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 qL³, equal compositeness, and fully composite tR. In the most phenomenologically viable case of a fully composite tR, we show that the strongest bound on the natural parameter space comes from next-to-leading log running of the 4-top operator Oₜₜ = ( tR γ_μ tR)( tR γ^μ tR) into the Peskin-Takeuchi T parameter. In general, we find that this 2-loop effect allows existing electroweak precision data to give a better constraint on 4-top operators compared to 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.