Accuracy complements energy: electroweak precision tests at Tera-Z

A Tera-$Z$ factory, such as FCC-ee or CEPC, will have indirect sensitivity to heavy new physics up to the tens of TeV scale through higher-order loop contributions to precision measurements at the $Z$ pole. These indirect quantum effects may provide complementary, or even better, sensitivity to potential deviations from the Standard Model that are typically thought to best be constrained at leading order at higher energies above the $Z$ pole. We show in the SMEFT framework how accuracy complements energy for operators that modify the Higgs and gauge boson two- and three-point functions, leading to improved projected sensitivities for models such as the real singlet scalar, weakly interacting massive particles, and a custodial weak quadruplet. A thorough Tera-$Z$ programme may thus anticipate aspects of physics runs at higher energies and provide a wider scope of quantum exploration of the TeV scale than had previously been appreciated.