Some remarks on the epsilon-expansion of dimensionally regulated Feynman diagrams

TL;DR

This paper discusses methods for constructing epsilon-expansions of dimensionally regulated Feynman integrals, expressing terms via log-sine integrals and polylogarithms, and explores their analytic continuation using Nielsen polylogarithms.

Contribution

It introduces a way to express epsilon-expansion terms of Feynman integrals using log-sine integrals and details their analytic continuation through generalized Nielsen polylogarithms.

Findings

Epsilon-expansion terms can be expressed via log-sine integrals.

Analytic continuation is achieved using generalized Nielsen polylogarithms.

Applicable to certain classes of Feynman diagrams.

Abstract

Some problems related to construction of the epsilon-expansion of dimensionally regulated Feynman integrals are discussed. For certain classes of diagrams, an arbitrary term of the epsilon-expansion can be expressed in terms of log-sine integrals related to the polylogarithms. It is shown how the analytic continuation of these functions can be constructed in terms of the generalized Nielsen polylogarithms.