The 4D Composite Higgs

TL;DR

The work develops a fully four-dimensional effective description of Composite Higgs Models (CHMs) with partial compositeness, treating the Higgs as a pseudo-Nambu-Goldstone boson arising from a coset such as $SO(5)/SO(4)$ and implementing resonances through a minimal 2-site moose-like construction with complete $G$ multiplets. By expressing results in terms of two-point correlators of the composite sector, the authors compute a finite one-loop Higgs potential and establish clear connections to 5D (deconstructed) models and SILH, while enabling straightforward collider implementation. A central finding is that with a single multiplet of resonances the potential is finite and the Higgs mass correlates with the lightest top partners, yielding testable predictions for LHC searches; non-minimal interactions can further affect resonance decays and the $S$ parameter, providing additional phenomenological flexibility. The framework thus bridges higher-dimensional CHMs and collider phenomenology, offering a practical, symmetry-based approach for exploring natural EWSB and guiding experimental tests at the LHC and beyond.

Abstract

We propose a four dimensional description of Composite Higgs Models which represents a complete framework for the physics of the Higgs as a pseudo-Nambu-Goldstone boson. Our setup captures all the relevant features of 5D models and more in general of composite Higgs models with partial compositeness. We focus on the minimal scenario where we include a single multiplet of resonances of the composite sector, as these will be the only degrees of freedom which might be accessible at the LHC. This turns out to be sufficient to compute the effective potential and derive phenomenological consequences of the theory. Moreover our simplified approach is well adapted to simulate these models at the LHC. We also consider the impact of non-minimal terms in the effective lagrangian which do not descend from a 5D theory and could be of phenomenological relevance, for example contributing to the S-parameter.

Figures (7)

• Figure 1: $Moose$ diagram of the theory. The white site on the left corresponds to the global $G$ symmetry, while the grey ones are gauged.
• Figure 2: Nearest neighbor interactions in the fermion sector. For fields associated to left-handed sources, the left chirality at site $n$ couples to the right chirality at site $n+1$.
• Figure 3: 2-site model $SO(5)/SO(4)$: gauge sector. The first site is the elementary sector, the second the composite sector with $SO(5)\times U(1)_X$ heavy multiplets.
• Figure 4: 2-site model $SO(5)/SO(4)$: fermionic sector. The spontaneous breaking of $SO(5)$ is achieved through Yukawa couplings (\ref{['yuk']}) in the composite sector, here drawn as red squares.
• Figure 5: Masses of the lightest fermionic partners as a function of the Higgs mass for $m_t\in [165,175]$ GeV. On the left $f=500$ GeV and on the right $f=800$ GeV. The six fermionic parameters are varied between $.5$ and $3$ TeV. The gauge contribution corresponds to $f_1=f_2=\sqrt{2}f$ and $m_\rho=2.5$ TeV.