Strong Higgs Interactions at a Linear Collider

TL;DR

This work assesses how high-energy $e^+e^-$ linear colliders can probe a strongly interacting Higgs sector, focusing on the link between deviations in Higgs couplings and the underlying compositeness scale. Using an effective Lagrangian framework with custodial symmetry, it analyzes single, double, and triple Higgs processes—especially vector-boson scattering and $VV\to hh$—to extract constraints on $\xi = v^2/f^2$ and the scale $\Lambda = 4\pi f$ for both PNGB and generic SILH scenarios. The study demonstrates that CLIC at $\sqrt{s}=3$ TeV with $1\ \text{ab}^{-1}$ can reach sensitivity to $\xi$ around a few $\%$ and probe $\Lambda$ up to about $15$–$20$ TeV via double-Higgs production, while triple-Higgs production offers a direct probe of coset symmetry and helps distinguish PNGB Higgs from other composites. Overall, the results emphasize the value of energetic, polarized lepton colliders in uncovering or constraining strong dynamics behind electroweak symmetry breaking and guide the design of future Higgs-precision programs.

Abstract

We study the impact of Higgs precision measurements at a high-energy and high-luminosity linear electron positron collider, such as CLIC or the ILC, on the parameter space of a strongly interacting Higgs boson. Some combination of anomalous couplings are already tightly constrained by current fits to electroweak observables. However, even small deviations in the cross sections of single and double Higgs production, or the mere detection of a triple Higgs final state, can help establish whether it is a composite state and whether or not it emerges as a pseudo-Nambu-Goldstone boson from an underlying broken symmetry. We obtain an estimate of the ILC and CLIC sensitivities on the anomalous Higgs couplings from a study of WW scattering and hh production which can be translated into a sensitivity on the compositeness scale 4πf, or equivalently on the degree of compositeness ξ=v^2/f^2. We summarize the current experimental constraints, from electroweak data and direct resonance searches, and the expected reach of the LHC and CLIC on ξand on the scale of the new resonances.

Figures (11)

• Figure 1: Summary of current constraints (orange curves and brown region) and expected sensitivities at CLIC and the LHC (horizontal regions) on $\xi = (v/f)^2$ and the mass of the lightest spin-1 resonance $m_\rho$ for $SO(5)/SO(4)$ composite Higgs theories. See text.
• Figure 2: Leading diagrams contributing to the $\chi\chi \rightarrow hhh$ amplitude. Dashed lines represent the NG bosons $\chi$, while solid lines denote the Higgs boson $h$. The sum of these diagrams with their crossings cancels out exactly in the gaugeless limit for a symmetric coset and at the $O(p^2)$ level for any coset. See text.
• Figure 3: Diagrams giving the dominant contribution to the $V_{T} \chi \rightarrow hhh$ cross-section. Continuous, dashed and wiggly lines denote a Higgs boson $h$, the NG bosons $\chi$, and a transverse gauge boson $V_T$ respectively.
• Figure 4: Partonic cross-sections of the processes $V_{L} V_{L} \rightarrow hhh$ (black), $V_{L} V_{T} \rightarrow hhh$ (red) and $V_{T} V_{T} \rightarrow hhh$ (blue) as a function of $\sqrt{\hat{s}}$ for a PNGB Higgs with $\xi = 0.1$ and $m_{h} = 125$ GeV. The dashed line shows the partonic cross section after applying the cuts $p_{T} > 0.05 \sqrt{\hat{s}}$ for each Higgs and $m_{hh} > 0.1 \sqrt{\hat{s}}$ for all Higgs pairs.
• Figure 5: Normalized differential cross sections $d\sigma/dm_{hh}$ and $d\sigma/d H_T$ for $e^+e^- \to \nu\bar{\nu} hh$ at CLIC with $\sqrt{s} = 3$ TeV after the identification cuts of eqs. (\ref{['idjets']}) and (\ref{['deltaminvh']}), for several values of $\delta_b$ and $\delta_{d_3}$.