I. INTRODUCTION The neutrino data show that neutrinos have tiny masses as compared to the electroweak scale. This is clear evidence for physics beyond the standard model (SM). The data also indicate that the structure of flavor mixing for neutrinos is largely different from that for charged leptons. These facts would suggest that, while charged leptons have Dirac type masses, the neutrino masses are of the Majorana type. The tiny Majorana masses of left- handed neutrinos are generated from the dimension-five effective operators where Λ represents a mass scale, c$_{ij}$ are dimensionless coefficients, and φ 0 is the Higgs boson. After electroweak symmetry breaking, the mass matrix M ij ν for left-handed neutrinos appears as M ij ν = c$_{ij}$ 〈 φ $^{0}$〉$^{2}$/ Λ. As the vacuum expectation value (VEV) 〈 φ $^{0}$〉 of the Higgs boson is O (100) GeV, the observed tiny neutrino masses ( M ij ν < ∼ 0 . 1 eV) are realized when ( c$_{ij}$/ Λ) ∼ O (10 − $^{14}$) GeV − $^{1}$. It has been an interesting problem how we can naturally explain such a small number with less fine tuning. If the operators in Eq. (1) appear at the tree level in the low energy effective theory, Λ has to be as large as O (10 $^{8}$) − O (10 $^{14}$) GeV for c$_{ij}$ being O (10 − $^{6}$) − O (1) to describe the data. For example, in the tree-level seesaw scenario where right-handed neutrinos are introduced, their Majorana masses have to be set much higher than the electroweak scale [1], corresponding to the scale Λ in Eq. (1). Although the scenario is simple, it requires another hierarchy between the mass of right-handed neutrinos and the electroweak scale, and in addition, physics at such a large mass scale is difficult to be tested at collider experiments. Quantum generation of neutrino masses is an alternative way to obtain ( c$_{ij}$/ Λ) ∼ O (10 − $^{14}$) GeV − $^{1}$. Due to the loop suppression factor, Λ in these models can be lower as compared to that in the tree-level seesaw models. Consequently, the tiny neutrino masses would be explained in a natural way by the TeV-scale dynamics without introducing very high mass scales. The original model of this line was proposed by Zee [2], where neutrino masses were generated at the one-loop level. Some variations were considered [3–7], for example, by Zee and Babu [3], Kraus-Nasri-Trodden [4], Ma [5], and the model in Ref. [6]. The last three models contain dark matter (DM) candidates with the odd quantum number under the discrete Z$_{2}$ symmetry. It must be a charming point in these TeV-scale radia- 2 L = c$_{ij}$ 2Λ ν c i $_{L}$ν j $_{L}$φ $^{0}$φ$^{0}$, (1)