Gluing Feynman diagrams in NDIM: Insights into the three-point vertex

Abstract

Three-point vertex diagram plays a key role in the whole renormalization program of several QFT (quantum field theory) models such as QED, QCD, the Standard Model of eletroweak interactions and so forth. The exact analytic result for the triangle diagram therefore is fundamental. In this work we calculate in two different ways a two-point two-loop massless Feynman diagram using what we call a "gluing" technique in the context of NDIM (Negative Dimensional Integration Method). 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 does not hold anymore and present a new solution for it with only three hypergeometric functions $F_{4}$.