deletions | additions       diff --git a/Measurements at the Z pole.tex b/Measurements at the Z pole.tex  index 7155a70..797f8b3 100644  --- a/Measurements at the Z pole.tex  +++ b/Measurements at the Z pole.tex 
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An extensive description of Electroweak measurements performed at LEP and SLC in 1988-1998 can be found in~\cite{ements_on_the_Z_resonance_2006}. It is beyond the scope of this article to revisit all the measurements to establish the improvements brought about by TLEP, and we limit ourselves to a few key measurements. The typical improvement in statistics over the LEP experiments being a factor $10^5$ (a factor 300 reduction in statistical errors!) it is clear that a detailed consideration of systematic errors will be essential before a precise conclusion will be drawn on the achievable precisions. In addition, uncertainties in the theoretical interpretation will need to be revisited, this implying a significant new program of calculations of higher order Electroweak corrections.   The Z mass was determined at LEP from the line-shape scan to be $91187.5 \pm 2.1$ MeV/$c^2$. The statistical error was 1.2 MeV; it would be below 10 keV at TLEP. The systematic error was dominated by the error related to the beam energy calibration (1.7 MeV). As seen in the previous section, a continuous measurement should allow a reduction to below 100 keV. Other errors include the theoretical uncertainties in the calculation of initial state radiation ( $\le 100 keV$), production of additional lepton pairs ( $\le 300 keV$) and in the theoretical line shape parametrization ( $\le 100 keV$). It is clear that revisiting the QED corrections will be a high priority item when embarking in a new program of precision measurements at TLEP. \\  {\em We consider that 100 keV is a an  reasonable target goal for the Z mass precision at TLEP}. The Z width was also determined from the line shape scan to be $2495.2 \pm 2.3$ MeV/$c^2$. The statistical error was 2 MeV and would be again less that 10 KeV at TLEP. The systematic uncertainty from the LEP energy calibration was 1.2 MeV, clearly dominated by the reproducibility issues. Again this should be reduced to below 100 keV at TLEP.   The theory systematics on $\Gamma_Z$ were estimated at the level of ( $\le 200 keV$) and should be revisited. \\  {\em We consider that 100 keV is a reasonable target goal for the Z width precision at TLEP}.      Determination of the Z partial widths requires measurements of branching ratios at the Z peak, in particular the ratio of branching fractions of the Z boson into lepton to hadrons and the peak hadronic cross-section. The hadronic to leptonic ratio was measured at LEP to be $R_\ell = \frac{\Gamma_{had}}{\Gamma_{\ell}}= 20.767\pm 0.025$   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 goal would be to reduce the uncertainty on $N_\nu$ down to $\pm 0.001$} 0.001$  but it is not clear that it can be achieved. achieved}.