1. The Ma model The model in Ref. [5], which we here refer to as the Ma model, is the simplest radiative seesaw model with right-handed neutrinos N α $_{R}$, in which the discrete Z$_{2}$ symmetry is intro- duced and its odd quantum number is assigned to N α $_{R}$. The Higgs sector is composed of two Higgs doublet fields, one of which (Ξ) is Z$_{2}$ odd. As long as the Z$_{2}$ symmetry is exact, the neutral components of Ξ do not receive VEVs. We have one SM-like Higgs boson h , and four physical Z$_{2}$ -odd scalar states; ξ 0 r (CP-even), ξ 0 i (CP-odd) and ξ ± as physical scalar states. This Z$_{2}$ odd Higgs doublet is sometimes called as the inert Higgs doublet [15] or the dark scalar doublet [17]. The LEP II limits are studied in this model in Ref. [18]. The neutrino masses are generated at the one loop level via the diagram depicted in Fig. 1 (center), in which Z$_{2}$ odd particles, ξ 0 and N α $_{R}$, are in the loop. The mass matrix is calculated as where ˆ h α i are the Yukawa coupling constants of ν i L ˜ Ξ N α $_{R}$, M$_{N}$ α R is the Majorana mass of the α -th generation right-handed neutrino N α $_{R}$, λ$_{5}$ = ( m 2 ξ$_{i}$ − m 2 $_{ξ$_{r}$}$) /v $^{2}$, r α = m 2 $_{0}$/M 2 N α R with m$_{0}$ = ( m$_{ξ}$$_{i}$ + m$_{ξ}$$_{r}$ ) / 2, where m$_{ξ}$$_{r}$ and m$_{ξ}$$_{i}$ are masses of ξ 0 r and ξ 0 $_{i}$, respectively. The universal scale for neutrino masses is determined by the one-loop suppression factor 1 / (16 π $^{2}$), λ$_{5}$ and M$_{N}$ α $_{R}$. The flavor structure in M ν ij is realized by the combination of ˆ h α i ˆ h α $_{j}$/M$_{N}$ α $_{R}$. Therefore, for M$_{N}$ α R ∼ O (1) TeV, the combination of the coupling constants would be | λ$_{5}$ | ( ˆ h α i ) 2 ∼ 10 − $^{9}$. In this model, there are two scenarios with respect to the DM candidate; i.e., the lightest right-handed neutrino N 1 R or the lightest Z$_{2}$ -odd neutral field ( ξ 0 r or ξ 0 $_{i}$). For both cases, there are parameter regions where the neutrino data are adjustable without contradicting other phenomenological constraints [13]. In this Letter, we consider the case where the dark doublet component ξ 0 r is the DM candidate $^{2}$. When the mass of the DM is around 50 GeV, the typical value of λ$_{5}$ ∼ 10 − 2 for the neutrino masses gives the mass difference between ξ 0 r and ξ 0 i about 10 GeV. 3 The relic abundance of such DM is consistent with the WMAP data [19]. 2 In Ref. [13], the scenario where the lightest right-handed neutrino is DM is explored. 3 In order to avoid constraint from the DM direct search results, it is required that | λ$_{5}$ | > 10 − $^{6}$. 6 M ν ij = − 3 ∑ α =1 ( 1 16 π 2 ) ˆ h α i ˆ h α $_{j}$λ$_{5}$ v 2 M$_{N}$ α R 1 1 − r α ( 1 + 1 1 − r α ln r α ) , (5)