deletions | additions       diff --git a/alphasW.tex b/alphasW.tex  index 29c701d..ce01e5e 100644  --- a/alphasW.tex  +++ b/alphasW.tex 
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Beyond the measurement of $R_\ell$ at the Z pole, another interesting possibility for the $\alpha_{\rm s}$ determination is to use to use the W hadronic width as measured from W-pair events at and above 161 GeV. The quantity of interest is the branching ratio $B_{\rm had}= \Gamma_{\rm W \to hadrons}/\Gamma^tot_{\rm W}$, which can extract be extracted by measuring the fractions of WW events to the  fully leptonic, semi-leptonic and fully hadronic final states:   \begin{equation}  {\rm BR({\rm WW} \to \ell^+ \nu \ell’^- \bar{\nu}) = (1-B_{\rm had})^2 \\ \end{equation}   \begin{equation}  {\rm BR({\rm WW} \to \ell^+ \nu {\rm q\bar{q’}}) = (1-B_{\rm had})\times B_{\rm had} \\ \end{equation}   \begin{equation}  {\rm BR({\rm WW} \to {\rm q\bar{q’} q’’\bar{q’’’}})= B_{\rm had}^2\\ had}^2  \end{equation}