Composite Higgses

TL;DR

This review analyzes composite Higgs scenarios in light of a 125 GeV Higgs, arguing that the Higgs quartic is loop-generated and that calculable, natural potentials require a careful balance between the compositeness scale and electroweak data. It provides a 4D EFT-based taxonomy, contrasting 4-Fermi condensation with partial compositeness and distinguishing anarchic versus symmetry-protected flavor structures, including MFV and U(2)^3 variants. The work catalogs custodial cosets such as SO(5)/SO(4), discusses EWPT and flavor constraints, and surveys UV completions, holographic realizations, and dark matter possibilities, highlighting viable spectra with light top partners and vector resonances. It concludes that all realistic models entail some tuning and outlines how current and future experiments can probe the composite-Higgs paradigm across Higgs couplings, direct searches, flavor, and cosmology.

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.

Figures (6)

• Figure 1: Masses of the top partners $Q_1$ and $Q_4$ that reproduce the Higgs mass $m_h = 125 \,\mathrm{GeV}$ for $v^2/f^2 = 0.2$, from Pomarol:2012qf. The different lines correspond to different $\textrm{SO}(5)$ embeddings for the top quark. In blue $q_L, t_R \in \mathbf{5}$, in red $q_L, t_R \in \mathbf{10}$ (with $Q_1 \to Q_6$) and in black $q_L \in \mathbf{5}$ and $t_R \in \textbf{1}$.
• Figure 2: Confidence level contours (at $65\%$, $95\%$ and $99\%$) for $\hat{S}$ and $\hat{T}$ from Grojean:2013qca. The IR contributions alone would imply $\xi=v^2/f^2\lesssim 0.1$.
• Figure 3: Best fit region for the $Z\bar{b}b$ couplings from Batell:2012ca favoring small positive $\delta g_{Rb}$. The SM is represented by the green point.
• Figure 4: Higgs fits from Falkowski:2013dza (left panel) and Chacko:2012vm (right panel). Left panel: Fit to $v/f$ for the MCHM with (black) or without (gray) including electroweak precision data, with $n_\psi = 0$ (solid), $n_\psi = 1$ (dashed), and $n_\psi = 2$ (dot-dashed). Right panel: Fit to $\xi = v^2/f^2$ and $c_{\gamma \gamma}/\xi$ from Higgs data, with $\epsilon \equiv \gamma_\psi$ marginalized in the range $0 \leqslant \epsilon \leqslant 0.6$. The star is the best-fit point, while the cross corresponds to Higgs-like dilaton limit.
• Figure 5: Preliminary CMS bounds from run 1 of the LHC on the production of spin 1 resonances. Left panel: bound on $\rho^\pm$ using decays to $WZ$, from CMS:2013vda. Right panel: bound on the KK gluon decaying to $t \bar{t}$, from Chatrchyan:2013lca. Note that the dashed curve is for a $Z'$, the KK gluon bound from the same plot is around 2.5 TeV.