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\subsubsection{The strong coupling constant}  The prospective TLEP precisions on the EWSB parameters call for a similar improvement of the strong coupling constant accuracy, which would otherwise become a leading systematic uncertainty in the determination of, e.g., the W boson and the top quark masses from a the  measurement of the {\rm WW} and $\ttbar$ production threshold cross sections. Complementary determinations of the strong coupling constant, $\alpha_{\rm s}$, may be obtained both at the Z pole and at energies at the WW threshold and above, with similar accuracies. The precise experimental measurement of the inclusive hadronic Z decay rate at the Z pole is sensitive to $\alpha_{\rm s}$. The theoretical prediction for such an inclusive observable is known with ${\rm N_3}{\rm LO}$ QCD corrections~\cite{Baikov_Chetyrkin_Kuhn_2008, Chetyrkin_Kuhn_Rittinger_2012}, with strongly suppressed non-perturbative effects. Some caveat is in order since Electroweak corrections can in principle be sensitive to the particle content of the Electroweak theory. The extraction of $\alpha_{\rm s}$ may therefore not be completely free of model dependence of Electroweak nature. A good way around this caveat is to constrain radiative-correction effects with other Electroweak measurements at the Z pole or elsewhere. In the case at stake here, the hadronic partial width is sensitive to new physics through the ``oblique'' Electroweak corrections known as $\epsilon_1 (\equiv \Delta\rho)$ and $\epsilon_3$, and through the vertex correction $\delta_{\rm b}$ to the $ {\rm Z} \to \bbbar$ partial width. The $\Delta \rho$ sensitivity cancels when taking the ratio $R_\ell$ with the leptonic partial width, and the $\epsilon_3$ corrections can be strongly constrained by the determination of $\sintw$ from leptonic asymmetries or from $\ALR$. The b-vertex contribution can be constrained by the direct extraction of $R_{\rm b}$, hence is not expected to be a limitation.