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

Abstract

In this work, we present the package 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 Mathematica and Singular, and the library 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. Program summaryProgram Title: NeatIBPCPC Library link to program files:https://doi.org/10.17632/ms85fpfm7b.1Developer's repository link:https://github.com/yzhphy/NeatIBPLicensing provisions: GPLv3Programming language:Mathematica, Singular, CNature of problem: The difficulty of the IBP reduction of Feynman integrals stems from the large size of the IBP system.Solution method: We apply the module intersection method to generate IBP relations by algebraic geometry methods, and compare the smaller IBP system we generate with that from Laporta's algorithm. NeatIBP generates the module intersection in Singular [1] and selects relevant and independent IBP relations via an algorithm relying on the library SpaSM [2]. The workflow is parallelized by a task manager written in Mathematica [3].