Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams

TL;DR

Forcer is a FORM-based program designed to automate the reduction of four-loop massless propagator integrals to master integrals, enabling efficient parametric IBP reductions similar to existing three-loop tools.

Contribution

The paper introduces Forcer, a novel automated tool for four-loop integral reduction, including its structure, automation, and application examples, advancing computational techniques in high-loop calculations.

Findings

Successfully reduces four-loop integrals to master integrals

Demonstrates performance and efficiency of the Forcer program

Provides a framework for automating complex IBP reductions

Abstract

We explain the construction of Forcer, a FORM program for the reduction of four-loop massless propagator-type integrals to master integrals. The resulting program performs parametric IBP reductions similar to the three-loop Mincer program. We show how one can solve many systems of IBP identities parametrically in a computer-assisted manner. Next, we discuss the structure of the Forcer program, which involves recognizing reduction actions for each topology, applying symmetries, and transitioning between topologies after edges have been removed. This part is entirely precomputed and automatically generated. We give examples of recent applications of Forcer, and study the performance of the program. Finally we demonstrate how to use the Forcer package and sketch how to prepare physical diagrams for evaluation by Forcer.