Researchers have calculated the one-loop effects of vector-like fermions (VLFs) on the Higgs-strahlung cross-section. This observable is a flagship precision measurement for future $e^+e^-$ Higgs factories like the FCC-ee. The study considers four benchmark extensions of the Standard Model (SM), including VLF quark and lepton doublets and singlets that couple to the Higgs boson, or that mix directly with third-generation SM fermions.

The calculations, performed using the on-shell renormalization scheme and imposing perturbativity bounds on couplings, include both universal self-energy and non-universal vertex contributions to the Higgs-strahlung amplitude. Oblique parameters S and T, and the $H\to\gamma\gamma$ decay rate were also computed as complementary cross-checks. The results indicate that a sizable fraction of the VLF parameter space, still allowed by current LHC searches, could produce shifts in $\sigma(ZH)$ detectable by the FCC-ee, with a per-mille sensitivity, offering a radiative probe of these couplings.

For scenarios where interactions are driven by Yukawa couplings, the FCC-ee could provide a new window to explore VLFs. However, in mixing-driven scenarios, existing electroweak precision bounds on the relevant mixing angles already preclude an observable effect. This work highlights that VLF Yukawa couplings are the more promising target for Higgs-strahlung precision measurements at a future $e^+e^-$ collider, rather than any residual mixing with SM fermions.