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\label{fig:ttbar} The $\ttbar$ cross section at the production threshold, for a top quark mass of 174 GeV, as a function of the centre-of-mass energy, taken from Ref.~\cite{cite:1303.3758}. (Note: the measured top quark mass from Tevatron and LHC is approximately 1 GeV smaller. The 1s peak is therefore around 346 GeV instead of 348 GeV as shown in the Figure.) The black curve is the next-to-next-to-leading-order QCD-corrected cross section. The green curve shows the effect of photon emission by the sole initial state radiation (ISR), as is expected in TLEP collisions. The For illustration, the  red curve includes the effects of ILC beamstrahlung at ${\sqrt{s}=350}$ GeV, in addition to those from ISR.