k !! ! ! ! ! "$_{L}$ i "$_{L}$ j º  v g ’ kl º  v e$_{L}$ !  k e$_{R}$ !  l e$_{R}$ !  k e$_{L}$ !  l " f$_{ik}$ f$_{j}$$_{l}$ º  º  v v º  ! $_{L}$j H " H " N$_{R}$ c  ! ! $_{L}$i h$_{j}$ ! h$_{i}$ ! e R "  i e R "  j S " S " y$_{i}$ y$_{j}$ # 0 κ κ º  º  v v º  ! $_{L}$j " 0 r,i " 0 r,i N$_{R}$ c  ! ! $_{L}$i h$_{j}$ ! h$_{i}$ ! "$_{5}$ ＾ ＾ FIG. 1: Feynman diagrams for neutrino masses in the model by Zee-Babu [3] (left), that by Ma [5] (center) and that in Ref. [6] (right). duced, both of which carry the lepton number of two-unit, and their interactions are given by where L$_{L}$ is the left-handed lepton doublet and ℓ$_{R}$ is the right-handed lepton singlet. The matrices f$_{ij}$ and g ′ ab are respectively an anti-symmetric and a symmetric couplings and the lepton number is violated by the interaction with the parameter µ . The neutrino mass matrix is generated at the two-loop level via the diagram in Fig. 1 (left); where y$_{i}$ [= √$_{2}$$_{m}$$_{i}$$_{/v}$ ( i = e , µ , τ )] are the SM Yukawa coupling constants of charged leptons with the masses m$_{i}$ and the VEV v ( ≃ 246 GeV), g$_{ij}$ are defined as g$_{ii}$ = g ′ ii and g$_{ij}$ = 2 g ′ ij ( i = j ), m$_{ω}$ and m$_{k}$ are masses of ω ± and k $^{±±}$, and where I$_{1}$ ( r ) takes the value of around 3 - 0.2 for 10 − 2 < ∼ r < ∼ 10 $^{2}$. The universal scale of neutrino masses is determined by the two-loop suppression factor 1 / (16 π $^{2}$)2 and the lepton number violating parameter µ . The charged lepton Yukawa coupling constants y$_{ℓ}$$_{i}$ ( y$_{e}$ ≪ y$_{µ}$ ≪ y$_{τ}$ < ∼ 10 − $^{2}$) give an additional suppression factor. Thus, any of f$_{ij}$ or g$_{ij}$ can be of O (1) when m$_{ω}$ and m$_{k}$ are at the TeV scale. The flavor structure of the mass matrix is determined by the combination of the coupling constants f$_{ij}$ and y$_{i}$g$_{ij}$y$_{j}$ . 4 I$_{1}$ ( r ) = − ∫ 1 0 dx ∫ 1 − x 0 dy 1 x + ( r − 1) y + y 2 ln y (1 − y ) x + ry , (4) M ν ij = 3 ∑ k,ℓ =1 ( 1 16 π 2 ) 2 4 µ m 2 ω f$_{ik}$ ( y$_{ℓ}$$_{k}$g$_{kℓ}$y$_{ℓ}$$_{ℓ}$ ) f$_{ℓj}$v $^{2}$I$_{1}$ ( m 2 $_{k}$/m 2 $_{ω}$) , (3) L int = f$_{ab}$ ( L ci $_{aL}$L j $_{bL}$) ϵ$_{ij}$ω + + g ′ $_{ab}$( ℓ c $_{aR}$ℓ$_{bR}$ ) k ++ − µ k $^{++}$ω $^{−}$ω− + H . c ., (2)