General Composite Higgs Models

Abstract: We construct a general class of pseudo-Goldstone composite Higgs models, within the minimal SO(5)/SO(4) coset structure, that are not necessarily of moose-type. We characterize the main properties these models should have in order to give rise to a Higgs mass around 125 GeV. We assume the existence of relatively light and weakly coupled spin 1 and 1/2 resonances. In absence of a symmetry principle, we introduce the Minimal Higgs Potential (MHP) hypothesis: the Higgs potential is assumed to be one-loop dominated by the SM fields and the above resonances, with a contribution that is made calculable by imposing suitable generalizations of the first and second Weinberg sum rules. We show that a 125 GeV Higgs requires light, often sub-TeV, fermion resonances. Their presence can also be important for the models to successfully pass the electroweak precision tests. Interestingly enough, the latter can also be passed by models with a heavy Higgs around 320 GeV. The composite Higgs models of the moose-type considered in the literature can be seen as particular limits of our class of models.

• The paper investigates generalized composite Higgs models based on SO(5)/SO(4), proposing a Minimal Higgs Potential approach constrained by Weinberg sum rules to achieve a 125 GeV Higgs mass.
• Achieving a Higgs mass around 125 GeV in these models necessitates light fermion resonances, demonstrating a direct correlation between the Higgs mass and resonance masses.
• The theoretical frameworks developed offer practical implications for collider experiments, guiding searches for characteristic signals of composite resonances.

Overview of General Composite Higgs Models

The paper "General Composite Higgs Models" presents a comprehensive investigation into a class of pseudo-Goldstone composite Higgs models derived from the $SO(5)/SO(4)$ coset structure. The focus is to explore models that do not strictly adhere to the moose-type configurations, typically associated with theories of extra-dimensional gauge-Higgs unification. The authors aim to delineate the requisite characteristics of these models to achieve a Higgs mass around 125 GeV.

Key Characteristics and Theoretical Foundations

The study advances the hypothesis of a Minimal Higgs Potential (MHP), proposing that the Higgs potential be dominated by one-loop contributions from the Standard Model (SM) fields alongside the spin 1 and 1/2 resonances. The calculations are performed under the enforcement of generalized Weinberg sum rules, which control the divergences often resurfacing in such models. The system of equations is thus designed to ensure that the potential remains calculable, bypassing a fundamental problem in composite Higgs scenarios—namely, the UV sensitivity of the Higgs potential.

Sub-TeV fermion resonances are essential in these models, as they align with passing electroweak precision tests. Interestingly, the models can also accommodate configurations where the Higgs weighs around 320 GeV while still conforming to required electroweak constraints. This adaptability reveals a broader spectrum of potential phenomenological realizations beyond the lightweight Higgs scenario typically sought.

Numerical Results and Parameterization

Through stringent computational analysis, the paper illustrates that a Higgs mass close to 125 GeV necessitates light fermion resonances, often resulting in a direct correlation between the mass of the Higgs and the masses of these resonances. The work quantifies the contributions from various model classes, employing one vector and one axial gauge field resonance and finding these sums to be pivotal for a viable Higgs mass proposition.

Furthermore, the authors show that models designed under their purview may indeed circumvent the large $S$ parameter problem when more vector or axial resonances are incorporated, which offers a path to achieving compatibility with experimental data without excessive fine-tuning.

Implications and Future Prospects

The implications of this research encompass both theoretical insights and pragmatic pathways for future model construction. By embracing a more generalized class of composite Higgs models without decretive constraints like strict moose-type architectures, this study broadens the toolkit available to researchers exploring beyond the Standard Model scenarios.

Additionally, the frameworks devised by this research could substantially impact collider experiment methodologies, especially in identifying characteristic signals of composite resonances. As a result, future developments in particle physics—both theoretical refinements and experimental validations—could benefit significantly from the foundational insights laid in this work.

While the current models provide a robust mechanism for achieving desired Higgs phenomenology, further studies are anticipated to better understand the deeper implications of the MHP hypothesis and explore if alternative symmetry mechanisms could further streamline these composite Higgs structures. This exploration could lead to discovering a symmetry principle that naturally aligns with or extends beyond the current understanding, offering potential insights into other outstanding problems in particle physics, such as flavor hierarchies and neutrino masses.