Abstract
The polarization of τ leptons is measured using leptonic and hadronic τ lepton decays in Z → τ
+
τ
−
events in proton-proton collisions at
$$ \sqrt{s} $$
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
$$ {\mathcal{P}}_{\tau}\left(\textrm{Z}\right) $$
P
τ
Z
= −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 =
$$ -{\mathcal{P}}_{\tau}\left(\textrm{Z}\right) $$
−
P
τ
Z
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
$$ {\theta}_{\textrm{W}}^{\textrm{eff}} $$
θ
W
eff
, independently of the Z boson production mechanism. The obtained value sin2
$$ {\theta}_{\textrm{W}}^{\textrm{eff}} $$
θ
W
eff
= 0.2319 ± 0.0008(stat) ± 0.0018(syst) = 0.2319 ± 0.0019 is in good agreement with measurements at e
+
e
−
colliders.
