The Discrete Composite Higgs Model

TL;DR

The paper presents the Discrete Composite Higgs Model (DCHM), a concrete four-dimensional realization of the composite Higgs paradigm that mirrors the predictive success of 5D holographic models while remaining simple enough for collider phenomenology. By employing dimensional deconstruction into two- and three-site structures and using an SO(5)/SO(4) coset, the authors develop a calculable framework where the Higgs potential is finite at one loop, thanks to collective breaking in the three-site model. They provide a detailed analysis of the Higgs potential, electroweak precision constraints, and the mass spectra of gauge and fermionic resonances, highlighting the role of spurions and NDA counting in establishing calculability and guiding parameter choices. The work emphasizes the presence of light top partners and heavy vector resonances as hallmark predictions, and argues for the DCHM’s practicality for LHC studies and its status as a complete, predictive alternative to higher-dimensional constructions. The model’s clear structure and testable implications offer a tractable path toward probing composite-Higgs dynamics at colliders.

Abstract

We describe a concrete, predictive incarnation of the general paradigm of a composite Higgs boson, which provides a valid alternative to the standard holographic models in five space-time dimensions. Differently from the latter, our model is four-dimensional and simple enough to be implemented in an event generator for collider studies. The model is inspired by dimensional deconstruction and hence it retains useful features of the five-dimensional scenario, in particular, the Higgs potential is finite and calculable. Therefore our setup, in spite of being simple, provides a complete description of the composite Higgs physics. After constructing the model we present a first analysis of its phenomenology, focusing on the structure of the Higgs potential, on the constraints from the EWPT and on the spectrum of the new particles.

Figures (8)

• Figure 1: Pictorial representation of the two-site DCHM. The Goldstone matrix $U$ is depicted as a "link", i.e. a segment with vertical lines at the endpoints representing the global $\textrm{SO}(5)_L$ and $\textrm{SO}(5)_R$ groups. The SM and $\widetilde{\rho}$ fields are located at two different "sites", represented respectively by a gray square or circle. The first site can be interpreted as the elementary group $\textrm{SU}(2)_L^0 \times \textrm{U}(1)_Y^0$ under which only $W$ and $B$ transform, the second one is the analogous group for $\widetilde{\rho}$, $\widetilde{\textrm{SO}}(4)$. The corresponding gauge couplings, or better their associated spurions $\mathcal{G}$, $\mathcal{G}'$ and $\widetilde{\mathcal{G}}$ are also indicated. Their location reminds the symmetry groups under which they transform.
• Figure 2: The same as figure \ref{['figstruct0']}, but for the three-site model.
• Figure 3: The matter sector of the two-site DCHM. The $q_L$ and $t_R$ fermions live at the first site, which indicates that they transform under the elementary group $\textrm{SU}(2)_L^0\times \textrm{U}(1)_R^0\times \textrm{U}(1)_X^0$. The resonance $\widetilde{\psi}$ transforms instead with the $\textrm{SO}(5)_R$($\times\textrm{U}(1)_X$) $\sigma$-model group, and therefore it is placed at the right endpoint of the link. The spurions $\Delta_{L/R}$ and $\widetilde{m}$ are also indicated, their location reminds the symmetry groups under which they transform.
• Figure 4: The matter sector of the three-site DCHM.
• Figure 5: Schematic structure of the three-site DCHM.