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

Abstract

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 ${\cal O}(α_s^5 m)$ corrections to the quarkonium 1S energy spectrum in the large-$β_0$ approximation to reduce theoretical uncertainties below the corresponding experimental error. We discuss the significance of the ${\cal O}(α_s^5 m)$ corrections and estimate theoretical uncertainties of our prediction.