# ${{\boldsymbol Z}}$ 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 .

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

This quantity is directly extracted from a measurement of the left-right forward-backward asymmetry in ${{\mathit c}}{{\overline{\mathit c}}}$ 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 DOCUMENT ID TECN  COMMENT
$\bf{ 0.670 \pm0.027}$ OUR FIT
$0.6712$ $\pm0.0224$ $\pm0.0157$ 1
 2005
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.24$ GeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.583$ $\pm0.055$ $\pm0.055$ 2
 2002 G
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.24$ GeV
$0.688$ $\pm0.041$ 3
 2001 C
SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $91.25$ GeV
1  ABE 2005 use hadronic ${{\mathit Z}}$ decays collected during $1996 - 98$ to obtain an enriched sample of ${{\mathit c}}{{\overline{\mathit c}}}$ events tagging on the invariant mass of reconstructed secondary decay vertices. The charge of the underlying c$-$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 (9970 events) ${{\mathit A}_{{c}}}$ = $0.6747$ $\pm0.0290$ $\pm0.0233$. Taking into account all correlations with earlier results reported in ABE 2002G and ABE 2001C, they obtain the quoted overall SLD result.
2  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 $\mathit A_{{{\mathit c}}}$.
3  ABE 2001C tag ${{\mathit Z}}$ $\rightarrow$ ${{\mathit c}}{{\overline{\mathit c}}}$ events using two techniques: exclusive reconstruction of ${{\mathit D}^{*+}}$, ${{\mathit D}^{+}}$ and ${{\mathit D}^{0}}$ mesons and the soft pion tag for ${{\mathit D}^{*+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{+}}$ . The large background from ${{\mathit D}}$ mesons produced in ${{\mathit b}}{{\overline{\mathit b}}}$ events is separated efficiently from the signal using precision vertex information. When combining the $\mathit A_{{{\mathit c}}}$ values from these two samples, care is taken to avoid double counting of events common to the two samples, and common systematic errors are properly taken into account.
References:
 ABE 2005
PRL 94 091801 Direct Measurements of $\mathit A_{b}$ and $\mathit A_{c}$ using Vertex/Kaon Charge Tags at SLD
 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 2001C
PR D63 032005 Measurement of $\mathit A_{c}$ with Charmed Mesons at SLD
 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