Dynamical Determination of the Cut-off Scale in Loop-Induced Neutrino Mass Models with Non-Invertible Symmetry

Abstract

We propose our framework as an effective field theory valid below the cut-off scale $\Lambda$, in which we explain the tiny scale of neutrino masses by integrating a non-invertible symmetry with the dynamical determination of the cut-off scale. In our model, we introduce three families of SU(2)$_L$ quintet fermions ($\Sigma_R$) and a quartet scalar ($\phi_4$), both of which are charged under the Fibonacci fusion rule (FFR). A central feature of this construction is that the vacuum expectation value (VEV) $v_4$ of $\phi_4$ is induced at the one-loop level via dynamical symmetry breaking. To resolve the inherent arbitrariness of the cut-off scale $\Lambda$ in loop-induced VEV models, we identify $\Lambda$ with the scale at which the SU(2)$_L$ gauge coupling $g_2$ encounters the renormalization group evolution (RGE) of $g_2$, naturally fixing the physical cut-off within the range of approximately $10^5$ to $10^7$ GeV. Quantitatively, this framework yields $v_4\sim 0.07-0.1$ GeV, which in turn leads to neutrino Yukawa couplings on the order of $10^{-3}$. This result provides a significantly more natural explanation for the neutrino mass hierarchy compared to standard seesaw models, which typically require couplings as small as $10^{-6}$ or less. Notably, our approach maintains a relatively simple particle content and does not necessitate additional (gauge) bosons for symmetry breaking.