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Future energy-frontier electron-positron colliders will be capable ofhigh-precision studies of top quark properties. The measurement of the top-pairproduction cross section around the threshold provides access to the mass ofthe top quark in theoretically well-defined schemes, with statisticaluncertainties of 20 MeV or less, depending on the assumed integrated luminosityof the measurement. At this level of precision, experimental and theorysystematics are likely to become important or even dominant. This contributionpresents a first analysis of the impact of the remaining uncertainties of therecently completed calculation of the top pair production cross section atNNNLO QCD including the exchange of Higgs bosons on the extraction of the topquark mass from a threshold scan. The analysis is based on reconstructionefficiencies and background levels obtained in full simulation studies forCLIC, combined with signal cross sections from the higher-order calculations.To assess possible differences between different collider options, the study isperformed in the context of CLIC, ILC and FCC-ee by considering the differencesin the luminosity spectra.

Impact of Theory Uncertainties on the Precision of the Top Quark Mass in a Threshold Scan at Future e+e- Colliders