Solving multi-loop Feynman diagrams using light-front coordinates

TL;DR

This paper presents a novel numerical method for evaluating scalar multi-loop Feynman diagrams using light-front coordinates, efficiently handling longitudinal momenta and threshold behaviors.

Contribution

It introduces a collective coordinate approach for numerical integration of multi-loop diagrams in light-front coordinates, improving accuracy and efficiency.

Findings

Accurate numerical values for generalized sunset diagrams

Efficient handling of longitudinal momenta and threshold behavior

Framework applicable to complex multi-loop Feynman diagrams

Abstract

We determine the numerical values of scalar multi-loop two-vertex Feynman diagrams, the generalized sunset diagrams, by integrating all but the longitudinal momenta analytically. For the longitudinal momenta we introduce one collective coordinate, which allows us to determine the numerical value of the diagram efficiently and to an arbitrary accuracy. The imaginary part and the threshold behavior of the diagram are also handled within this framework.