New Physics Off the $Z$-Pole: $e^+ e^- \rightarrow f \bar f$ at Future Lepton Colliders

We explore the prospects for probing new physics (NP) beyond the Standard Model (SM) at future lepton colliders through precision measurements of $e^+e^-\to f{\bar f}$ observables off the $Z$ resonance. We consider interference between SM contributions and those arising from dimension-6, four-fermion effective operators that encode the effects of NP, yielding a linear dependence on the latter. This linear dependence in general increases with magnitude of the collision energy offset from the $Z$ pole. We consider a variety of asymmetries in order to enhance the NP-sensitivity while reducing experimental systematic and theoretical, SM uncertainties: an inclusive above and below $Z$-resonance total cross section asymmetry ($A_\sigma$) as well as the conventional forward-backward ($A_{\rm FB}$) and polarization ($A_{\rm pol}$) asymmetries. Based on projected statistical uncertainties at the Circular Electron-Positron Collider (CEPC), we find that t measurement of $A_\sigma$ could extend the sensitivity to the NP mass scale by as much as a factor of $\sim 7$ compared to the present reach obtained with the CERN Large Electron Positron Collider. Inclusion of projected systematic theoretical SM uncertainties substantially reduce this sensitivity gain. For $A_{\rm FB}$, inclusion of experimental systematic uncertainties has a marginal impact on the gain in NP reach, whereas SM theoretical uncertainties remain a significant barrier to realizing the full NP sensitivity. Analogous conclusions apply to the CERN Future Circular Collider (FCC-ee) and International Linear Collider (ILC).