This sole measurement would already be a very sensitive probe of new physics, able to provide indirect evidence for the existence of particles that could not be observed directly at the LHC. One example is provided by the supersymmetric partners of the top quark, from the analysis of Ref.~\cite{1207.7355}, as illustrated in Fig.~\ref{fig:veronica}. The TLEP precision of 500~keV on the W mass would give sensitivity to a stop squark of about 3~TeV, far heavier than could be detected at the HL-LHC, and independently of the stop decay mode. This is another example of how the unparallelled TLEP precision could give access to physics beyond the Standard Model.