${{\mathit Z}}$ ASYMMETRY PARAMETERS

For each fermion-antifermion pair coupling to the ${{\mathit Z}}$ these quantities are defined as
$\mathit A_{\mathit f}$ = ${2 {\it g}^{\it f}_{\it V} {\it g}^{\it f}_{\it A}\over ({\it g}^{\it f}_{\it V}){}^{2}+({\it g}^{\it f}_{\it A}){}^{2}}$
where ${\it g}^{\it f}_{\it V}$ and ${\it g}^{\it f}_{\it A}$ are the effective vector and axial-vector couplings. For their relation to the various lepton asymmetries see the note “The ${{\mathit Z}}$ boson” and ref. LEP-SLC 2006.

$\mathit A_{{{\mathit \tau}}}$

INSPIRE   JSON  (beta) PDGID:
S044AT
The LEP and LHC Collaborations collaboration derive this quantity from the measurement of the ${{\mathit \tau}}$ polarization in ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$. The SLD Collaboration directly extracts this quantity from its measured left-right forward-backward asymmetry in ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ produced using a polarized ${{\mathit e}^{-}}$ beam. This double asymmetry eliminates the dependence on the ${{\mathit Z}}-{{\mathit e}}-{{\mathit e}}$ coupling parameter $\mathit A_{{{\mathit e}}}$.
VALUE EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 0.143 \pm0.004}$ OUR AVERAGE
$0.144$ $\pm0.015$ 1
HAYRAPETYAN
2024T
 CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV
$0.1456$ $\pm0.0076$ $\pm0.0057$ 144810 2
ABBIENDI
2001O
 OPAL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.136$ $\pm0.015$ 16083 3
ABE
2001B
 SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.24$ GeV
$0.1451$ $\pm0.0052$ $\pm0.0029$ 4
HEISTER
2001
ALEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.1359$ $\pm0.0079$ $\pm0.0055$ 105000 5
ABREU
2000E
 DLPH ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.1476$ $\pm0.0088$ $\pm0.0062$ 137092
ACCIARRI
1998H
 L3 ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
1  HAYRAPETYAN 2024T analyse the polarisation of tau leptons in ${{\mathit Z}}$ bosons decaying to tau pairs.
2  ABBIENDI 2001O fit for $\mathit A_{{{\mathit e}}}$ and $\mathit A_{{{\mathit \tau}}}$ from measurements of the ${{\mathit \tau}}~$polarization at varying ${{\mathit \tau}}~$production angles. The correlation between $\mathit A_{{{\mathit e}}}$ and $\mathit A_{{{\mathit \tau}}}$ is less than $0.03$.
3  ABE 2001B obtain this direct measurement using the left-right production and left-right forward-backward polar angle asymmetries in ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ decays of the ${{\mathit Z}}$ boson obtained with a polarized electron beam.
4  HEISTER 2001 obtain this result fitting the ${{\mathit \tau}}$ polarization as a function of the polar production angle of the ${{\mathit \tau}}$.
5  ABREU 2000E obtain this result fitting the ${{\mathit \tau}}~$polarization as a function of the polar ${{\mathit \tau}}~$production angle. This measurement is a combination of different analyses (exclusive ${{\mathit \tau}}~$decay modes, inclusive hadronic 1-prong reconstruction, and a neural network analysis).
References