Improved Direct Measurement of Leptonic Coupling Asymmetries with Polarized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">Z</mml:mi></mml:math>Bosons

Abstract

We present final measurements of the $Z$ boson-lepton coupling asymmetry parameters ${A}_{e}$, ${A}_{\ensuremath{\mu}}$, and ${A}_{\ensuremath{\tau}}$ with the complete sample of polarized $Z$ bosons collected by the SLD detector at the SLAC Linear Collider. From the left-right production and decay polar angle asymmetries in leptonic $Z$ decays we measure ${A}_{e}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.1544\ifmmode\pm\else\textpm\fi{}0.0060$, ${A}_{\ensuremath{\mu}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.142\ifmmode\pm\else\textpm\fi{}0.015$, and ${A}_{\ensuremath{\tau}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.136\ifmmode\pm\else\textpm\fi{}0.015$. Combined with our left-right asymmetry measured from hadronic decays, we find ${A}_{e}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.1516\ifmmode\pm\else\textpm\fi{}0.0021$. Assuming lepton universality, we obtain a combined effective weak mixing angle of ${sin}^{2}{\ensuremath{\theta}}_{W}^{\mathrm{eff}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.23098\ifmmode\pm\else\textpm\fi{}0.00026$.