The Four-Jet Rate in Electron-Positron Annihilation at Order $\alpha_s^4$

Abstract

We compute for the first time the production rate for four jets in electron-positron annihilation at next-to-next-to-leading order. Our calculation exhibits the highest final-state jet multiplicity considered at this perturbative accuracy to date. The cancellation of infrared singularities is achieved in the antenna subtraction scheme, relying particularly on generalized antenna functions. The evaluation of the two-loop virtual corrections is enabled by the construction of a new basis of transcendental special functions tailored to four-particle decay kinematics. Our results are compared with LEP data, finding improved agreement with respect to the next-to-leading order calculation. In the region where perturbative predictions are most reliable, we observe a significant reduction of theory uncertainties, which now fall below the experimental ones.