The Scotogenic Model with Two Inert Doublets: Parameters Space and Electroweak Precision Tests

Abstract

In this work, we study a scotogenic extension of the Standard Model featuring two inert scalar doublets and three singlet Majorana fermions, where neutrino masses are generated radiatively at one loop. The lightest among the Majorana fermions and neutral scalars can serve as dark matter candidates. We explore the parameter space, considering theoretical constraints (perturbativity, unitarity, vacuum stability) and experimental limits (lepton flavor violation, Higgs measurements, electroweak precision observables). Our analysis identifies regions where sizable Yukawa couplings naturally arise due to constructive interference in the scalar sector. Additionally, we estimate the oblique parameters, finding that only $ΔT$ is sensitive to charged mass splittings, while $ΔS$ and $ΔU$ remain small across the viable parameter space. However, 60\% of the viable parameter space is excluded by the recent CMS measurement of the $W$ boson mass, since the shift $ΔM_W$ depends on the oblique parameters, particularly $ΔT$ that is sensitive to scalar mass splittings.

Figures (5)

• Figure 1: The 12 Feynman diagrams responsible for neutrino mass generation.
• Figure 2: Top left: Squared scalar mixing angles $s_{H}^{2}$ vs. $s_{A}^{2}$, colored by $s_{C}^{2}$ for the 5000 BPs, that are satisfying all theoretical and experimental constraints mentioned above. Top right: The hierarchy between the minimum and maximum absolute values of the new Yukawa couplings, $\min(|h_{\alpha i}|)$ vs. $\max(|h_{\alpha i}|)$, where the palette represents the lightest Majorana mass $M_{1}$. Bottom left: The total Yukawa coupling strength $\sum_{\alpha i}|h_{\alpha i}|^{2}$ vs. $M_{1}$, and the mass of the lighter charged scalar $m_{H_{1}^{\pm}}$ shown in the palette. Bottom right: The mass splittings between scalar states, $\delta_{\text{even}}$ vs. $\delta_{\text{odd}}$, and $\delta_{\text{charged}}$ shown in the palette.
• Figure 3: The LFV branching ratios for the decays $\mu\to e\gamma$ (right), $\tau\to e\gamma$ (middle), and $\tau\to\mu\gamma$ (left) as functions of the lightest fermion mass $M_{1}$, where the light charged scalar mass $m_{H_{1}^{\pm}}$ is shown in the palette. The horizontal dashed lines indicate the current experimental upper limits.
• Figure 4: The palette shows the Yukawa coupling magnitude $|h|$ across the scalar mixing plane $(s_{H}^{2},s_{A}^{2})$ for three different scalar mass spectra, with a color scale indicating the magnitude of $|h|$. Left (set A): nearly degenerate scalars; Middle (Set B): mild mass splitting; Right (set C): strong mass splitting. Darker (more intense) regions correspond to larger Yukawa couplings needed to reproduce the observed neutrino masses.
• Figure 5: Left panel: The oblique parameters $\Delta S$ vs $\Delta T$ vs $\Delta U$, with the 68%, 95%, and 99% confidence ellipses from global EW fits. Middle panel: EW‐fit $\chi^{2}$ function vs the light charged scalar mass $m_{H_{1}^{\pm}}$, where the charged mass splitting $\delta_{charged}$ is shown in the palette. Right panel: The predicted $W$ boson mass $M_{W}$ as a function of the light charged scalar mass $m_{H_{1}^{+}}$. The palette represents the charged mass splitting parameter $\delta_{charged}$. The CMS central value and its $1\sigma$ uncertainty are indicated by the dashed line and the shaded band, respectively.