Testing Higgs Coupling Precision and New Physics Scales at Lepton Colliders

The next-generation lepton colliders, such as CEPC, FCC-ee, and ILC will make precision measurement of the Higgs boson properties. We first extract the Higgs coupling precision from Higgs observables at CEPC to illustrate the potential of future lepton colliders. Depending on the related event rates, the precision can reach percentage level for most couplings. Then, we try to estimate the new physics scales that can be indirectly probed with Higgs and electroweak precision observables. The Higgs observables, together with the existing electroweak precision observables, can probe new physics up to 10TeV (40TeV for the gluon-related operator $\mathcal O_g$) at 95% C.L. Including the $Z/W$ mass measurements and $Z$-pole observables at CEPC further pushes the limit up to 35TeV. Although $Z$-pole running is originally for the purpose of machine calibration, it can be as important as the Higgs observables for probing the new physics scales indirectly. The indirect probe of new physics scales at lepton colliders can mainly cover the energy range to be explored by the following hadron colliders of pp (50-100TeV), such as SPPC and FCC-hh.