Tasi 2009 lectures: The Higgs as a Composite Nambu-Goldstone Boson (1005.4269v1)

Abstract: This is an introduction to theories where the Higgs is a composite Nambu-Goldstone boson of a new strongly-interacting dynamics not much above the weak scale. A general discussion is presented based on the pattern of global symmetries at low energy, and the analogy with the QCD pion is analyzed. The last part of the lectures shows how a composite Higgs can emerge as the hologram of a 5-dimensional gauge field.

• The paper demonstrates that the Higgs emerges as a light composite state from new strong dynamics, offering a solution to the hierarchy problem.
• It utilizes an SO(5) to SO(4) symmetry breaking to produce Nambu-Goldstone bosons while preserving custodial SU(2) for electroweak precision.
• A five-dimensional holographic framework is employed to model composite dynamics, predicting observable deviations in Higgs couplings at colliders.

An Examination of Theories Describing the Higgs as a Composite Nambu-Goldstone Boson

The paper "The Higgs as a Composite Nambu-Goldstone Boson" by R. Contino explores theoretical frameworks where the Higgs boson is not an elementary particle but emerges as a composite Nambu-Goldstone boson due to a new strong interaction at an energy scale just above the electroweak scale. This review highlights key theoretical insights and ramifications of this concept, including comparisons with existing models like QCD and implications for electroweak symmetry breaking (EWSB).

Theoretical Underpinnings

Contino discusses two paradigms of EWSB: the traditional Higgs model with a weak scalar field and Technicolor models with a strong gauge interaction. The composite Higgs model acts as an interpolation between these paradigms, proposing a scenario where the Higgs is a light bound state of a new strong sector. This approach addresses the hierarchy problem by suggesting that the Higgs mass is shielded from large quantum corrections by virtue of being composite.

Symmetry Structure and Electroweak Precision

A central theme of composite Higgs models is their symmetry structure. The paper primarily investigates a model where an $SO(5)$ symmetry is spontaneously broken to $SO(4)$. This breaking pattern naturally yields a set of four Nambu-Goldstone bosons, one of which can be identified with the Higgs doublet. Notably, the embedding of the Standard Model (SM) within a larger symmetry group such as $SO(5)$ permits custodial $SU(2)$ symmetry, which protects the precision electroweak parameter $\rho$ from large corrections.

Contino explores how SM fermions and gauge bosons, which do not respect the full global symmetry, generate an effective potential for the Higgs at loop level. This mechanism potentially leads to a realistic pattern of EWSB where the electroweak scale emerges as a fraction of the strong scale. Detailed quantitative results demonstrate the viability of such models in aligning with electroweak precision data, provided that the scale of compositeness is sufficiently large compared to the electroweak scale.

Composite Higgs Models and Technicolor

In addition to discussing the Higgs as a pNG boson, the paper revisits and contrasts it with Technicolor theories. The latter often struggle with flavor-changing neutral currents and precision test anomalies due to large contributions to the Peskin-Takeuchi $S$ parameter. Composite Higgs models alleviate these tensions by maintaining a light Higgs that reconciles LEP data while suppressing unwelcome deviations via partial compositeness and additional gauge symmetry protection.

A Five-Dimensional Perspective

A major section of the work presents composite Higgs models as holographic constructions within a five-dimensional setting. The idea posits that the fifth component of a gauge field, residing in a warped extra dimension, can manifest as the low-energy Higgs boson. This framework provides a calculable, yet theoretically rich, avenue to paper composite dynamics akin to AdS/CFT correspondence, encapsulating the physics of extra-dimensional theories within a strongly coupled four-dimensional boundary.

Conclusion and Future Outlook

Composite Higgs models, particularly those invoking higher-dimensional holography, present themselves as compelling alternatives to the standard Higgs paradigm, offering solutions to long-standing issues like the hierarchy problem while adhering to precision tests. These models predict a rich phenomenology, including deviations in Higgs couplings and distinctive spectroscopic signatures at collider experiments. While fine-tuning issues and parameter space constraints recur in model-building, the ongoing evolution of theoretical constructs, supported by data from LHC and future colliders, will continue to refine our understanding of electroweak symmetry breaking. The essay underscores composite Higgs theories as a promising frontier in particle physics, potentially illuminating the path toward new particles and interactions beyond the Standard Model.