Composite Higgses

Abstract: We present an overview of composite Higgs models in light of the discovery of the Higgs boson. The small value of the physical Higgs mass suggests that the Higgs quartic is likely loop generated, thus models with tree-level quartics will generically be more tuned. We classify the various models (including bona fide composite Higgs, little Higgs, holographic composite Higgs, twin Higgs and dilatonic Higgs) based on their predictions for the Higgs potential, review the basic ingredients of each of them, and quantify the amount of tuning needed, which is not negligible in any model. We explain the main ideas for generating flavor structure and the main mechanisms for protecting against large flavor violating effects, and present a summary of the various coset models that can result in realistic pseudo-Goldstone Higgses. We review the current experimental status of such models by discussing the electroweak precision, flavor and direct search bounds, and comment on UV completions and on ways to incorporate dark matter.

• The paper presents a systematic classification of composite Higgs models based on their Higgs potential and required tuning.
• It analyzes flavor generation methods and examines experimental constraints including EW precision tests and top partner limits.
• The study outlines future research directions to improve naturalness and advance UV completions in composite Higgs theories.

Composite Higgs Models: A Comprehensive Analysis

The paper by Bellazzini, Csaki, and Serra offers a detailed review of composite Higgs models in the context of the Higgs boson discovery. It systematically classifies these models based on their predictions for the Higgs potential and discusses the degree of tuning required, which remains substantial across different variants of the models.

Overview of Composite Higgs Models

Composite Higgs models aim to provide a natural explanation for electroweak symmetry breaking through strong dynamics, where the Higgs boson emerges as a light composite field. The paper categorizes various models, such as bona fide composite Higgs, little Higgs, holographic composite Higgs, twin Higgs, and dilatonic Higgs, according to their predicted Higgs potential characteristics and the necessary parameter tuning.

Key Highlights:

1. Classifications Based on Higgs Potential:
   • Bona Fide Composite Higgs: Here, both the mass and quartic coupling of the Higgs are tree-level, typically resulting in heavy Higgs and requiring fine-tuning.
   • Little Higgs Models: These introduce collective symmetry breaking to protect the Higgs mass at loop level while generating a tree-level quartic coupling, thereby mitigating the hierarchy problem but failing to avoid tuning after the Higgs mass measurement.
   • Holographic Models: Both the Higgs mass and quartic terms arise at loop level. These models necessitate some degree of tuning but are naturally aligned with the observed Higgs mass.
   • Twin Higgs Models: They utilize a discrete symmetry that stabilizes the Higgs potential at loop level, allowing for weakly charged partners, which evade stringent collider bounds.
   • Dilatonic Higgs Models: Featuring a scale-invariant sector, these models propose the Higgs as a dilaton. However, they require accidental alignment to match Higgs-like behavior.
2. Flavor Structure Generation:

The paper distinguishes between flavor generation methods, notably partial compositeness, which involves mixing elementary fields with composite sector operators to generate Yukawa couplings. Two primary approaches are discussed: - Anarchic Couplings: This scenario involves random composite Yukawa entries with hierarchical elementary mixings, utilizing RS-GIM mechanisms to address flavor constraints. - Flavor Symmetries: Employing MFV (Minimal Flavor Violation) or NMFV approaches, these models impose flavor symmetries on the composite sector to comply with experimental flavor constraints.

1. Phenomenological Implications: The paper addresses the implications of these models for flavor physics, electroweak precision tests, and Higgs couplings. It assesses current experimental bounds, focusing on EWPT parameters like S and T, and notes the protective role of custodial symmetry.
2. Experimental Constraints and Signals:
   • Top Partners: The presence of top partners is a common prediction, crucially affecting the Higgs potential and flavor transitions. Experimental limits on such partners are intensively discussed.
   • Electroweak Precision Tests and Higgs Couplings: The models predict modifications in the Higgs couplings to gauge bosons and fermions, which are currently being tested at the LHC.
   • Coset Structure and Additional Scalars: Various coset models are explored, and the necessity of additional symmetry for realistic Higgs potentials is emphasized.
3. Future Directions: The paper suggests avenues for future research, including improving the naturalness in various composite models, developing consistent UV completions, and exploring new experimental signatures.

Conclusion

The paper provides an exhaustive classification and examination of composite Higgs models, underscoring the necessity of tuning to comply with the observed Higgs properties. It highlights the theoretical underpinnings of each model variant, and discusses their connection to experimental observations, especially focusing on electroweak and flavor constraints. Importantly, it calls for further research to refine these models and resolve outstanding issues in tuning and consistency with data. As the experimental boundary expands, it will be crucial to validate these models' predictions, potentially guiding the discovery of new physics beyond the Standard Model.