${{\boldsymbol Z}}$ 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 $\mathit A_{{{\mathit e}}}$.
VALUE EVTS DOCUMENT ID TECN  COMMENT
$0.142$ $\pm0.015$ 16844 1
 2001 B
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
 2015 BT
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.
References:
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
PRL 86 1162 An Improved Direct Measurement of Leptonic Coupling Asymmetries with Polarized ${{\mathit Z}}$ Bosons