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

TL;DR

This paper introduces a 'gluing' technique within NDIM to calculate the three-point vertex diagram in quantum field theory, revealing new solutions and confirming the method's consistency with traditional calculations.

Contribution

It presents a novel 'gluing' approach in NDIM for evaluating complex Feynman diagrams, providing new solutions for the massless off-shell triangle diagram.

Findings

Both gluing methods produce identical results.

The usual off-shell triangle result is revised with a new hypergeometric function solution.

The approach confirms consistency with traditional NDIM calculations.

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 $F_{4}$.