Erratum: Three-gluon vertex in arbitrary gauge and dimension [Phys. Rev. D54, 4087 (1996)]

Abstract

One-loop off-shell contributions to the three-gluon vertex are calculated, in arbitrary covariant gauge and in arbitrary space-time dimension, including quark-loop contributions (with massless quarks). It is shown how one can get the results for all on-shell limits of interest directly from the general off-shell expression. The corresponding general expressions for the one-loop ghost-gluon vertex are also obtained. They allow for a check of consistency with the Ward-Slavnov-Taylor identity.

Quark mass dependence of the one-loop three-gluon vertex in arbitrary dimension

“…[8,10] (see also in [18]). The scalar three-point integrals with equal masses associated with all three internal lines are defined as…”

“…Table 1 of [8] gives an overview of the results for the one-loop three-gluon vertex obtained in the preceding papers. The results of [8] have contributed towards covering all remaining "white spots" in Table 1, with only one restriction: the case of massless quarks was considered.…”

“…The purpose of the present paper is to extend the work started in [8] and complete the study of the one-loop-order three-gluon vertex, by considering massive quarks in the quark-loop contributions, for an arbitrary value of the space-time dimension. We note that these contributions do not depend on the gauge parameter at one loop.…”

“…More recently, general one-loop results for the three-gluon vertex, in an arbitrary covariant gauge and dimension, have been presented in [8] (see also [9] for a brief review). Table 1 of [8] gives an overview of the results for the one-loop three-gluon vertex obtained in the preceding papers.…”

“…Thereby, we would allow for non-zero quark masses in all configurations listed in Table 1 of [8], including the most general off-shell case. Taking into account that the corresponding investigation of the quark-gluon vertex with massive quarks is given in [10], and remembering that the one-loop ghost-gluon vertex [8] does not involve any quark contributions, one can see that this is indeed the last step, in addition to Refs. [8,10], needed to complete the most general study of the one-loop three-point vertices in QCD.…”