Longitudinal-$e^{\mathrm{-}}$-beam-polarization asymmetry in $e^{+}$$e^{\mathrm{-}}$→hadrons

We introduce and analyze the longitudinal-polarization asymmetry of the process $e^{+}$ $e^{\mathrm{-}}$→hadrons with longitudinally polarized electron beams on and near the $Z^0$ resonance. We show that, in spite of the intrinsic strong-interaction presence in the final state, the vast majority of the diagrams which contribute to one electroweak loop are free of strong-interaction effects. Further, on $Z^0$ resonance the asymmetry is independent of the final states, giving a commensurate increase in statistics. We show that for these reasons the total theoretical strong-interaction uncertainty on $Z^0$ resonance is Δ$A_{\mathrm{LR}}^{e^{+}{e}^{\mathrm{-}}\to \mathrm{hadrons}\lesssim 0.004}$, allowing a measurement of $A_{\mathrm{LR}}$ to ±0.015 (which can be interpreted as a measurement of ${\sin }^2$ ${\mathrm{\theta }}_{\mathrm{W}}$ to ±0.002) with only ∼5×${10}^4$ $Z^0$’s. Further, a measurement of $A_{\mathrm{LR}}$ to ±0.008, or ${\sin }^2$ ${\mathrm{\theta }}_{\mathrm{W}}$ to ±0.001, can be done with ∼${10}^6$ $Z^0$’s. This rather peculiar property of the asymmetry could allow Stanford Linear Collider and CERN LEP experiments to test the standard Glashow-Salam-Weinberg (GSW) theory and possible new physics beyond GSW early in the lifetime of these accelerators.