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Precise energy calibration with resonant depolarization.   \end{itemize}  In the following we will describe briefly the potential of TLEP for precise measurements at or around the Z pole, at the W pair threshold, and the top quark pair threshold. A summary of the potential of TLEP for precision electroweak measurements is given in Table~\ref{tab:EW-TLEP}. Combined with the permil precision measurements of the Higgs boson properties, TLEP could offer definitive investigations on the Electroweak Symmetry breaking, and on the possible existence of weakly interacting particles beyond those already known, with a precision sufficient for discovery. It will be the task of the upcoming design study to examine what are the requirements and possible difficulties in turning this potential into reality.   \begin{landscape}   \begin{table}[htbp]   \begin{center}   \caption{Table~\ref{tab:EW-TLEP} Selected set of precision measurements at TLEP. Statistical errors have been calculated using the following assumptions: \\   1 year scan of the Z line shape with 50\% data at the peak, using resonant depolarization of single for energy calibration at O(20min) intervals leading to $710^{11}$ Z decays ($M_Z,\Gamma_Z, R_{\ell} , N_{\nu}$ from peak cross-section, $R_b$). \\   1 year data taking with longitudinal polarized beams at 40\% beam polarization and luminosity reduced to 20\% of nominal (requires spin rotators).\\   1 Year data taking around 161 GeV (WW threshold scan) with resonant depolarization for energy calibration at O(20min) intervals ($M_W , N_{\nu}$ from ratio of $Z\gamma$ events with invisible Z vs leptonic Z decays).\\   5 years of data taking at 350 GeV (top threshold scan).   Systematic errors are only a “first look” estimate and will be revisited in the course of the design study.\label{tab:EW-TLEP}}   \begin{tabular}{|l|c|c|c|c|c|c|c|}   \hline Quantity & Physics & Present precision & &TLEP Stat errors & Possible TLEP Syst. Errors & TLEP key & Challenge \\   \hline \hline   $M_Z $ (keV) & Input & $ 91187500 \pm 2100 $ & Z Line shape scan & $5$ keV &   $<100$ keV & $E_{beam}$ calibration & QED corrections\\   \hline   $\Gamma_Z $ (keV) & $ \Delta_{\rho}$ (T) (not $\Delta_{\alpha}$(had))& $ 2495200 \pm 2300$ & Z Line shape scan & $ 8 $ keV &$<100$ keV & $E_{beam}$ calibration & QED corrections \\   \hline   $R_{\ell}$ & $\alpha_s , \delta_b$ & $ 20.767 \pm 0.025$& Z Peak& $ 0.0001$&$ <0.001$& Statistics &QED corrections\\   \hline   $N_{\nu}$ & PMNS Unitarity, sterile $\nu$’s & $ 2.984 \pm 0.008$ & Z Peak & $0.00008$ & $<0.004 $ & & Bhabha scat.\\   \hline   $N_{\nu}$ & PMNS Unitarity, sterile $\nu$’s & $ 2.92 \pm 0.05$ & $Z\gamma$, 161 GeV & $0.001$ & $<0.001 $ & statistics & \\   \hline   $R_b$ &$ $ $\delta_b$ & $ 0.21629 \pm 0.00066$& Z Peak&$0.000003$&$<0.000060$& Statistics, small IP& Hemisphere correlations\\   \hline   $A_{LR}$& $\Delta_{\rho}$ (T) , $\epsilon_3$(S),$\Delta_{\alpha}$(had))& $ 0.1514   \pm 0.0022$& Z peak, polarized&$ 0.000015$&$ <0.000015$& 4 bunch scheme,   2exp& Design experiment \\   \hline   $M_W$   (MeV) & $\Delta_{\rho}$ (T) , $\epsilon_3$(S),$\epsilon_2$(U),$\Delta_{\alpha}$(had))& $80385   \pm 15$& Threshold scan (161 GeV)&$ 0.3 $ MeV&$ <0.5 $ MeV& $E_{beam}$ calibration   Statistics& QED corections\\   \hline   $m_{top}$ (MeV) &Input&$173200 \pm 900$&Threshold scan (350 GeV) &$10$ MeV& $<10$ MeV & Statistics& Theory interpretation 40 MeV?\\   \hline   \end{tabular}   \end{center}   \end{table}   \end{landscape}