Abstract
We present the next-to-leading-order $[O({\ensuremath{\alpha}}_{s}^{3})$] perturbative QCD predictions for ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into four jets. A previous calculation omitted the $O({\ensuremath{\alpha}}_{s}^{3})$ 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 the small jet resolution parameter ${y}_{\mathrm{cut}}$ can be resummed. We match the resummed results to our fixed-order calculation in order to improve the small ${y}_{\mathrm{cut}}$ prediction.
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