The Three-point Function in Split Dimensional Regularization in the Coulomb Gauge

We use a gauge-invariant regularization procedure, called split dimensional regularization, to evaluate the quark self-energy Σ(p) and quark-quark-gluon vertex function Λμ(p , p) in the Coulomb gauge, ~ ▽ · ~ A = 0. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regulating parameters, ω and σ, is shown to generate a well-defined set of Coulomb-gauge integrals. A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, some of which are nonlocal. It is further argued that the standard one-loop BRST identity relating Σ and Λμ, should by rights be replaced by a more general BRST identity which contains two additional contributions from ghost vertex diagrams. Despite the appearance of nonlocal Coulomb integrals, both Σ and Λμ are local functions which satisfy the appropriate BRST identity. Application of split dimensional regularization to two-loop energy integrals is briefly discussed. Permanent address: On leave from the Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario NIG 2W1. E-mails: [email protected] – [email protected] CERN–TH/97–174 DAMTP–97–46 July 1997