The three-point function in split dimensional regularization in the Coulomb gauge Original Research Article

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, ∇ · Aa = 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 non-local. 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 non-local 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.