A general method to calculate next-to-leading-order multijet cross sections is presented. The emphasis is on how to isolate the soft and collinear divergences in multiparton matrix elements at all orders in the number of colors. As an example, the method is used to isolate the divergences in $e^{+}{e}^{-}\to q\overline{q}+n$ gluons and $e^{+}{e}^{-}\to q\overline{q}q\overline{q}+n$ gluons, where, for simplicity we keep only the terms at leading order in the number of colors. The usual algebraic complexity of calculating next-to-leading-order corrections in QCD is avoided, especially the $d$-dimensional squaring of the real matrix elements and the hard phase-space integrals. Some remarks about the structure of the virtual contributions are made. As a first application, and to examine the feasibility of the approach, explicit Monte Carlo programs are constructed which contain the complete next-to-leading-order corrections to $e^{+}{e}^{-}\to 2$ jets and $e^{+}{e}^{-}\to 3$ jets. It is demonstrated that the method works and can be readily applied to a variety of processes.

• Received 23 March 1992

DOI:https://doi.org/10.1103/PhysRevD.46.1980