Three-gluon decay function using space-like jet calculus beyond the leading order

Three-gluon decay functions in space-like gluon branching are calculated in the next-to-leading order of QCD. The calculated results satisfy the cross ing symmetry between spacelike branching and time-like branching. Some prop erties of the decay functions are also examined in the case of soft gluon r adiations and the case of branching to a space-like gluon with small moment um fraction. Furthermore, kinematical constraints for the leading logarithm ic branching due to interference effects are studied. It is pointed out tha t the next-to-leading order contributions are not negligible, even if the a ngular-ordering conditions are imposed on two-body branching processes.