Analytic properties of the vertex function in gauge theories. II

The analytic properties of the three-gluon vertex function for quantum chromodynamics in covariant gauges are investigated. First, a general tensor form for the vertex consistent with the Ward identity and free of kinematic singularities is constructed. The vertex is then calculated to one-loop order in the Feynman gauge. The complete expression for the off-shell one-loop vertex is expressed in terms of elementary functions plus one nonelementary function, the dilogarithm. Various kinematic limits of the vertex are considered. The most interesting results are the following. (1) Gluon mass-shell singularities occur in the transverse terms as well as the longitudinal terms. (2) The leading IR singularity is in the longitudinal part of the vertex, as is the case for QED; however, it is a pole singularity rather than the usual logarithmic singularity.