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NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals

Zihao Wu, Janko Boehm, Rourou Ma, Hefeng Xu, Yang Zhang

TL;DR

The paper presents NeatIBP 1.0, a package that generates small-size IBP identities for multi-loop Feynman integrals using the module intersection method in the Baikov representation. By constraining propagator indices and employing syzygy-based relations, NeatIBP delivers a significantly smaller IBP system than Laporta-based approaches, suitable for finite-field and analytic reduction. The workflow combines Singular-based module intersections, SpaSM for finite-field row reduction, and Mathematica-driven orchestration with sector-wise parallelism, including zero-sector and symmetry handling. Demonstrations on pentagon-box, non-planar two-loop, and three-loop planar diagrams illustrate substantial reductions in both IBP count and computation time, highlighting practical impact for high-precision amplitude calculations.

Abstract

In this work, we present the package {\sc NeatIBP}, which automatically generates small-size integration-by-parts (IBP) identities for Feynman integrals. Based on the syzygy and module intersection techniques, the generated IBP identities' propagator degree is controlled and thus the size of the system of IBP identities is shorter than that generated by the standard Laporta algorithm. This package is powered by the computer algebra systems {\sc Mathematica} and {\sc Singular}, and the library {\sc SpaSM}. It is parallelized on the level of Feynman integral sectors. The generated small-size IBP identities can subsequently be used for either finite field reduction or analytic reduction. We demonstrate the capabilities of this package on several multi-loop IBP examples.

NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals

TL;DR

The paper presents NeatIBP 1.0, a package that generates small-size IBP identities for multi-loop Feynman integrals using the module intersection method in the Baikov representation. By constraining propagator indices and employing syzygy-based relations, NeatIBP delivers a significantly smaller IBP system than Laporta-based approaches, suitable for finite-field and analytic reduction. The workflow combines Singular-based module intersections, SpaSM for finite-field row reduction, and Mathematica-driven orchestration with sector-wise parallelism, including zero-sector and symmetry handling. Demonstrations on pentagon-box, non-planar two-loop, and three-loop planar diagrams illustrate substantial reductions in both IBP count and computation time, highlighting practical impact for high-precision amplitude calculations.

Abstract

In this work, we present the package {\sc NeatIBP}, which automatically generates small-size integration-by-parts (IBP) identities for Feynman integrals. Based on the syzygy and module intersection techniques, the generated IBP identities' propagator degree is controlled and thus the size of the system of IBP identities is shorter than that generated by the standard Laporta algorithm. This package is powered by the computer algebra systems {\sc Mathematica} and {\sc Singular}, and the library {\sc SpaSM}. It is parallelized on the level of Feynman integral sectors. The generated small-size IBP identities can subsequently be used for either finite field reduction or analytic reduction. We demonstrate the capabilities of this package on several multi-loop IBP examples.
Paper Structure (22 sections, 29 equations, 5 figures)

This paper contains 22 sections, 29 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Review of methods and their implementations
  3. IBP reduction
  4. IBP relations from the Baikov representation
  5. The sectors of a Feynman integral family
  6. The symmetries of Feynman integrals
  7. Propagator cuts
  8. Algorithms
  9. Generating IBP relations referring to sectors
  10. Generating IBP relations in one sector
  11. Additional remarks
  12. Manual
  13. Installation
  14. Preparing inputs
  15. Running NeatIBP
  16. ...and 7 more sections

Figures (5)

  • Figure 1: An example of a web structure of the sectors in a slashed box family, as a sub family of the double box.
  • Figure 2: Distributed computation based on registration table.
  • Figure 3: A two-loop five-point diagram example
  • Figure 4: A nonplanar two-loop diagram for the tW production
  • Figure 5: The planar triple box diagram with an external massive leg