The Three-Jet Rate in \(e^{+}e^{-}\) Annihilation

Progress has been made on the calculation of $R_{3}$, the three-jet rate in $e^{+}e^{-}$ annihilation, in the $k_\bot$ (Durham) scheme. Using the coherent branching formalism \cite{b,c,d}, an explicit expression for $R_{3}$ is calculated. In this, leading and next-to-leading large logarithms (LL and NLL) are resummed to all orders in QCD perturbation theory. In addition to exponentials an error function is involved.