A Minimal Realization of Radiative Dirac Neutrino Masses via a Non-Invertible Fusion Rule

Abstract

We propose a minimal one-loop radiative framework for Dirac neutrino mass matrix. As a consequence, the Yukawa hierarchies among the SM fermions are alleviated, and radiative type-I seesaw framework is realized. To regulate divergent loop contributions, we introduce an effective cutoff scale $Λ\sim 100 \, {\rm TeV}$. By introducing a scalar leptoquark and imposing appropriate assignments of ising fusion rule to the particle content, we successfully realize a minimal construction. Furthermore, the presence of the leptoquark leads to rich phenomenology, including semi-leptonic decays, neutral meson mixing, lepton flavor violations and lepton $g-2$, thereby rendering the model experimentally testable. After formulating each sector of our model, we perform a comprehensive numerical analysis, taking into account all relevant experimental constraints for both normal and inverted hierarchies of neutrino masses. Our analysis reveals characteristic tendencies within the viable parameter space.

Figures (7)

• Figure 1: Dirac neutrino mass matrix at one-loop level after dynamical breaking of IFR. $\mathbbm{I}, \sigma, \epsilon$ in parentheses indicate corresponding assignments of our IFR.
• Figure 2: Neutral meson mixings in terms of $m_S$ in case of NH. Here, blue points satisfy $\sum D_{\nu} \le 120 \, {\rm meV}$, while the red ones do not satisfy.
• Figure 3: Predictions of LFVs and lepton $g-2$ in case of NH, where the color legends are the same as the ones in Fig. \ref{['fig:nh1']}. The dotted horizontal line of ${\rm BR} (\mu \to e \gamma)$ represents the futures accessible sensitivity, ${\rm BR} (\mu \to e \gamma) = 6 \times 10^{-14}$.
• Figure 4: Neutrino observations in case of NH.
• Figure 5: Neutral meson mixings in case of IH, where all the legends are the same as the ones in Fig. \ref{['fig:nh1']}.