On the new physics in Bhabha luminometry at future $e^+e^-$ colliders

The absolute machine luminosity is a key quantity to achieve the high-precision physics program of future $e^+e^-$ collider. It is determined by measuring a theoretically well-known process, which, ideally, can be computed with arbitrary precision in the perturbation theory. However, yet undiscovered new physics could give a non-negligible contribution to the cross section of the luminosity monitoring process, thus invalidating the uncertainty determination of measured quantities. We assess the theoretical error of non-Standard Model origin to the small-angle Bhabha scattering in various future colliders scenarios. In addition, a possible running strategy to constrain unknown heavy interactions is proposed, relying on asymmetries that do not depend on the absolute luminosity.