Analytic multi-loop results using finite fields and dataflow graphs with FiniteFlow

TL;DR

FiniteFlow is a versatile framework that simplifies complex finite field computations and rational function reconstruction using dataflow graphs, with recent updates enhancing its capabilities for advanced physics calculations.

Contribution

The paper introduces new features of FiniteFlow, demonstrating its application to complex multi-loop calculations in particle physics.

Findings

Effective for two-loop five-point scattering

Applied to four-loop cusp anomalous dimension

Provides an easy-to-use Mathematica interface

Abstract

FiniteFlow is a public framework for defining and executing numerical algorithms over finite fields and reconstructing multivariate rational functions. The framework allows to build complex algorithms by combining basic building blocks into graphical representations of the calculation, known as dataflow graphs. It offers an easy-to-use Mathematica interface for implementing efficient custom algorithms without any low-level coding. We report on some new features of FiniteFlow which have been published after its initial release, give some simple example of usage for common tasks and review recent cutting-edge applications to two-loop five-point scattering and the four-loop cusp anomalous dimension.