Potential blind directions at TeraZ

The next generation of high-luminosity electron-positron colliders, such as the electron-positron Future Circular Collider and the Circular Electron-Positron Collider operating at the Z pole (TeraZ), is expected to deliver unprecedented precision in electroweak measurements. These precision observables are typically interpreted within the Standard Model effective field theory (SMEFT), offering a powerful tool to constrain new physics. However, the large number of independent SMEFT operators allows for the possibility of blind directions, parameter combinations to which electroweak precision data are largely insensitive. In this work, we demonstrate that such blind directions are not merely an artifact of agnostic effective field theory scans, but arise generically in realistic ultraviolet completions involving multiple heavy fields. We identify several concrete multifield extensions of the Standard Model whose low-energy SMEFT projections align with known blind subspaces, and show that these persist even after accounting for renormalization group evolution and finite one-loop matching effects. Our analysis shows that TeraZ will set a new benchmark in precision for indirect searches, but fully probing the space of possible ultraviolet physics requires going beyond this stage. Later electron-positron Future Circular Collider runs at higher center-of-mass energies, together with the hadron-hadron Future Circular Collider, will provide the necessary complementary probes, enabling a far more complete exploration of the SMEFT parameter space.