Libra: a package for transformation of differential systems for multiloop integrals

TL;DR

Libra is a Mathematica package that simplifies the transformation of differential systems in multiloop integrals, aiding in reduction to epsilon-form and solution construction.

Contribution

It introduces tools for transforming differential systems, reducing them to epsilon-form, and constructing solutions, specifically tailored for multiloop integral calculations.

Findings

Efficient reduction of differential systems to epsilon-form.

Tools for constructing solutions via perturbative and series expansions.

Determination of minimal coefficients for boundary conditions.

Abstract

We present a new package for Mathematica system, called Libra. Its purpose is to provide convenient tools for the transformation of the first-order differential systems $\partial_i \boldsymbol j = M_i \boldsymbol j$ for one or several variables. In particular, Libra is designed for the reduction to $\epsilon$-form of the differential systems which appear in multiloop calculations. The package also contains some tools for the construction of general solution: both via perturbative expansion of path-ordered exponent and via generalized power series expansion near regular singular points.Libra also has tools to determine the minimal list of coefficients in the asymptotics of the original master integrals, sufficient for fixing the boundary conditions.