The dimension-six terms in the SM effective field theory (SMEFT) provide a complete basis parameterizing the leading effects of heavy new physics (NP) at short distances. This has motivated an immense effort in recent years to reinterpret experimental data as constraints on the Wilson coefficients of SMEFT operators. Given the large proliferation of parameters due to flavor, however, it is clear that the flavor structure of NP must play a crucial role in such analyses. Flavor data and the lack of new resonances at the LHC have given us two important clues on this front: 1) we have no hints of deviations in flavor-changing neutral currents and 2) NP does not couple strongly to valence quarks at nearby energy scales. What is needed for compatibility with both observations is NP that couples universally to the light families, while it may have a different coupling to the third generation. While this may sound rather baroque, NP that couples strongly to the Higgs and the top is precisely what we need to address the electroweak (EW) hierarchy problem.
To illustrate these points, I will discuss composite Higgs models, which remain a classic and well-motivated solution to the hierarchy problem. The leading low-energy effects of this class of models are captured by an EFT featuring a strongly interacting light Higgs and top quark. I systematically analyze the RGE of tree-generated operators in this scenario, finding large mixings of flavor non-universal operators into those affecting EW precision observables. In the most phenomenologically viable case of a fully composite right-handed top, I show that the strongest bound on the natural parameter space comes from next-to-leading log running of the 4-top operator (tR*γ*tR)(tR*γ*tR) into the Peskin-Takeuchi T parameter. In general, I find this 2-loop effect allows existing EW precision data to give a better constraint on 4-top operators compared to high-energy probes from top production at the LHC. Looking forward, I find that a future tera-Z machine such as FCC-ee has the potential to indirectly probe composite Higgs models up to a scale of at least 25 TeV, and test the naturalness of the EW scale at the 1e-4 level.
