A radiative seesaw model in a non-invertible selection rule with the assistance of a non-holomorphic modular $A_4$ symmetry

TL;DR

The paper addresses the challenge of generating tiny neutrino masses while incorporating a stable dark matter candidate by building a radiative two-loop seesaw model. It employs a Z_3 Tambara-Yamagami non-invertible fusion rule and a non-holomorphic modular A_4 symmetry to forbid tree-level masses and interactions, enabling loop-induced masses for both the heavy fermions and the active neutrinos. A detailed mass-matrix analysis and a χ^2 fit to NuFIT 6.0 show that normal ordering is viable with specific predictions for CP phases, neutrinoless double beta decay, and the DM relic density in agreement with Planck, whereas inverted ordering is disfavored by the cosmological mass bound. The framework yields testable predictions for lepton flavor violation and the muon anomalous magnetic moment, while keeping the fermionic dark matter relic density in the observed range, highlighting a tightly constrained and falsifiable radiative seesaw scenario.

Abstract

We propose a two-loop neutrino mass model where fermionic and bosonic dark matter (DM) candidates are simultaneously connected to the neutrinos. But the fermionic DM candidate is favored compared to the bosonic one due to generating the fermionic DM mass at one-loop level. In order to obtain our desired Lagrangian and Higgs potential, we introduce a $Z_3$ gauging TY non-invertible fusion rule with the assistance of a non-holomorphic modular $A_4$ symmetry. The fusion rule forbids the mass of DM candidate at tree level but its mass is generated at one-loop level where the DM mass term dynamically violates the fusion rule. After that, the neutrino mass matrix is induced at one-loop level where a remnant $Z_2$ symmetry is still remained. The symmetry assures the stability of our DM candidate. The non-holomorphic modular $A_4$ symmetry plays a role in forbidding the interactions between the SM particles and heavier fermions $X_R$ and an isospin singlet inert scalar boson $S_0$ that run in the DM mass loop, in addition to reduction our free parameters that leads to our predictions for lepton sector. We perform $χ^2$ numerical analysis for the lepton masses, mixing angles, and phases, and we show several predictions for NH and IH. Then, we demonstrate our lepton flavor violations, muon anomalous magnetic dipole moment, and the relic density of the DM candidate fixing the best fit point of the lepton sector.

Figures (5)

• Figure 1: Allowed region for Im[$\tau$] in terms of Re[$\tau$] within the fundamental region through the numerical $\chi^2$ analysis. Here, the red points are within 5$\sigma$, yellow ones within 3$\sigma$, green ones within 2$\sigma$, and, blue ones within 1$\sigma$.
• Figure 2: Allowed regions for Majorana phases (left), $\langle m_{ee}\rangle$ (center), and $\delta_{\rm CP}$ (right) in term $\sum m_i$ meV, where all the color legends are the same as the ones of Fig. \ref{['fig:tau_nh']}. In the center, the cyan region is experimentally allowed, the magenta and black dotted vertical lines (in the center and right) are respectively the upper bounds of 72 meV (DESI and CMB) and 120 meV (the minimal cosmological model), the horizontal dotted line at 28 meV (in the center) represents the lower upper bound on KamLAND-Zen data.
• Figure 3: Allowed regions for LFVs (left) and muon $g-2$ (right) in terms of the DM mass. In the left figure, the blue, red, yellow points correspond allowed region of BR($\mu\to e \gamma$), BR($\tau\to e \gamma$), and BR($\tau\to e \gamma$), respectively.
• Figure 4: Allowed region for Im[$\tau$] in terms of Re[$\tau$] within the fundamental region through the numerical $\chi^2$ analysis. Here, the red points are within 5$\sigma$, yellow ones within 3$\sigma$, green ones within 2$\sigma$, and, blue ones within 1$\sigma$.
• Figure 5: Allowed regions for Majorana phases (left), $\langle m_{ee}\rangle$ (center), and $\delta_{\rm CP}$ (right) in term $\sum m_i$ meV, where all the color legends are the same as the ones of Fig. \ref{['fig:tau_nh']}. In the center, the cyan region is experimentally allowed, the magenta and black dotted vertical lines (in the center and right) are respectively the upper bounds of 72 meV (DESI and CMB) and 120 meV (the minimal cosmological model), the horizontal dotted line at 28 meV (in the center) represents the lower upper bound on KamLAND-Zen data.