deletions | additions       diff --git a/aphas.tex b/aphas.tex  index 4a802d3..beb8915 100644  --- a/aphas.tex  +++ b/aphas.tex 
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{\ }^{+0.0002\ (m_{\rm top} = 180\ {\rm GeV}/c^2)}_{-0.0002\ (m_{\rm top} = 170\ {\rm GeV}/c^2)} \pm 0.0002\ ({\rm th}).  \end{equation}  Now that {\it (i)} the uncertainty due to the Higgs boson mass dependence is no longer relevant; {\it (ii)} the uncertainty due to the top-quark mass dependence is negligible; and {\it (iii)} the pQCD scale uncertainty from the latest ${\rm N_3}{\rm LO}$ calculations~has dropped to 0.0002, this method potentially allows access to high precision on $\alpha_{\rm s}$. As shown in Eq.~\ref{eq:Rl}, $R_\ell$ was measured at LEP with a relative uncertainty is of  0.12\%. As mentioned in Section~\ref{sec:Rell}, this precision is expected to improve to $5 \times 10^{-5}$ with TLEP. The LEP experimental error of 0.0038 on $\alpha_s (m^2_{\rm Z})$ will scale accordingly to 0.00015 at TLEP, of the same order as the theory uncertainty.\\ \textbf{\textit{A reasonable target for the measurement of $\boldsymbol{\alpha_s (m^2_Z)}$ with a run at the Z pole with TLEP is therefore a precision of 0.0002.}}