Explicit results for all orders of theɛexpansion of certain massive and massless diagrams

Abstract

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