${{\boldsymbol Z}}$ 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 .

$\boldsymbol A_{{{\boldsymbol \mu}}}$ INSPIRE search

This quantity is directly extracted from a measurement of the left-right forward-backward asymmetry in ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ production at SLC using a polarized electron beam. This double asymmetry eliminates the dependence on the ${{\mathit Z}}-{{\mathit e}}-{{\mathit e}}$ coupling parameter $\mathit A_{{{\mathit e}}}$.
$0.142$ $\pm0.015$ 16844 1
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.24$ GeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.153$ $\pm0.012$ 1.7M 2
ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 7 TeV
1  ABE 2001B obtain this direct measurement using the left-right production and left-right forward-backward polar angle asymmetries in ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ decays of the ${{\mathit Z}}$ boson obtained with a polarized electron beam.
2  AAD 2015BT study ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ events where ${{\mathit \ell}}$ is an electron or a muon in the dilepton mass region $70 - 1000$ GeV. The background in the ${{\mathit Z}}$ peak region is estimated to be $<$ 1$\%$ for the muon channel. The muon asymmetry parameter is derived from the measured forward-backward asymmetry assuming the value of the quark asymmetry parameter from the SM. For this reason it is not used in the average.
AAD 2015BT
JHEP 1509 049 Measurement of the Forward-Backward Asymmetry of Electron and Muon Pair-Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with the ATLAS Detector
ABE 2001B
PRL 86 1162 An Improved Direct Measurement of Leptonic Coupling Asymmetries with Polarized ${{\mathit Z}}$ Bosons