Feynman Diagram Calculations with FeynArts, FormCalc, and LoopTools

TL;DR

FeynArts/FormCalc/LoopTools address automated one-loop cross-section calculations by integrating diagram generation, amplitude construction, and numerical evaluation in a single Mathematica-based workflow. The paper details a three-step diagram-generation pipeline (topologies, field insertion, amplitude creation), a Weyl-van der Waerden approach to amplitudes, and a FORM–Mathematica bridge that reduces intermediate expression sizes. It also describes automated Fortran code generation for squared amplitudes and renormalization constants, and the LoopTools numerical library providing scalar and tensor one-loop integrals across multiple interfaces. The work delivers an efficient, interoperable, open-source toolchain for high-energy phenomenology with broad applicability.

Abstract

This article describes the latest versions of the Mathematica packages FeynArts, FormCalc, and LoopTools for the generation and evaluation of one-loop diagrams.