paper

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

arXiv:2603.17587

Abstract

We propose our framework as an effective field theory valid below the cut-off scale $I^$ , 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 ( $I^£_{R}$ ) and a quartet scalar ( $I ¨ _{4}$ ), 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 $I ¨ _{4}$ is induced at the one-loop level via dynamical symmetry breaking. To resolve the inherent arbitrariness of the cut-off scale $I^$ in loop-induced VEV models, we identify $I^$ 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 $1 0^{5}$ to $1 0^{7}$ 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 $1 0^{- 3}$ . 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 $1 0^{- 6}$ or less. Notably, our approach maintains a relatively simple particle content and does not necessitate additional (gauge) bosons for symmetry breaking.

12 pages, 2 figures, 1 table