Automatic application of successive asymptotic expansions of Feynman diagrams

TL;DR

The paper presents EXP, a C++ tool that automates successive asymptotic expansions of multi-scale Feynman diagrams by systematically generating hard subgraphs and determining topologies, with outputs that feed FORM-based packages MINCER and MATAD for single-scale integrals. It details backtracking-based subgraph generation and a topology-matching algorithm driven by momentum distributions, enabling nested expansions across multiple large scales. The approach is demonstrated on the singlet contributions to $H\rightarrow b\bar b$ at $O(\alpha_s^2)$, using $M_t^2 \gg q^2 \gg M_b^2$ to obtain a nested series and validating against established results. The work provides concrete algorithms for automating complex multi-loop, multi-scale calculations, expanding the reach of perturbative predictions in particle physics.

Abstract

We discuss the program EXP used to automate the successive application of asymptotic expansions to Feynman diagrams. We focus on the generation of the relevant subgraphs and the determination of the topologies for the remaining integrals. Both tasks can be solved by using backtracking-type recursive algorithms. In addition, an application of EXP is presented, where the integrals were calculated using the FORM packages MINCER and MATAD.

Figures (2)

• Figure 1: Double triangle graphs contributing to $\Gamma(H \rightarrow b\bar{b})$.
• Figure 2: Successive asymptotic expansion of diagram \ref{['fig1']}(a).