Radiative lepton model in a non-invertible fusion rule

TL;DR

The paper introduces a radiative lepton-mass model built on a $Z_2$ gauging of a $Z_5^{NI}$ non-invertible fusion rule, which forbids tree-level lepton masses while enabling one-loop generation of charged-lepton and neutrino masses. The charged-lepton sector originates from dynamical breaking of the fusion rule and links to LFV, $g-2$, and EDMs, while the neutrino sector obtains masses at one loop without breaking the rule, yielding testable predictions for CP phases and $0 uetaeta$. Through a comprehensive $ riangle ext{χ}^2$-based scan under NH and IH, the authors identify benchmark regions consistent with oscillation data and LFV/$g-2$/EDM constraints, uncovering characteristic phase correlations and EDM magnitudes that can exceed minimal flavor-violation expectations. The work highlights distinctive phenomenology, including stringent electron EDM constraints implying upper bounds on $m_{ee}$ and predicting sizable muon/tau EDMs, offering avenues for near-future experimental tests and refining the role of non-invertible fusion rules in beyond-Standard Model model-building.

Abstract

We propose a radiatively induced lepton mass model introducing a $Z_2$ gauging $Z_5$ fusion rule. In our framework, the charged-lepton mass matrix is generated at one loop level via dynamical breaking of the fusion rule. On the other hand, the neutrino mass matrix is induced at one-loop level without breaking the fusion rule. As a direct consequence of the loop induced charged lepton masses, we can also consider lepton flavor violations, electron and muon $g-2$, and charged-lepton electric dipole moments that come into our valid phenomenological discussion. Then, we perform numerical analysis and show some interesting tendency on Dirac CP phase, two Majorana phases, charged-lepton electric dipole moments and the neutrinoless double beta decay, all of which depends on their arguments where we fix the absolute values of our free parameters in order to satisfy experimental data of the lepton masses and mixing angles.

Figures (4)

• Figure 1: Allowed regions for $\langle m_{ee}\rangle$ in terms of phases $\delta_{\rm CP}$ (blue), $\alpha_2$ (red), and $\alpha_3$ (green) in case of NH. Brown (lower) and purple (upper) dashed lines correspond to $\langle m_{ee} \rangle = 28 \ {\rm meV}$ and $122 \ {\rm meV}$, respectively.
• Figure 2: Allowed regions for EDMs in terms of phases $\delta_{\rm CP}$, $\alpha_2$, and $\alpha_3$ in case of NH, with same color manner as in Fig. \ref{['fig:nh1']}. Black dashed line is the direct experimental upper bound, while brown one corresponds to the indirect upper bound.
• Figure 3: Allowed regions for $\langle m_{ee}\rangle$ in terms of phases $\delta_{\rm CP}$ (blue), $\alpha_2$ (red), and $\alpha_3$ (green) in case of IH. The meanings of dashed lines are same as in Fig. \ref{['fig:nh1']}.
• Figure 4: Same plot as Fig. \ref{['fig:nh2']}, but for the case of IH.