\subsubsection{The Z hadronic and leptonic partial widths}
\label{sec:Rell}

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 and into hadrons -- and the peak hadronic cross section. The hadronic-to-leptonic ratio was measured at LEP to be 
\begin{equation}
\label{eq:Rl} R_\ell = \frac{\Gamma_{\rm had}}{\Gamma_{\ell}}= 20.767\pm 0.025,
\end{equation}
with a systematic uncertainty of 0.007. The experimental uncertainty was dominated by the statistics of leptonic decays, and other uncertainties related to the event selection will tend to decrease with statistics. The remaining systematic uncertainties were related to the $t$-channel contribution in the electron channel (which would vanish by the sole use of the muon channel) 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. The measurements of the partial widths into electron, muon and tau pairs will also allow tests of the lepton universality in Z decays with considerably improved precision with respect to what was achieved LEP.\\ 
\textbf{\textit{A relative precision of $\boldsymbol{\it 5 \times 10^{-5}}$ is considered to be a reasonable target for the ratio of the Z hadronic-to-leptonic partial widths at TLEP, as well as for the ratios of the Z leptonic widths (as a test of lepton universality).}}\\

