Full One-loop Electro-Weak Corrections to Three-jet Observables at the Z pole and Beyond

TL;DR

This work computes the full one-loop electroweak corrections to unflavoured three-jet production in e+e- collisions, covering energies from the Z pole to the TeV scale, and includes both factorisable and non-factorisable virtual corrections plus photon bremsstrahlung while excluding real W/Z bremsstrahlung. The calculation employs a mass-regulated IR treatment, a DRbar renormalisation scheme, and multiple numerical strategies (including pentagon integrals and complex masses) to obtain precise predictions for jet rates and event shapes. The results show corrections ranging from a few percent to over ten percent, with large negative Sudakov-like contributions from WW non-factorisable graphs at high energy and dominant QED ISR near the Z peak, underscoring the need to include EW effects alongside two-loop QCD for accurate alphaS extractions. An erratum later corrected a 1/3 multiplicative error in the published cross sections, but the qualitative conclusions and relative effects remain unchanged.

Abstract

We describe the impact of the full one-loop EW terms of O(alpha_s alpha_EM^3) entering the electron-positron into three-jet cross-section from \sqrt{s}=M_Z to TeV scale energies. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of W and Z bosons. Their importance for the measurement of alpha_S from jet rates and shape variables is explained qualitatively and illustrated quantitatively.