Two-Point Function at Two Loops via Triangle Diagram Insertion

Abstract

In this work we calculate in two different ways a well-known two-point two-loop massless Feynman diagram to illustrate the feasibility of lgluing'' that is, inserting or embedding-simpler diagrams into more complex ones, to allow for stepwise calculation in the context of negative dimensional integration method (NDIM). The two-loop diagram in question can be glued'' in two different ways and we show that both yield the same result and reproduce the one calculated via NDIM for the complete diagram, which, of course, is equivalent to the exact solution obtained by normal positive dimensional calculation. Furthermore, in the process we conclude that the usual massless off-shell triangle diagram result is not appropriate for the gluing purpose and present a new solution for it with only three hypergeometric functions F-4 that suits the gluing loop-by-loop technique.