Space-like jet calculus for single gluon radiating processes

Three-body decay functions in space-like parton branching for a single gluon radiation accompanied by a quark (or an anti-quark) are calculated using jet calculus. Explicit expressions of the calculated results are presented. Some properties of the three-body decay functions for soft gluon radiation are also examined. It is pointed out that the three-body decay function for a quark in an initial state that decays into a gluon with a space-like virtuality gives a large positive contribution whose singularity is not absorbed by the angular ordering condition imposed on the two-body branching process. (author)