UV Completions of Composite Higgs Models with Partial Compositeness

TL;DR

We construct UV completions of bottom-up composite Higgs models with a pNGB Higgs and partial compositeness by embedding the composite sector in ${ m SO}(N)$ ${ m N}=1$ SUSY gauge theories and exploiting Seiberg duality. Two explicit realizations are presented: Model I with a semi-composite right-handed top and Model II with a fully composite right-handed top; in both cases the SM–composite fermion mixing arises from IR flow of UV trilinear Yukawas, and the Higgs emerges as a NGB of the ${ m SO}(5)/{ m SO}(4)$ coset. Gauge and fermion resonances have masses controlled by different couplings, enabling a natural separation of scales, while the Higgs potential remains radiatively generated and protected by SUSY and its Nambu–Goldstone nature. The main challenge identified is the appearance of Landau poles for SM gauge couplings at relatively low energies ($ ext{10}^2$–$ ext{10}^3$ TeV), which complicates embedding all SM fermions via partial compositeness and motivates exploring alternative SUSY-breaking mechanisms or flavor structures. The work thus provides a concrete, calculable route to UV-complete pCHMs and clarifies key phenomenological and theoretical hurdles, including the role of scalar resonances and CCWZ matching in such completions.

Abstract

We construct UV completions of bottom-up models with a pseudo Nambu-Goldstone Boson (NGB) composite Higgs and partial compositeness, admitting a weakly coupled description of the composite sector. This is identified as the low energy description of an SO(N) supersymmetric gauge theory with matter fields in the fundamental of the group. The Higgs is a NGB associated to an SO(5)/SO(4) coset of a global symmetry group and is identified with certain components of matter fields in a Seiberg dual description of the theory. The Standard Model (SM) gauge fields are obtained by gauging a subgroup of the global group. The mass mixing between elementary SM and composite fermion fields advocated in partial compositeness arise from the flow in the IR of certain trilinear Yukawa couplings defined in the UV theory. We explicitly construct two models of this kind. Most qualitative properties of the bottom-up constructions are derived. The masses of gauge and fermion resonances in the composite sector are governed by different couplings and can naturally be separated. Accommodating all SM fermion masses within the partial compositeness paradigm remains the main open problem, since the SM gauge couplings develop Landau poles at unacceptably low energies.