Minimal Gauge Invariant Classes of Tree Diagrams in Gauge Theories

TL;DR

This paper presents a method to explicitly construct minimal gauge invariant classes of tree-level Feynman diagrams in gauge theories, applicable to complex processes with many particles without summing over complete gauge multiplets.

Contribution

It introduces the concept of groves, the smallest gauge invariant classes of diagrams, valid for theories with multiple gauge group factors and arbitrary external matter fields.

Findings

Constructed explicit gauge invariant classes called groves.

Applicable to complex processes with many observed particles.

No need for summation over complete gauge multiplets.

Abstract

We describe the explicit construction of groves, the smallest gauge invariant classes of tree Feynman diagrams in gauge theories. The construction is valid for gauge theories with any number of group factors which may be mixed. It requires no summation over a complete gauge group multiplet of external matter fields. The method is therefore suitable for defining gauge invariant classes of Feynman diagrams for processes with many observed final state particles in the standard model and its extensions.