# ${{\boldsymbol Z}}$ 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 .

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

This quantity is directly extracted from a measurement of the left-right forward-backward asymmetry in ${{\mathit b}}{{\overline{\mathit b}}}$ production at SLC using polarized electron beam. This double asymmetry eliminates the dependence on the ${{\mathit Z}}-{{\mathit e}}-{{\mathit e}}$ coupling parameter $\mathit A_{{{\mathit e}}}$. OUR FIT is obtained by a simultaneous fit to several ${{\mathit c}}$- and ${{\mathit b}}$-quark measurements as explained in the note The ${{\mathit Z}}~$boson'' and ref. LEP-SLC 2006 .
VALUE EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 0.923 \pm0.020}$ OUR FIT
$0.9170$ $\pm0.0147$ $\pm0.0145$ 1
 2005
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= 91.24 GeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.907$ $\pm0.020$ $\pm0.024$ 48028 2
 2003 F
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= 91.24 GeV
$0.919$ $\pm0.030$ $\pm0.024$ 3
 2002 G
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.24$ GeV
$0.855$ $\pm0.088$ $\pm0.102$ 7473 4
 1999 L
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= 91.27 GeV
1  ABE 2005 use hadronic ${{\mathit Z}}$ decays collected during $1996 - 98$ to obtain an enriched sample of ${{\mathit b}}{{\overline{\mathit b}}}$ events tagging on the invariant mass of reconstructed secondary decay vertices. The charge of the underlying b$-$quark is obtained with an algorithm that takes into account the net charge of the vertex as well as the charge of tracks emanating from the vertex and identified as kaons. This yields (25917 events) ${{\mathit A}_{{b}}}$ = $0.9173$ $\pm0.0184$ $\pm0.0173$. Taking into account all correlations with earlier results reported in ABE 2003F, ABE 2002G and ABE 1999L, they obtain the quoted overall SLD result.
2  ABE 2003F obtain an enriched sample of ${{\mathit b}}{{\overline{\mathit b}}}$ events tagging on the invariant mass of a 3-dimensional topologically reconstructed secondary decay. The charge of the underlying ${{\mathit b}}~$quark is obtained using a self-calibrating track-charge method. For the 1996--1998 data sample they measure $\mathit A_{{{\mathit b}}}$ = $0.906$ $\pm0.022$ $\pm0.023$. The value quoted here is obtained combining the above with the result of ABE 1998I (1993--1995 data sample).
3  ABE 2002G tag ${{\mathit b}}$ and ${{\mathit c}}$ quarks through their semileptonic decays into electrons and muons. A maximum likelihood fit is performed to extract simultaneously $\mathit A_{{{\mathit b}}}$ and $\mathit A_{{{\mathit c}}}$.
4  ABE 1999L obtain an enriched sample of ${{\mathit b}}{{\overline{\mathit b}}}$ events tagging with an inclusive vertex mass cut. For distinguishing ${{\mathit b}}$ and ${{\overline{\mathit b}}}$ quarks they use the charge of identified ${{\mathit K}^{\pm}}$.
References:
 ABE 2005
PRL 94 091801 Direct Measurements of $\mathit A_{b}$ and $\mathit A_{c}$ using Vertex/Kaon Charge Tags at SLD
 ABE 2003F
PRL 90 141804 Improved Direct Measurement of the Parity Violation Parameter $\mathit A_{b}$ using a Mass Tag and Momentum-Weighted Track Charge
 ABE 2002G
PRL 88 151801 Improved Direct Measurement of $\mathit A_{b}$ and $\mathit A_{c}$ at the ${{\mathit Z}^{0}}$ Pole using a Lepton Tag
 ABE 1999L
PRL 83 1902 Direct Measurement of $\mathit A_{b}$ in ${{\mathit Z}}$ Decays Using Charged Kaon Tagging
 ABE 1998I
PRL 81 942 A Direct Measurement of Parity Violation in the Coupling of ${{\mathit Z}}$ Bosons to b Quarks using a Mass Tag and Momentum Weighted Track Charge
 ABE 2005H
hep-ex/0512071 A High Statistics Study of the Decay ${{\mathit \tau}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{0}}{{\mathit \nu}_{{\tau}}}$
 LEP-SLC 2006
PRPL 427 257 Precision Electroweak Measurements on the ${{\mathit Z}}$ Resonance