Non-universal probes of composite Higgs models: new bounds and prospects for FCC-ee

We study the leading loop-level phenomenology of composite Higgs models via the effective field theory of a strongly interacting light Higgs and top quark (SILH+TQ). We systematically analyze the renormalization group evolution (RGE) of tree-generated operators in the SILH+TQ scenario, finding large mixings of flavor non-universal operators into those affecting electroweak precision observables. We show that these model-independent RG contributions are more important than typical estimates for finite parts. Flavor non-universal effects are completely captured by examining three options for the top mixing: fully composite $q_L^3$ \( {q}_L^3 \) , equal compositeness, and fully composite t_R. In the most phenomenologically viable case of a fully composite t_R, we show that the strongest bound on the natural parameter space comes from next-to-leading log running of the 4-top operator ${\mathcal{O}}_{\mathit{tt}}=\left({\overline{t}}_R{\gamma }_{\mu }{t}_R\right)\left({\overline{t}}_R{\gamma }^{\mu }{t}_R\right)$ \( {\mathcal{O}}_{tt}=\left({\overline{t}}_R{\gamma}_{\mu }{t}_R\right)\left({\overline{t}}_R{\gamma}^{\mu }{t}_R\right) \) into the Peskin-Takeuchi T parameter. In general, we find that this 2-loop effect allows existing electroweak precision data to give better constraints on 4-top operators than high-energy probes from top production at the LHC. Independent of the top mixing, we find that a future tera-Z machine such as FCC-ee has the potential to probe composite Higgs models up to a scale of m_∗ ≳ 25 TeV, and test the naturalness of the electroweak scale at the ≲ 10⁻⁴ level.