Complete Order alpha_s^3 Results for e^+ e^- to (gamma,Z) to Four Jets

Abstract

We present the next-to-leading order (O(alpha_s^3)) perturbative QCD predictions for e^+e^- annihilation into four jets. A previous calculation omitted the O(alpha_s^3) terms suppressed by one or more powers of 1/N_c^2, where N_c is the number of colors, and the `light-by-glue scattering' contributions. We find that all such terms are uniformly small, constituting less than 10% of the correction. For the Durham clustering algorithm, the leading and next-to-leading logarithms in the limit of small jet resolution parameter y_{cut} can be resummed. We match the resummed results to our fixed-order calculation in order to improve the small y_{cut} prediction.