Fuchsia and master integrals for splitting functions from differential equations in QCD

Abstract

We report on the recent progress in reducing differential equations for Feynman master integrals to canonical form with the help of a method proposed by Roman Lee. For the first time, we present Fuchsia --- our open-source implementation of the Lee algorithm written in Python using mathematical routines of a free computer algebra system SageMath. We demonstrate Fuchsia by reducing differential equations for NLO contributions to splitting functions in QCD, which contain both loops and legs integrals.

7 pages; Contribution to Loops and Legs in Quantum Field Theory 2016; *.m files with examples

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Cited by in corpus (7)

• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• Solving differential equations for Feynman integrals by expansions near singular points
• The $n_f^2$ contributions to fermionic four-loop form factors
• Evaluating `elliptic' master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points
• Bubble diagram through the Symmetries of Feynman Integrals method