DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions

TL;DR

DiffExp is a Mathematica package that computes Feynman integrals using one-dimensional series expansions, enabling efficient solutions of differential equations for complex integral families in high-energy physics.

Contribution

It provides a public implementation of series expansion methods for Feynman integrals, applicable to any integral family with known differential equations and boundary conditions.

Findings

Successfully applied to three-loop banana graph families.

Handles both equal-mass and unequal-mass cases.

Demonstrates effectiveness for complex multi-loop integrals.

Abstract

DiffExp is a Mathematica package for integrating families of Feynman integrals order-by-order in the dimensional regulator from their systems of differential equations, in terms of one-dimensional series expansions along lines in phase-space, which are truncated at a given order in the line parameter. DiffExp is based on the series expansion strategies that were explored in recent literature for the computation of families of Feynman integrals relevant for Higgs plus jet production with full heavy quark mass dependence at next-to-leading order. The main contribution of this paper, and its associated package, is to provide a public implementation of these series expansion methods, which works for any family of integrals for which the user provides a set of differential equations and boundary conditions (and for which the program is not computationally constrained.) The main functions of the DiffExp package are discussed, and its use is illustrated by applying it to the three loop equal-mass and unequal-mass banana graph families.