deletions | additions       diff --git a/Measurements at the Z pole.tex b/Measurements at the Z pole.tex  index 7bd1872..a8cb19d 100644  --- a/Measurements at the Z pole.tex  +++ b/Measurements at the Z pole.tex 
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with a common systematic error of 0.007. The experimental error was dominated by the statistics of leptonic decays; selection systematics will tend to decrease with statistics. The remaining systematics are related to the t-channel contribution in the electron channel (this could be removed by using the muon channel only) 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. \\   {\em We consider that a relative precision of $10^{-4}$ is a reasonable target goal for the ratio of the hadronic to leptonic partial widths at TLEP-Z }.  This measurement of the peak hadronic cross-section is already dominated by theoretical systematics related to the understanding of the low angle Bhabha cross-section. It is a measurement of great interest as it determines the Z invisible width, a direct test of the unitarity of the PMNS matrix -- or of the existence of sterile neutrinos. The present measurement expressed in terms of a number of active neutrinos $N_\nu = 2.984 \pm 0.008$ is ~2$\sigma$ below the SM value of 3. The experimental conditions at TLEP will be adequate to improve the experimental uncertainty considerably but a considerable effort will have to be invested in the theoretical calculations to make this measurement worthwhile. {\em A wishful desirable  goal would be to reduce the uncertainty on $N_\nu$ down to $\pm 0.001$ but it is not clear that it can be achieved}. Determination of the weak mixing angle $\sin^2\vartheta_W^{eff}$ are made from a variety of measurments, such as the leptonic and hadronic forward-backward asymmetries, the $\tau$ polarization. The most precise is the inclusive left-right beam polarization asymmetry $A_{LR}$, since this quantity can be measured with from the total cross-section asymmetry upon reversal of the $\epem$ system polarization. Assuming the same level of polarization in collisions at TLEP than what was observed at LEP, and that a fraction of the bunches can be selectively depolarized to ensure longitudinal polarization of the $\epem$ system, a simultaneous measurement~\cite{Blondel:1987wr} of the beam polarization and of the left-right asymmetry $A_{LR}$ can be envisaged. For one year of data taking a precision on $A_{LR}$ of the order of $10^{-5}$ – or a precision on $\sin^2\theta_W^{eff}$ of the order of $10^{-6}$ would be achieved. Other beam polarization asymmetries for selected final states, $A_{FB}^{pol,f}$, will allow precise measurements of the electroweak couplings as well as being an interesting tool for flavour selection.  Determination of the weak mixing angle $\sin^2\vartheta_W^{eff}$ are made from a variety of measurments, such as the leptonic and hadronic forward-backward asymmetries, the $\tau$ polarization. The most precise is the inclusive left-right beam polarization asymmetry $A_{LR}$, since this quantity can be measured with from the total cross-section asymmetry upon reversal of the $\epem$ system polarization.