Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams

TL;DR

This paper derives explicit formulas for all orders of the epsilon-expansion of certain massless and massive Feynman diagrams using log-sine integrals, revealing their connection to polylogarithms and two-loop vacuum diagrams.

Contribution

It provides a comprehensive epsilon-expansion for off-shell massless and massive diagrams, linking them through a 'magic connection' and addressing analytic continuation.

Findings

Explicit epsilon-expansion formulas for massless diagrams.

Extension to massive vacuum diagrams with arbitrary masses.

Discussion on analytic continuation of the results.

Abstract

An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these diagrams and two-loop massive vacuum diagrams, the epsilon-expansion of the latter is also obtained, for arbitrary values of the masses. The problem of analytic continuation is also discussed.