Determination of the first-generation quark couplings at the Z-pole

Electroweak Precision Measurements are stringent tests of the Standard Model and sensitive probes to New Physics. Accurate studies of the $Z$-boson couplings to the first-generation quarks, which are currently constrained from LEP data to a few percent, could reveal potential discrepancies from the theory predictions. Future $e^+e^-$ colliders running at the $Z$-pole would be an excellent tool for an analysis based on a comparison of radiative and non-radiative $Z$ boson decays. In this paper, we present a method to extract the values of the $Z$ couplings to light quarks and discuss the uncertainty of the measurement, including contributions from various systematic effects. We show that systematic uncertainty in the heavy-flavour tagging performance is the key factor in the analysis and reducing it to a sub-permille level might be crucial to fully profit from the high luminosity of future $e^+e^-$ machines. The measurement could improve the LEP results by at least an order of magnitude.