Split dimensional regularization for the Coulomb gauge at two loops

TL;DR

This paper introduces split dimensional regularization for two-loop Coulomb gauge calculations, demonstrating its effectiveness in producing well-defined integrals and local pole coefficients, with extensive tabulated results and implications.

Contribution

It develops and applies split dimensional regularization to two-loop Coulomb gauge integrals, providing a new method for handling noncovariant divergences.

Findings

Split dimensional regularization yields well-defined two-loop integrals.

The leading pole coefficient for the quark self-energy is strictly local.

Extensive tables of Coulomb integral pole parts are provided.

Abstract

We evaluate the coefficients of the leading poles of the complete two-loop quark self-energy \Sigma(p) in the Coulomb gauge. Working in the framework of split dimensional regularization, with complex regulating parameters \sigma and n/2-\sigma for the energy and space components of the loop momentum, respectively, we find that split dimensional regularization leads to well-defined two-loop integrals, and that the overall coefficient of the leading pole term for \Sigma(p) is strictly local. Extensive tables showing the pole parts of one- and two-loop Coulomb integrals are given. We also comment on some general implications of split dimensional regularization, discussing in particular the limit \sigma \to 1/2 and the subleading terms in the epsilon-expansion of noncovariant integrals.