Measurement of the Parity-Violation Parameter<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>from the Left-Right Forward-Backward Asymmetry of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">b</mml:mi></mml:math>Quark Production in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">Z</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Decays Using a Momentum-Weighted Track-Charge Technique

Using an impact parameter tag to select an enriched sample of ${Z}^{0}\ensuremath{\rightarrow}b\overline{b}$ events, and the net momentum-weighted track charge to identify the sign of the charge of the underlying $b$ quark, we have measured the left-right forward-backward asymmetry for $b$ quark production as a function of polar angle. Based on $1.8{\mathrm{pb}}^{\ensuremath{-}1}$ of ${Z}^{0}$ decay data produced with a mean electron beam polarization of ${P}_{e}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}63%$, this yields a direct measurement of the extent of parity violation in the $\mathrm{Zbb}$ coupling of ${A}_{b}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.87\ifmmode\pm\else\textpm\fi{}0.11(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.09(\mathrm{syst})$.