Realistic Composite Higgs Models

TL;DR

This work analyzes composite Higgs frameworks based on the $SO(5)/SO(4)$ symmetry breaking pattern, focusing on how extended fermionic resonances impact electroweak precision and flavor observables. By performing exact one-loop calculations of the $T$ parameter and the anomalous $Z b_L \bar b_L$ coupling for arbitrary heavy-quark content, the authors demonstrate that minimal fermion sectors generally conflict with precision data, while non-minimal sectors can be fully realistic over large parameter regions. The study shows that a rich spectrum of light vector-like quarks below the cut-off can reconcile EWPT with natural EWSB and yields distinctive LHC signatures via pair and single production, potentially preceding bosonic resonance discoveries. The results bridge four-dimensional effective descriptions with warped extra-dimensional constructions and highlight fermionic resonances as promising early indicators of a composite-Higgs mechanism.

Abstract

We study the role of fermionic resonances in realistic composite Higgs models. We consider the low energy effective description of a model in which the Higgs arises as the pseudo-Goldstone boson of an SO(5)/SO(4) global symmetry breaking pattern. Assuming that only fermionic resonances are present below the cut-off of our effective theory, we perform a detailed analysis of the electroweak constraints on such a model. This includes the exact one-loop calculation of the T parameter and the anomalous Zbb coupling for arbitrary new fermions and couplings. Other relevant observables, like b to s gamma and Delta B=2 processes have also been examined. We find that, while minimal models are difficult to make compatible with electroweak precision tests, models with several fermionic resonances, such as the ones that appear in the spectrum of viable composite Higgs models from warped extra dimensions, are fully realistic in a large region of parameter space. These fermionic resonances could be the first observable signature of the model at the LHC.

Figures (6)

• Figure 1: $68\%$, $95\%$ and $99\%$ C.L. limits on $S$ and $T$ for a fit to electroweak observables with three independent parameters ($S$, $T$ and $\delta g_{b_L}$), fixing the optimal value of $\delta g_{b_L}=-2.5\times 10^{-4}$ and a reference Higgs mass $m_{\mathrm{h,ref}}=120$ GeV. The dots at the start and the tip of the arrows show the effects due to Higgs compositeness, Eq. (\ref{['ST:Higgs']}), and to UV effects on $S$, Eq. (\ref{['S:Lambda']}), respectively. The effect is shown (from top to bottom) for the values of $s_\alpha = 0.25, 0.33$ and $0.5$.
• Figure 2: $95\%$ and $99\%$ C.L. limits on $T$ and $\delta g_{b_L}$ for a fit to electroweak observables with three independent parameters ($S$, $T$ and $\delta g_{b_L}$) assuming $s_\alpha \approx 0.5$ ($f = 500$ GeV) and a reference Higgs mass $m_{\mathrm{h,ref}}=120$ GeV (no projection). The top and right axes show the value of the $T$ parameter and $\delta g_{b_L}$ in terms of the SM one-loop contribution. For this value of $s_\alpha$ there is no allowed region at $68\%$ C.L..
• Figure 3: Diagrams with heavy quarks contributing to the $Z b_L \bar{b}_L$ amplitude.
• Figure 4: Contribution to $\delta g_{b_L}$ as a function of $s_L$. The other input parameters are left free (keeping the total $\chi^2$ using the estimation for $\delta g_{b_L}$ within $99\%$ C.L.). The full red (empty green) squares correspond to the full contribution (large Yukawa estimation) of $\delta g_{b_L}$. The horizontal lines correspond to the maximum allowed contribution to $\delta g_{b_L}$ (assuming an optimal contribution to $T$).
• Figure 5: Spectrum of light (below $\Lambda$) fermionic states (including the top quark) for the region of parameter space compatible with EWPT. The (green) crosses, (blue) dots and (red) empty squares correspond to charge $5/3$, $2/3$ and $-1/3$ quarks, respectively. The latter, together with one charge $2/3$ quark, are typically above $\Lambda$.