Fermionic UV completions of Composite Higgs models

Abstract: We classify the four-dimensional purely fermionic gauge theories that give a UV completion of composite Higgs models. Our analysis is at the group theoretical level, addressing the necessary (but not sufficient) conditions for the viability of these models, such as the existence of top partners and custodial symmetry. The minimal cosets arising are those of type SU(5)/SO(5) and SU(4)/Sp(4). We list all the possible "hyper-color" groups allowed and point out the simplest and most promising ones.

• The paper establishes a detailed group-theoretical classification of fermionic gauge theories for UV completions in composite Higgs models.
• It identifies minimal cosets, such as SU(5)/SO(5) and SU(4)/Sp(4), ensuring key features like asymptotic freedom and custodial symmetry.
• The study outlines implications for collider phenomenology and highlights challenges in anomaly cancellation and top partner configurations.

Overview of Fermionic UV Completions of Composite Higgs Models

This paper by Gabriele Ferretti and Denis Karateev presents a classification of four-dimensional purely fermionic gauge theories that potentially offer ultraviolet (UV) completions of composite Higgs models. The research identifies group-theoretical conditions necessary for these models to be viable, acknowledging the need for alignment with concepts such as custodial symmetry and the existence of top partners, while not claiming sufficiency for their practical realization.

The paper explores the implications of the 126 GeV Higgs boson discovery, emphasizing that a composite Higgs approach could potentially stabilize its mass against higher energy scales, contrary to the traditional fine-tuning challenges in the Standard Model (SM). This study asserts that such stability might arise by manifesting the Higgs as a pseudo Nambu-Goldstone boson (pNGB).

Key Findings

The analysis identifies the minimal cosets for viable composite Higgs models to be SU(5)/SO(5) and SU(4)/Sp(4). Notably, the classification is supported by the identification of permissible "hyper-color" groups, the simplest of which, such as SU(N), Sp(2N), and SO(N), fulfill these theoretical requirements.

The paper segments its results into several key constraints and findings:

1. Group Theoretical Classification: The authors rigorously examine the suitability of various hyper-color groups under asymptotic freedom conditions. Asymptotic freedom is a crucial property, ensuring that the theories remain non-trivial and predictive at higher energy scales.
2. Custodial Symmetry and Anomaly Considerations: Emphasis is placed on maintaining custodial symmetry to mitigate unwanted radiative corrections. The paper ensures gauge and global anomalies are absent, primarily under SU(N) and Sp(2N) with specific combinations of irreducible representations such as fundamental (F), symmetric (S2), adjoint (Ad), and pseudo-real components (A2), among others.
3. Top Partner Configuration: The analysis provided top partner construction by employing models with minimal pNGB cosets, focusing on achieving the necessary partner masses and charges.

Implications and Speculations

This classification implies several practical and theoretical interconnections:

• Particle Spectrum and Collider Phenomenology: The presence of exotic fields, as outlined, including an "exotic" top quark with distinctive electromagnetic charges, demands further scrutiny in particle colliders to identify predictive signals that align with these results.
• Constraints on Beyond SM Physics: The work provides guidance for potential UV models aspiring to explain phenomena beyond the SM, such as enhanced symmetry considerations leading to unexpected bosonic field masses when group theoretical breakdown occurs (e.g., SO(5) to SO(4)).
• Model Limitations: The paper critically addresses already-existing issues such as proton decay tendencies and the detailed interplay between non-minimal sets of hyper-color groups and the pNGB mass spectrum. Novel cosmological implications from potential Nambu-Goldstone bosons that remain massless (neutral) under custodial breakdowns are flagged as areas requiring further examination.

Conclusion

Ferretti and Karateev's paper delivers a comprehensive theoretical landscape for fermionic UV completions of composite Higgs models within the particle physics domain. While the classifications and conclusions remain theoretical at this juncture, the approach offers a lens for refining searches for beyond standard model physics, notably within collider-based examinations. Future work is indicated in the clarification and validation of symmetry-breaking patterns, MAC hypothesis applications, and top partner configurations, given bound state energetics. Ultimately, the paper encourages additional empirical validation to reconcile theoretical insights with experimental observations in particle physics.