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.