deletions | additions       diff --git a/aphas.tex b/aphas.tex  index c527413..14603c9 100644  --- a/aphas.tex  +++ b/aphas.tex 
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The ratio $ R_\ell$ of the partial width of the Z into hadrons to that to one massless charged-lepton flavour has been used for the determination of $\alpha_s$ at LEP. As shown in Eq.~\ref{eq:Rl}, $R_\ell$ was measured at LEP with a relative uncertainty is 0.12\%. Up to a few years ago, when only NNLO QCD predictions were available, and the Higgs boson mass was still unknown, this measurement was translated to~\cite{Bethke_2004}  \begin{equation}  \alpha_{\rm s} (m^2_{\rm Z}) = 0.1226 \pm 0.0038 \ ({\rm exp}) %^{+0.0028 {\ }^{+0.0028  (\mu = 2m_{\rm Z})}_{−0.0005 (\mu = 0.25 m_{\rm Z}) %+0.0033 −0.0 (MH = 900 -100 GeV)  %\pm 0.0002 (m_{\rm top} = \pm 5 {\rm GeV}/c^2) \pm 0.0002 ({\rm renormal. \ schemes}) = 0.1226^{+0.0058}_{−0.0038}  \end{equation}