Measurement of the $\tau$ lepton polarization in Z boson decays in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The polarization of $\tau^{-}$ leptons is measured using leptonic and hadronic $\tau^{-}$ lepton decays in $Z\rightarrow \tau^{+}\tau^{-}$ events in proton-proton collisions at $\sqrt{s}=13\,\mathrm{TeV}$ recorded by CMS at the CERN LHC with an integrated luminosity of $36.3\,\mathrm{fb}^{-1}$.The measured $\tau^{-}$ polarization at the $\mathrm{Z}$ boson mass pole is $\mathcal{P}_{\tau}(\mathrm{Z})=-0.144\pm0.006\,(\text{stat})\,\pm0.014\,(\text{syst})=-0.144\pm0.015$,in good agreement with the measurement of the $\tau$ lepton asymmetry parameter of $A_{\tau}=0.1439\pm0.0043=-\mathcal{P}_{\tau}(\mathrm{Z})$ at LEP.The $\tau$ polarization depends on the ratio of the vector to axial-vector couplings of the $\tau$ leptons in the neutral current expression, and thus on the effective weak mixing angle $ \sin^{2}\theta_{\mathrm{W}}^{\mathrm{eff}}$, independently of the $\mathrm{Z}$ boson production mechanism.The obtained value $ \sin^{2}\theta_{\mathrm{W}}^{\mathrm{eff}}=0.2319\pm0.0008\,(\text{stat})\pm0.0018\,(\text{syst})=0.2319\pm0.0019$is in good agreement with measurements at $\mathrm{e^{+}e^{-}}$ colliders.