deletions | additions       diff --git a/Z partial widths and peak cross section.tex b/Z partial widths and peak cross section.tex  index 2e6a40b..522720c 100644  --- a/Z partial widths and peak cross section.tex  +++ b/Z partial widths and peak cross section.tex 
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\begin{equation}  R_\ell = \frac{\Gamma_{\rm had}}{\Gamma_{\ell}}= 20.767\pm 0.025,  \end{equation}  with a systematic uncertainty of 0.007. The experimental uncertainty was dominated by the statistics of leptonic decays, and other uncertainties related to the event selection will tend to decrease with statistics. The remaining systematic uncertainty were related to the $t$-channel contribution in the electron channel (which would vanish by the sole use of the muon channel) and to the detailed modelling of final-state radiation or emission of additional lepton pairs. Here, theory should be considerably helped by the large sample of leptonic Z decays available for the study of these rare processes. The measurements of the partial widths into electron, muon and tau pairs will also allow tests of the lepton universality in Z decays with considerably improved precision wit with  respect to what was achieved LEP.\\ {\em A relative precision of less than $10^{-5}$ is considered to be a reasonable target for the ratio of the Z hadronic-to-leptonic partial widths at TLEP, as well as for the ratios of the Z leptonic widths (as a test of lepton universality).}\\  \subsubsection{The peak hadronic cross section and the number of neutrinos}