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.