# ${{\boldsymbol Z}}$ 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 .

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

Using polarized beams, this quantity can also be measured as ($\sigma{}_{\mathit L}$ $−$ $\sigma{}_{\mathit R})/$ ($\sigma{}_{\mathit L}$ $+$ $\sigma{}_{\mathit R}$), where $\sigma{}_{\mathit L}$ and $\sigma{}_{\mathit R}$ are the ${{\mathit e}^{+}}{{\mathit e}^{-}}$ production cross sections for ${{\mathit Z}}$ bosons produced with left-handed and right-handed electrons respectively.

VALUE EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 0.1515 \pm0.0019}$ OUR AVERAGE
$0.1454$ $\pm0.0108$ $\pm0.0036$ 144810 1
 2001 O
OPAL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.1516$ $\pm0.0021$ 559000 2
 2001 B
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.24$ GeV
$0.1504$ $\pm0.0068$ $\pm0.0008$ 3
 2001
ALEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.1382$ $\pm0.0116$ $\pm0.0005$ 105000 4
 2000 E
DLPH ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.1678$ $\pm0.0127$ $\pm0.0030$ 137092 5
 1998 H
L3 ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV
$0.162$ $\pm0.041$ $\pm0.014$ 89838 6
 1997
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.27$ GeV
$0.202$ $\pm0.038$ $\pm0.008$ 7
 1995 J
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.31$ 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 use the left-right production and left-right forward-backward decay asymmetries in leptonic ${{\mathit Z}}$ decays to obtain a value of $0.1544$ $\pm0.0060$. This is combined with left-right production asymmetry measurement using hadronic ${{\mathit Z}}$ decays (ABE 2000B) to obtain the quoted value.
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).
5  Derived from the measurement of forward-backward ${{\mathit \tau}}$ polarization asymmetry.
6  ABE 1997 obtain this result from a measurement of the observed left-right charge asymmetry, $\mathit A{}^{{\mathrm {obs}}}_{\mathit Q}$ = $0.225$ $\pm0.056$ $\pm0.019$, in hadronic ${{\mathit Z}}~$decays. If they combine this value of $\mathit A{}^{{\mathrm {obs}}}_{\mathit Q}$ with their earlier measurement of $\mathit A{}^{{\mathrm {obs}}}_{ }$ they determine $\mathit A_{{{\mathit e}}}$ to be $0.1574$ $\pm0.0197$ $\pm0.0067$ independent of the beam polarization.
7  ABE 1995J obtain this result from polarized Bhabha scattering.
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
 ABE 1997
PRL 78 17 First Measurement of the Left Right Charge Asymmetry in Hadronic ${{\mathit Z}}$ Boson Decays and a New Determination of sin$^2{{\mathit \theta}}{}^{eff}_{\mathit W}$
 ABE 1995J
PRL 74 2880 Polarized Bhabha Scattering a Precision Measurement of the Electron Neutral Current Couplings
 ABE 1997W
PRL 79 3819 Search for New Particles Decaying into ${\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}$ and Produced in Association with ${{\mathit W}}$ Bosons Decaying into ${{\mathit e}}{{\mathit \nu}}$ or ${{\mathit \mu}}{{\mathit \nu}}$ at the Tevatron
 ABE 2000B
PRL 84 5945 A High Precision Measurement of the Left-Right ${{\mathit Z}}$ Boson Cross Section Asymmetry