deletions | additions       diff --git a/aphas.tex b/aphas.tex  index b0aee4d..add391c 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_3LO} 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 0.12\%. This precision is expected to be improved improve  to better than $10^{-5}$ at with  TLEP. The LEP experimental error of 0.0038 on $\alpha_s (m^2_{\rm Z})$ will scale accordingly to better than 0.0001.\\ {\em A reasonable target for the measurement of $\alpha_s (m^2_{\rm Z})$ with a run at the Z pole with TLEP is therefore a precision of 0.0002.}