Next-to-leading order calculation of four-jet observables in electron-positron annihilation

The production of four jets in electron-positron annihilation allows for measuring the strong coupling and the underlying group structure of the strong interaction simultaneously. This requires a next-to-leading order perturbative prediction for four-jet observables. In this paper we describe the theoretical formalism of such a calculation with sufficient details. We use the dipole method to construct a Monte Carlo program that can be used for calculating any four-jet observable at the next-to-leading order accuracy. As new results, we present the next-to-leading order prediction for the thrust minor, $y_4$ and C parameter (at $\mathrm{C}>~0.75)$ four-jet shape variables and the four-jet rates with the Cambridge jet clustering algorithm.