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

The polarization of τ leptons is measured using leptonic and hadronic τ lepton decays in Z → τ + τ − events in proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded by CMS at the CERN LHC with an integrated luminosity of 36.3 fb −1. The measured τ − lepton polarization at the Z boson mass pole is ${P}_{\tau }\left(Z\right)$ = −0.144 ± 0.006 (stat) ± 0.014 (syst) = −0.144 ± 0.015, in good agreement with the measurement of the τ lepton asymmetry parameter of A τ = 0.1439 ± 0.0043 = $-{P}_{\tau }\left(Z\right)$ at LEP. The τ lepton polarization depends on the ratio of the vector to axial-vector couplings of the τ leptons in the neutral current expression, and thus on the effective weak mixing angle sin2 ${\theta }_{W}^{\mathrm{eff}}$ , independently of the Z boson production mechanism. The obtained value sin2 ${\theta }_{W}^{\mathrm{eff}}$ = 0.2319 ± 0.0008(stat) ± 0.0018(syst) = 0.2319 ± 0.0019 is in good agreement with measurements at e + e − colliders.