Two-loop induced Majorana neutrino mass in a radiatively induced quark and lepton mass model

A two-loop induced radiative neutrino model is proposed as an extension of our previous work in which the first- and second-generation standard model fermion masses are generated at the one-loop level in both quark and lepton sectors. Then we discuss the current neutrino oscillation data, lepton flavor violations, muon anomalous magnetic moment, and a bosonic dark matter candidate, for both the normal and inverted neutrino mass hierarchy. Our numerical analysis shows that fewer hierarchical Yukawa coupling constants can fit the experimental data with TeV-scale dark matter.

Figure 1

The two-loop diagram for generating a Majorana mass term for active neutrinos.

Figure 2

The plots at the left upper (NH) and the right upper (IH) represent the allowed region in terms of the DM mass and the muon $g-2$. The red region is the case of $m_{{\eta }^{\pm }}=m_{H_2}\in [11M_X/10,12M_X/10]$, and the maximum value of muon $g-2$ reaches $\mathcal{O}(1.0\times {10}^{-13})$ for NH and $\mathcal{O}(4.0\times {10}^{-13})$ for IH. On the other hand, the blue one is the case of $m_{{\eta }^{\pm }}=m_{H_2}\in [11M_X/10,11.1M_X/10]$, and the maximum value of muon $g-2$ reaches $\mathcal{O}(1.5\times {10}^{-13})$ for NH and $\mathcal{O}(5.0\times {10}^{-13})$ for IH. One also finds the lower bound of the DM mass to be $1000\mathrm{GeV}\lesssim M_X$, which comes from the LFVs for both cases. The plot at the bottom represents the allowed region in terms of the DM mass and its relic density. The red region and blue region correspond to the same parameter setting as the upper figures. These analyses give the constraints on the DM mass and $\mathrm{\Delta }{a}_{\mu }$: $1000\mathrm{GeV}\lesssim M_X\lesssim 4500\mathrm{GeV}$, and $0\lesssim \mathrm{\Delta }{a}_{\mu }\lesssim (1–1.5)\times {10}^{-13}$ for NH and $0\lesssim \mathrm{\Delta }{a}_{\mu }\lesssim (4–5)\times {10}^{-13}$ for IH.

Figure 3

The left figure (NH) and the right one (IH) represent the allowed region in terms of the DM mass and $(y_S^{\prime }{)}_{e\mu }$. These figures tell us that its scale of IH is about 10 times as large as the one of NH, where $m_{{\eta }^{\pm }}=m_{H_2}\in [11M_X/10,12M_X/10]$ is used for both cases, since its scale does not depend on the degeneracy.