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Article
Report number	hep-th/9804109 ; CERN-TH-97-174 ; DAMTP-97-46 ; CERN-TH-97-174 ; DAMTP-97-46
Title	The three-point function in split dimensional regularization in the Coulomb gauge
Author(s)	Leibbrandt, G. (Cambridge U. ; CERN)
Publication	1998
Imprint	23 Jul 1997
Number of pages	13
Note	Latex, 17 pages, 4 figures, uses epsf.sty, epsfig.sty; to appear in Nuc. Phys. B Report-no: CERN-TH/97-174, DAMTP-97-46
In:	Nucl. Phys. B 521 (1998) 383-400
DOI	10.1016/S0550-3213(98)00211-9
Subject category	Particle Physics - Theory
Abstract	We use a gauge-invariant regularization procedure, called ``split dimensional regularization'', to evaluate the quark self-energy $\Sigma (p)$ and quark-quark-gluon vertex function $\Lambda_\mu (p^\prime,p)$ in the Coulomb gauge, $\vec{\bigtriangledown}\cdot\vec{A}^a = 0$. 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, $\omega$ and $\sigma$, 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 $\Sigma$ and $\Lambda_\mu$, 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 $\Sigma$ and $\Lambda_\mu$ are local functions which satisfy the appropriate BRST identity. Application of split dimensional regularization to two-loop energy integrals is briefly discussed.
Copyright/License	Copyright @ unknown. Published by Elsevier B.V.

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