# ${{\boldsymbol Z}}$ 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 .

# $\boldsymbol A_{{{\boldsymbol \tau}}}$ INSPIRE search

The LEP Collaborations 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
$0.1456$ $\pm0.0076$ $\pm0.0057$ 144810 1
 2001 O
OPAL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.136$ $\pm0.015$ 16083 2
 2001 B
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.24$ GeV
$0.1451$ $\pm0.0052$ $\pm0.0029$ 3
 2001
ALEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.1359$ $\pm0.0079$ $\pm0.0055$ 105000 4
 2000 E
DLPH ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.1476$ $\pm0.0088$ $\pm0.0062$ 137092
 1998 H
L3 ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
1  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 $0.03$.
2  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.
3  HEISTER 2001 obtain this result fitting the ${{\mathit \tau}}$ polarization as a function of the polar production angle of the ${{\mathit \tau}}$.
4  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:
 ABBIENDI 2001O
EPJ C21 1 Precision Neutral Current Asymmetry Parameter Measurements from the ${{\mathit \tau}}$ Polarization at LEP
 ABE 2001B
PRL 86 1162 An Improved Direct Measurement of Leptonic Coupling Asymmetries with Polarized ${{\mathit Z}}$ Bosons
 HEISTER 2001
EPJ C20 401 Measurement of the ${{\mathit \tau}}$ Polarization at LEP
 ABREU 2000E
EPJ C14 585 A Precise Measurement of the ${{\mathit \tau}}$ Polarization at LEP-1
 ACCIARRI 1998H
PL B429 387 Measurement of ${{\mathit \tau}}$ Polarization at LEP