Massless and massive one-loop three-point functions in negative dimensional approach

TL;DR

This paper computes one-loop three-point functions in quantum field theory using the negative dimensional integration method, providing new solutions for various mass configurations and demonstrating the method's effectiveness.

Contribution

It introduces a comprehensive application of NDIM to massless and massive one-loop triangle diagrams, revealing new solutions and unifying existing results.

Findings

Derived complete results for massless and massive cases

Reproduced known solutions and found new ones

Demonstrated NDIM as a promising technique for Feynman integrals

Abstract

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time D. Our approach reproduces the known results as well as other solutions as yet unknown in the literature. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories.