Dirac Scoto Inverse-Seesaw from $A_4$ Flavor Symmetry

TL;DR

This work presents a Dirac scotogenic-like radiative model based on $A_4$ flavor symmetry, where breaking $A_4$ to a residual $\\mathcal{Z}_2$ stabilizes dark matter and enables a scoto-seesaw mechanism that generates Dirac neutrino masses. The model combines a tree-level inverse-seesaw with a one-loop scotogenic contribution, yielding two nonzero neutrino masses and a massless state, and it accommodates both normal and inverted ordering. Neutrino-sector observables tightly constrain the singlet VEV $u$, which in turn limits dark-sector scalar and fermion masses to around the 10s–700 GeV range, linking DM phenomenology to neutrino data. Correlations among $\\sum m_i$, $\\langle m_\\beta \\rangle$, and $\\delta_{CP}$-$\\theta_{23}$ predictions provide concrete, testable signatures for upcoming neutrino experiments and dark-sector searches, while CLFV rates place additional constraints on the parameter space.

Abstract

We present a Dirac scotogenic-like one loop radiative model where the stability of dark matter is intricately linked to the breaking of $A_4$ flavor symmetry. This breaking induces a $Z_2$ dark symmetry, stabilizing the dark matter candidate. The breaking of $A_4 \to Z_2$ leads to cutting the loop and facilitating a "scoto inverse-seesaw" mass mechanism responsible for neutrino mass generation. This elucidates the explicit explanation of two mass-squared differences, $Δm^2_{\rm{atm}}$ and $Δm^2_{\rm{sol}}$ observed in neutrino oscillations. Our model accounts for normal and inverted ordering of neutrino masses, revealing sharp correlations between $\sum m_i$ and $\langle m_β \rangle$. It also shows strong compatibility with current data in the $δ_{CP}$-$θ_{23}$ plane. Moreover, stringent constraints on scalar masses narrow down the viable dark matter mass regions, accommodating $SU(2)_L$ singlet and doublet scalar dark matter as well as fermionic dark matter. Additionally, our model presents a viable avenue for addressing lepton flavor violating decays while remaining consistent with current experimental constraints.

Figures (18)

• Figure 1: Dirac scotogenic model for neutrino mass generation.
• Figure 2: Correlation between the upper bound of dark sector scalar masses and singlet scalar VEV.
• Figure 3: Breaking of $A_4 \to \mathcal{Z}_2$ leading to a scoto inverse-seesaw mass mechanism. The residual $\mathcal{Z}_2$ stabilizes the DM candidate running inside the loop. We have shown the $A_4$ ($\mathcal{Z}_2$) charges in the left (right) panel of the diagram.
• Figure 4: Correlation between sum of neutrino masses $\sum m_i$ and effective mass $\langle m_{\beta} \rangle$ of beta decay in the NO case.
• Figure 5: Correlation between $\delta_{CP}$ and $\theta_{23}$ for NO, where left (right)-panel represents case-I (-II).