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Patrick Janot added Mixing angle.tex
almost 11 years ago
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Determinations of the weak mixing angle $\sin^2\vartheta_W^{eff}$ are made from a variety of measurements, such as the leptonic and hadronic forward-backward asymmetries and the $\tau$ polarization. The single most precise measurement comes from the inclusive left-right beam polarization asymmetry $A_{LR}$, since this quantity can be measured from the total cross-section asymmetry upon reversal of the polarization of the $\epem$ system. 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.
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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 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.
