deletions | additions       diff --git a/Measurements at the Z pole.tex b/Measurements at the Z pole.tex  index feafeb6..bff3bde 100644  --- a/Measurements at the Z pole.tex  +++ b/Measurements at the Z pole.tex 
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  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 $10^{-4}$ $< 10^{-5}$  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 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}.  
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\\  {\em A precision of $10^{-6}$ on $\sin^2\theta_W^{eff}$ is a reasonable goal for the measurement of the leptonic weak mixing angle at TLEP}  An electroweak correction of great interest is the vertex correction to the $b$ partial width, which affects $\Gamma_Z$, $R_\ell$, the peak hadronic cross-section and, most sensitively, $R_b \equiv \frac{\Gamma_b}{\Gamma_{had}}$. $R_b$ was measured at LEP and SLC by tagging $b\bar{b}$ by the presence of one tagged $b$-jet and the efficiency was controlled by double tag. The present experimental value is $R_b = 0.21629 \pm 0.00066$ with a roughly equal sharing between systematic and statistical errors. The double $b$ tagging method is self-calibrating, and indeed most of the systematics are based on experimental tests related to the modeling of events, and should decrease with accumulated statistics. The  SLD detector at SLC was the most efficient by the double effect of having a more precise detector, and the beam spot being smaller, thus allowing a more precise determination of the impact parameter of secondary hadrons. We expect the experimental conditions at TLEP  to be similar to LEP with the exception that the beam size at the IP is smaller in all dimension, thus dimensions, ensuring that  the $b$-tagging abilities should be rather similar to those of SLD than to those of LEP. \\   {\em A precision of $2-510^{-5}$ seems to be a reasonable goal for the measurement of on $R_b$ at TLEP}  The very large statistics accumulated at TLEP-Z, including $3 \times10^{10}$ tau pairs or muon pairs, should allow a new range of searches for rare phenomena and tests of conservation laws that remain to be investigated. It will be the prupose of the upcoming design study to examine and complete our first look at the immense physics potential of TLEP-Z.