A theoretical account of tiny multi-Higgs vacuum expectation values from non-invertible symmetry

TL;DR

This paper introduces a minimal theoretical mechanism using non-invertible symmetries to naturally generate tiny multi-Higgs vacuum expectation values, consistent with experimental constraints.

Contribution

It proposes a novel, symmetry-based approach to explain small exotic Higgs VEVs without additional particles, applicable to various neutrino mass models.

Findings

VEVs naturally suppressed to 10^{-3}-10^{-2} GeV

No extra particles needed for loop-induced VEVs

Compatible with neutrino mass generation mechanisms

Abstract

We propose a novel mechanism to explain the naturally small vacuum expectation values (VEVs) of exotic multi-Higgs fields by employing non-invertible symmetries. Specifically, we introduce an $SU(2)_L$ quartet $H_4$ and a quintet $H_5$ within the framework of the minimal Fibonacci fusion rule (FFR). This non-invertible symmetry strictly forbids the generation of tree-level VEVs for these exotic fields. However, once the symmetry is broken, these VEVs are generated radiatively at the one-loop level.This mechanism is highly minimal, as it requires no additional loop-inducing particles. We demonstrate that for various benchmark energy scales, the resulting VEVs are naturally suppressed to the order of $10^{-3}-10^{-2}$ GeV, satisfying experimental constraints from the $\rho$ parameter. Finally, we illustrate the phenomenological viability of this setup by applying it to three representative neutrino mass models: the type-III seesaw, the Dirac neutrino seesaw, and the inverse seesaw mechanisms.