Radiative Dirac Neutrino Masses from Modular $S_3$ Symmetry in an Axion Model

TL;DR

This work presents a unified framework in which Dirac neutrino masses arise radiatively at one loop within a KSVZ-type axion model endowed with a global U(1)_{PQ} symmetry and a modular S_3 flavor structure. The mechanism yields a rank-2 neutrino mass matrix with one massless state and links leptonic flavor to axion phenomenology, simultaneously addressing the strong CP problem and dark matter. The axion sector fixes f_a and m_a in a range that yields a detectable axion–photon coupling g_{aγγ}, with predictions compatible with current astrophysical bounds and within reach of upcoming experiments. A detailed χ^2 analysis for normal and inverted hierarchies constrains τ and yields specific correlations among neutrino masses, mixing angles, and δ_{CP}, while cLFV and lepton g−2 predictions remain consistent with experimental limits. Overall, the model provides a testable, interconnected picture of neutrino masses, flavor, axion DM, and CP violation that can be probed by neutrino experiments and dedicated axion searches.

Abstract

We present a unified axion model framework that simultaneously addresses the origin of neutrino masses, leptonic flavor structure, the strong CP problem, and dark matter. The model is based on a global $U(1)_{\rm PQ}$ symmetry combined with a modular $S_3$ symmetry and is realized within a novel class of KSVZ-type axion model. Exotic colored fermions and scalars mediate radiative neutrino mass generation at the one loop-level. The PQ charge assignment forbids tree-level neutrino masses and leaves a residual $Z_3$ symmetry that ensures the Dirac nature of neutrinos. In the minimal realization, the neutrino mass matrix is of rank two, predicting one massless neutrino. Consequently, the sum of neutrino masses is constrained for both the normal and inverted hierarchies. We analyze the implications for charged lepton flavor violation and the lepton $g-2$. The axion emerging from this framework dynamically resolves the strong CP problem and accounts for the observed dark matter abundance. Notably, the predicted axion-photon coupling is within reach of upcoming experiments and consistent with existing astrophysical and cosmological bounds.

Figures (8)

• Figure 1: One loop Dirac neutrino masses mediated by colored fields.
• Figure 2: Allowed region of Re[$\tau$] and Im[$\tau$] on the fundamental region in case of NH. Here, green points represent the range of ($1\sigma-2\sigma$), yellow ones ($2\sigma-3\sigma$), and red ones ($3\sigma-5\sigma$).
• Figure 3: Allowed regions on $s^2_{12}$ (left), $s^2_{13}$ (right), $s^2_{23}$ (bottom) in terms of $\sum D_\nu$, where the color legends of plots are the same as the case of Fig. \ref{['fig:tau_nh']}.
• Figure 4: Allowed regions on $\delta_{\rm CP}$ (left) and $m_{\nu_e}$ (right) in terms of $\sum D_\nu$, where the color legends of plots are the same as the case of Fig. \ref{['fig:sum_angles_nh']}.
• Figure 5: Allowed region on Im[$\tau$] in terms of Re[$\tau$], where the color legends of plots are the same as the one in Fig. \ref{['fig:tau_nh']}.