A First Look at the Impact of NNNLO Theory Uncertainties on Top Mass Measurements at the ILC

A scan of the top production threshold at a future electron-positron collider provides the possibility for a precise measurement of the top quark mass in theoretically well-defined mass schemes. With statistical uncertainties of 20 MeV or below, systematics will likely dominate the total uncertainty of the measurement. This contribution presents a first look at the impact of the renormalization scale uncertainties in recent NNNLO calculations of the top pair production cross section in the threshold region on the measurement of the top quark mass at the International Linear Collider.