Neutrino mass model at a three-loop level from a non-holomorphic modular $A_4$ symmetry

TL;DR

This work develops a three-loop radiative neutrino-mass model based on a non-holomorphic modular $A_4$ symmetry and demonstrates that a minimal parameter set can fit lepton masses and neutrino oscillation data, with a rank-2 neutrino mass matrix implying $m_1=0$ in NH. The model yields concrete predictions for neutrino observables, including $\sum m_ν \approx 58-60$ meV and $\langle m_{ee} \rangle \approx 1-4$ meV, while LFV and muon g-2 are analyzed under current constraints; however, achieving the observed DM relic density within perturbativity is problematic in the minimal setup. A simple extension by adding a singlet scalar $S_0$ with a Higgs-portal coupling can restore the correct relic density without modifying the neutrino sector predictions, enabling resonant and non-resonant annihilation channels. Overall, the paper links a highly constrained flavor-symmetric framework to testable predictions in neutrino physics, LFV, DM, and collider phenomenology, offering clear avenues for near-future experimental tests.

Abstract

We study a three-loop induced neutrino mass scenario from a non-holomorphic modular $A_4$ flavor symmetry and reach the minimum scenario leading predictions of the lepton masses, mixing angles, and Dirac and Majorana phases, which are shown through the chi square analyses. In addition, we discuss the lepton flavor violations, muon anomalous magnetic moment, lepton universality, and relic density of the dark matter candidate. And, we find that we need to extend our model if we satisfy the observed relic density of dark matter within the limit of perturbation where it can be done by adding one singlet scalar boson without changing predictions in neutrino sector.

Figures (5)

• Figure 1: Allowed region for real $\tau$ and imaginary $\tau$ in NH.
• Figure 2: Allowed regions for absolute values (left) and argument ones (right) of $\tilde{d}_\nu$ and $\tilde{c}_\nu$ in NH.
• Figure 3: Allowed regions for $\delta_{CP}$ deg (left) and $\langle m_{ee}\rangle$ meV (right) in terms of $\sum D_\nu$ meV in NH. The vertical magenta dotted line is upper bound on results of Planck+DESI DESI:2024mwx$\sum D_\nu\le$72 meV. The cyan region in the left panel indicates allowed region by experimental result of Nufit 6.0.
• Figure 4: Allowed region for $\langle m_{ee}\rangle$ meV (left) and $\delta_{CP}$ deg (right) in terms of $\delta_{CP}$ deg in NH.
• Figure 5: Allowed region for electron $g-2$(left), muon $g-2$(center), and LFVs(right), where these points do not satisfy the observed relic density.