Counting the number of Feynman Graphs in QCD

TL;DR

This paper develops a method based on zero-dimensional field theory to count Feynman graphs with symmetry factors, extending it to complex models like QCD for automated higher-order calculations.

Contribution

It generalizes a counting method to QCD using symbolic computation, aiding verification of automated Feynman graph generation in complex theories.

Findings

Effective counting of Feynman graphs in QCD

Application to models with counter terms

Supports automated perturbative calculations

Abstract

Information about the number of Feynman graphs for a given physical process in a given field theory is especially useful for confirming the result of a Feynman graph generator used in an automatic system of perturbative calculations. A method of counting the number of Feynman graphs with weight of symmetry factor was established based on zero-dimensional field theory, and was used in scalar theories and QED. In this article this method is generalized to more complicated models by direct calculation of generating functions on a symbolic calculating system. This method is applied to QCD with and without counter terms, where many higher order are being calculated automatically.