Impact of Higgs precision measurements at the LHC and FCC-ee on the spectrum of composite Higgs models

Abstract

We investigate the minimal composite Higgs model based on the symmetry-breaking pattern $\mathrm{SU}(4)\rightarrow\mathrm{Sp}(4)$, where electroweak symmetry breaking is governed by the vacuum alignment angle $θ$. Through the leading-order relations $κ_V=\cosθ$ and $m_η=m_h/\sinθ$, precision measurements of Higgs couplings are translated into direct constraints on the vacuum structure and the singlet pseudo-Nambu--Goldstone boson mass. Using the current ATLAS Run-2 measurement of $κ_V$, we construct a Bayesian posterior for $θ$, including the Jacobian associated with the transformation from $κ_V$ to $θ$, and validate the results through an independent frequentist $Δχ^2$ analysis. The same framework is then applied to the projected sensitivities of the High-Luminosity LHC and FCC-ee. The current data imply a conservative lower bound of approximately $440~\mathrm{GeV}$ on the singlet mass at the $95\%$ credibility level, while the projected sensitivities improve this limit to about $600~\mathrm{GeV}$ at the HL-LHC and beyond $2~\mathrm{TeV}$ at FCC-ee. The close agreement between the Bayesian and frequentist determinations demonstrates the robustness of the extracted constraints. These results show that future Higgs precision measurements will probe the vacuum alignment of the minimal $\mathrm{SU}(4)/\mathrm{Sp}(4)$ composite Higgs model with unprecedented sensitivity, placing increasingly stringent constraints on the allowed parameter space and establishing the singlet scalar as a compelling target for upcoming collider programs.