Next-to-leading order calculation of three-jet observables in hadron-hadron collisions

The production of three jets in hadron-hadron collisions is the first complex process which allows us to define a branch of variables in order to make more precise measurements of the strong coupling and the parton distribution function of the proton. This process is also suitable for studying the geometrical properties of the hadronic final state at hadron colliders. This requires a next-to-leading order prediction of the three-jet observables. In this paper we describe the theoretical formalism of such a calculation with sufficient detail. We use the dipole method to construct a Monte Carlo program for calculating three-jet observables at next-to-leading order accuracy. We present a theoretical prediction for inclusive and exclusive cross sections and for some relevant event shape variables such as the transverse thrust, transverse jet broadening, and $E_{t3\mathrm{}}$ variable.