Top quark mass determination near t\bar{t} threshold at lepton colliders

Future e^+ e^- linear colliders will enable us to determine the top quark mass with high accuracy from the measurement of the 1S peak position of (remnant of) toponium. The estimated statistical error in this measurement is about 50 MeV with integrated luminosity of 30 ${\rm fb^{-1}}$. We calculate ${\cal O}(\alpha_s^5 m)$ corrections to the quarkonium 1S energy spectrum in the large-$\beta_0$ approximation to reduce theoretical uncertainties below the corresponding experimental error. We discuss the significance of the ${\cal O}(\alpha_s^5 m)$ corrections and estimate theoretical uncertainties of our prediction.