Three-jet cross section in hadron collisions at next-to-leading order: pure gluon processes

The next-to-leading order three-jet cross section in hadron collisions is calculated in the simplified case when the matrix elements of all QCD subprocesses are approximated by the pure gluon matrix element. The longitudinally-invariant $k_\perp$ jet-clustering algorithm is used. The important property of reduced renormalization and factorization scale dependence of the next-to-leading order physical cross section as compared to the Born cross section is demonstrated.