The flavor off-diagonal coupling constants f$_{ij}$ and g$_{ij}$ induce lepton flavor violation (LFV). From the results of µ → eγ , τ → eγ and τ → µγ , | f$_{µτ}$f$_{τ e}$ | , | f$_{τ µ}$f$_{µe}$ | and | f$_{τ e}$f$_{eµ}$ | are respectively constrained as a function of m$_{ω}$ . The data of rare decays of µ → eee , τ → µµe and τ → µee are also used to constrain the combinations | g$_{µe}$g$_{ee}$ | , | g$_{τ e}$g$_{µµ}$ + g$_{τ µ}$g$_{µe}$ | and | g$_{τ e}$g$_{µe}$ + g$_{τ µ}$g$_{ee}$ | , respectively, depending on m$_{k}$ . The g − 2 data can also be used to constrain a combination of these coupling constants with m$_{ω}$ and m$_{k}$ $^{1}$. 

In the scenario with hierarchical neutrino masses, f$_{ij}$ satisfy f$_{eµ}$ ≃ f$_{eτ}$ ≃ f$_{µτ}$/ 2. The typical relative magnitudes among the coupling constants g$_{ij}$ can be g$_{µµ}$ : g$_{µτ}$ : g$_{τ τ}$ ≃ 1 : m$_{µ}$/m$_{τ}$ : ( m$_{µ}$/m$_{τ}$ ) $^{2}$. For g$_{µµ}$ ≃ 1, the neutrino data and the LFV data give the constraints such as m$_{k}$ > ∼ 770 GeV and m$_{ω}$ > ∼ 160 GeV [10]. On the other hand, the constraints on the couplings and masses are more stringent for the inverted neutrino mass hierarchy. The current data then gives m$_{ω}$ ≃ 825 GeV for g$_{µµ}$ ≃ 1 [10]. One of the notable things in this case is the lower bound on sin $^{2}$2 θ$_{13}$ , which is predicted as around 0.002 [9]. 

## B. Models with TeV-scale Right-handed Neutrinos with a discrete Z$_{2}$ symmetry 

Similar to the tree-level seesaw model, tiny masses of left-handed neutrinos would also come from Majorana masses M$_{N}$ α R of gauge-singlet right-handed neutrinos N α R in the radia- tive seesaw scenario [4–6]. One simple way to realize the absence of the tree-level Yukawa interaction ν i $_{L}$˜ Φ N α R is introduction of a discrete Z$_{2}$ symmetry, with the assignment of the odd quantum number to N α R and the even to the SM particles. To obtain the dimension five operator in Eq. (1) at the loop level, we need to introduce additional Z$_{2}$ -odd scalar fields. The lightest of all the Z$_{2}$ -odd particles can be a candidate of DM if it is electrically neutral. The original model of the radiative seesaw model with such a discrete symmetry is proposed by Krauss, Nasri, and Trodden [4], in which neutrino masses are induced at the three-loop level. In the following, we consider two variant models of the Kraus-Nasri-Trodden (KNT) model. 

