Dynamical scotogenic generation of the Linear and Inverse seesaws

TL;DR

This work proposes a scotogenic extension of the Standard Model with a local $U(1)'$ gauge symmetry and discrete $Z_3\otimes Z_4$ symmetries, where linear and inverse seesaw contributions to active neutrino masses are dynamically generated at the two-loop level. The model yields two dark matter candidates (scalar and fermionic) stabilized by residual symmetries, with the fermionic DM mass generated at one loop and scalar DM at tree level, linking neutrino mass generation to dark matter phenomenology. A main finding is that the inverse seesaw dominates the atmospheric mass splitting while the linear seesaw accounts for the solar splitting; the parameter scan shows a mild preference for normal ordering and predicts accessible charged lepton flavor violation signals, especially from scalar-sector loops, within upcoming experiments. The framework provides a coherent link between neutrino mass generation, dark matter stability, and testable phenomenology at both energy and intensity frontiers, with potential implications for collider searches and lepton-flavor experiments.

Abstract

We propose an economical model in which the tiny active neutrino masses arise from an interplay of linear and inverse seesaw mechanisms. The Standard Model is extended by a local $U(1)'$ gauge symmetry and discrete $\mathbb{Z}_{3}\otimes\mathbb{Z}_{4}$ symmetries, together with gauge-singlet scalars and neutral leptons. Owing to the preserved discrete symmetries after spontaneous symmetry breaking, the linear and inverse seesaw mechanisms are dynamically generated at the two-loop level, while the same symmetries ensure the stability of both scalar and fermionic dark matter candidates. One of the distinctive features of the model is a fermionic dark matter candidate whose mass is generated at one loop, whereas scalar dark matter masses arise at tree level. The model satisfies current constraints from neutrino oscillation data, dark matter direct detection, invisible Higgs decays, $Z'$ searches, and charged lepton flavor violation, in addition we also discuss predictions for muonium states. The outcome of our analysis is that the inverse seesaw contribution dominates over the linear one, suggesting that atmospheric neutrino mass squared splitting arises from the inverse seesaw mechanism, whereas the solar one is generated from the linear seesaw. Finally, our model offers an explanation of the hierarchy between the atmospheric and solar neutrino mass squared splittings, in addition to the smallness of active neutrino masses, feature not presented in many low-scale seesaw models. In addition, our parameter-space scan shows a slight preference for the normal neutrino mass ordering.

Figures (6)

• Figure 1: Two-loop diagrams for the neutrino mass submatrix $\varepsilon$ (a) and for the lepton number violating Majorana mass term $\mu$ (b).
• Figure 2: Correlation among cLFV observables. Points allowed by the model and consistent with neutrino oscillation data assuming normal (inverted) ordering are shown in the left (right) panel. Current bounds are indicated by solid lines, while future projections are shown as dashed lines.
• Figure 3: Most constraining cLFV $\tau$ decays are shown. In the left panel, we display $\mathrm{Br}(\tau \to \mu\gamma)$ as a function of $M_N$, and in the right panel, the equivalent plot for $\mathrm{Br}(\tau \to \mu\gamma)$. Red and blue crosses correspond to predictions consistent with normal (NO) and inverted (IO) neutrino mass orderings, respectively. Grey crosses indicate points excluded by other experimental constraints. The solid black lines denote the current experimental limits, while future projections are shown as dashed lines.
• Figure 4: Points consistent with neutrino oscillation data and allowed by the model. Red (blue) points correspond to normal (inverted) mass ordering. The gray shaded regions denote current experimental constraintsFernandez-Martinez:2023phj, while gray points are excluded by existing cLFV constraints.
• Figure 5: Correlation between the inverse seesaw parameter ($\mu$) and the linear seesaw term ($\varepsilon$). Points consistent with neutrino oscillation data and allowed by the model are shown. Red (blue) points correspond to normal (inverted) mass ordering, while gray points are excluded by current cLFV constraints.