Measurement of the polarization of tau leptons produced in Z decays at CMS and determination of the effective weak mixing angle

In this thesis the first measurement of the $\tau$-lepton polarization in $Z \rightarrow \tau\tau$ decays is performed at a proton-proton collider. A sample of 8818 events of the decay $Z^{0} \rightarrow \tau^{+}\tau^{-} \rightarrow \mu\nu\nu$, $a_{1}\nu$ is used. It is selected in data corresponding to a luminosity of 19.6 fb$^{-1}$ collected by the CMS detector at 8 TeV. The average polarization is measured to be: \begin{equation*}= -0.1261 \pm 0.073 (stat) ^{+0.018}_{-0.019} (syst).\end{equation*} From the value of the measured $\tau$ polarization the effective weak mixing angle is derived: \begin{equation*}\sin^{2}\theta_{eff} = 0.2336 \pm 0.0096.\end{equation*} The ratio of vector to axial-vector neutral current couplings for $\tau$ leptons derived from the measured value of $\sin^{2}\theta_{eff}$: \begin{equation*}g^{\tau}_{V}/g^{\tau}_{A} = 0.0656 \pm 0.0384.\end{equation*} The result for the weak mixing angle is consistent with previous measurements and the value of the ratio between vector and axial-vector couplings supports lepton universality