Classification of Higgs sectors from group theoretical properties of UV gauge theories

TL;DR

This work investigates an ultraviolet completion of extended Higgs sectors by positing an $SU(2)_H$ gauge theory with confinement, whose fundamental flavor structure dictates the low-energy bound-state scalars observed as the extended Higgs content. By analyzing the flavor symmetry $SU(2n)$ and its explicit breaking patterns, the authors classify the resulting scalar spectra for $n\le 4$ into familiar frameworks such as 2HDM, inert doublet, Zee-type, Zee-Babu, dark matter scenarios, and neutrino-mass models, all organized by UV charge assignments and discrete symmetries. The mechanism yields Yukawa interactions via confinement-induced four-fermion operators, with a natural Yukawa alignment in the 2HDM limit and a shared flavor structure across different bound-state fields. The study highlights a coherent UV picture in which low-energy Higgs sectors emerge as bound states determined by the underlying flavor symmetries, and discusses implications for phenomenology, including DM candidates, neutrino masses, and potential connections to grand unification. Overall, the work offers a novel route to UV-complete, symmetry-guided extended Higgs sectors and motivates further exploration of their nonperturbative dynamics and experimental signatures.

Abstract

Extended Higgs sectors are often introduced to explain phenomena beyond the standard model (BSM). The existence of multiple scalar fields may cause the Landau pole below the Planck scale. In this case, the low-energy theory may be replaced by an asymptotic-free gauge theory. In this paper, we consider an $\mathrm{SU}(2)$ gauge theory with confinement as such an ultraviolet theory of the extended Higgs sectors. We investigate the relation between scalar particle contents at the low energy and group theoretical properties of fundamental fermions of the gauge theory. We find that particle contents of various extended Higgs sectors previously proposed to explain the BSM problems are deduced by each charge assignment of flavor symmetry of the fundamental fermions of the $\mathrm{SU}(2)$ gauge symmetry. Our findings may provide a new picture for the ultraviolet completion of the extended Higgs sectors.