The Composite Nambu-Goldstone Higgs

TL;DR

The notes review the composite Higgs framework, where the Higgs is a pseudo-Nambu-Goldstone boson arising from a new strong sector with global symmetry G broken to H. Using CCWZ, vacuum misalignment, and partial fermion compositeness, they derive universal predictions for Higgs couplings and discuss fermion mass generation and flavor. A central theme is the 1S1C power counting and spurion analysis, which organize the Higgs potential, higher-derivative operators, and flavor effects into calculable structures with controllable tuning. The work connects EFT techniques, symmetry considerations, and phenomenology to assess naturalness, EWPT constraints, and flavor bounds, highlighting the role of custodial symmetry and top-partner dynamics. Overall, it provides a comprehensive, symmetry-driven blueprint for building and testing realistic composite Higgs models, including their flavor and precision-physics implications.

Abstract

The composite Higgs scenario, in which the Higgs emerges as a composite pseudo-Nambu-Goldstone boson, is extensively reviewed in these Notes. The material is presented in a pedagogical fashion, with great emphasis on the conceptual and technical foundations of the construction. A comprehensive summary of the flavor, collider and electroweak precision phenomenology is also presented.

Figures (46)

• Figure 1.1.1: Pictorial view of the SM as an effective field theory, with its Lagrangian generated at the scale $\Lambda_{\textrm{SM}}$.
• Figure 1.2.1: Some representative top, gauge and Higgs boson loop diagrams that contribute to the Higgs mass.
• Figure 1.3.1: The basic structure of the composite Higgs scenario.
• Figure 2.1.1: A geometrical illustration of EWSB through vacuum misalignment, in the case of the spatial rotations group ${\mathpzc{G}}=\;$SO$(3)$ with ${\mathpzc{H}}=\;$SO$(2)$. The SO$(2)$ breaking from vacuum misalignment is proportional to the projection of $\vec{F}$ on the SO$(2)$ plane, $v=f\sin\langle\theta\rangle$.
• Figure 2.4.1: A pictorial view of the partial compositeness approach to SM fermion couplings compared with the old-fashioned technicolor way.