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

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.

8 pages, latex

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• The Standard Model Effective Potential at Two Loops
• Two-loop self-energy master integrals on shell
• Single mass scale diagrams: construction of a basis for the $\epsilon$-expansion
• Transcendental numbers and the topology of three-loop bubbles

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