AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow

TL;DR

AMFlow is a Mathematica package that automates the numerical computation of Feynman integrals using the auxiliary mass flow method, enabling efficient solutions via differential systems.

Contribution

This paper introduces AMFlow, a novel Mathematica package that implements the auxiliary mass flow method for automatic numerical evaluation of Feynman integrals.

Findings

Successfully computes two-loop Feynman integrals for top quark pair production.

Demonstrates the effectiveness of the auxiliary mass flow approach in complex integral calculations.

Provides a detailed example of double-box family integral evaluation.

Abstract

AMFlow is a Mathematica package to numerically compute dimensionally regularized Feynman integrals via the recently proposed auxiliary mass flow method. In this framework, integrals are treated as functions of an auxiliary mass parameter and their results can be obtained by constructing and solving differential systems with respect to this parameter, in an automatic way. The usage of this package is described in detail through an explicit example of double-box family involved in two-loop $t\bar{t}$ hadroproduction.