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

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 ${\partial }_i\mathbf{j}=M_i\mathbf{j}$ 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.

32 pages

References in corpus (3)

• Reducing differential equations for multiloop master integrals
• Normalized Fuchsian form on Riemann sphere and differential equations for multiloop integrals
• Matching the heavy-quark fields in QCD and HQET at four loops

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