephasing invariance can select two phases provided by α=arg(Meμ) and β=arg(Meτ), giving γ=(β−α)/2.