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A Feynman Diagram Analyser DIANA

M. Tentyukov, J. Fleischer

TL;DR

This work introduces DIANA, a C-based Feynman Diagram Analyser that automates the generation and evaluation of large numbers of Feynman diagrams in the Standard Model. It integrates with QGRAF to obtain diagrams, uses a TeX-like TM language to produce source code for analytical or numerical evaluation, and can drive FORM for symbolic calculations, all while providing macros and styles for high-level customization. The approach yields generated configuration files and per-diagram FORM inputs, enabling scalable, automated multi-loop computations, exemplified by the $Z \to b \bar{b}$ process. Overall, DIANA provides a flexible, modular workflow for topology/momentum handling and automated code generation, with potential extensions to handle numerators and scalar integrals for broader applicability in high-precision theory calculations.

Abstract

A C-program DIANA (DIagram ANAlyser) for the automatic Feynman diagram evaluation is presented. It consists of two parts: the analyzer of diagrams and the interpreter of a special text manipulating language. This language is used to create a source code for analytical or numerical evaluations and to keep the control of the process in general.

A Feynman Diagram Analyser DIANA

TL;DR

This work introduces DIANA, a C-based Feynman Diagram Analyser that automates the generation and evaluation of large numbers of Feynman diagrams in the Standard Model. It integrates with QGRAF to obtain diagrams, uses a TeX-like TM language to produce source code for analytical or numerical evaluation, and can drive FORM for symbolic calculations, all while providing macros and styles for high-level customization. The approach yields generated configuration files and per-diagram FORM inputs, enabling scalable, automated multi-loop computations, exemplified by the process. Overall, DIANA provides a flexible, modular workflow for topology/momentum handling and automated code generation, with potential extensions to handle numerators and scalar integrals for broader applicability in high-precision theory calculations.

Abstract

A C-program DIANA (DIagram ANAlyser) for the automatic Feynman diagram evaluation is presented. It consists of two parts: the analyzer of diagrams and the interpreter of a special text manipulating language. This language is used to create a source code for analytical or numerical evaluations and to keep the control of the process in general.

Paper Structure

This paper contains 8 sections, 1 equation, 3 figures.

Table of Contents

  1. Introduction
  2. Brief description
  3. Topologies and momenta
  4. TM language
  5. Generating configuration files
  6. The structure of the generated files
  7. Generating the FORM input and executing FORM
  8. Conclusion

Figures (3)

  • Figure 1: Typical flowchart of Feynman diagram evaluations by DIANA.
  • Figure 2: Topology (-2,2)(-1,1)(5,1)(1,3)(3,4)(4,2)(2,5)(5,6)(3,6)(4,6).
  • Figure 3: To the left there is the QGRAF output for the diagram "number 452". t and T stand for t and anit-t quarks, b and B stand for b and anit-b quarks, A is the photon, Z is the Z boson. External legs are numerated by negative numbers and vx stands for the vertex. The corresponding graph is shown on the right. The lines are numbered corresponding to QGRAF output. The numbers in brackets correspond to the numbering defined by "topology 8" in the file "settings.zbb". Bold italic digits numerate vertices according to the topology 8.