S-bases as a tool to solve reduction problems for Feynman integrals

Abstract

We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a recently suggested reduction algorithm which uses Groebner bases. New results obtained with its help for a family of three-loop Feynman integrals are outlined.

5 pages, uses espcrc2.sty

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Cited by in corpus (11)

• FIRE6: Feynman Integral REduction with Modular Arithmetic
• FIRE4, LiteRed and accompanying tools to solve integration by parts relations
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• FeynHelpers: Connecting FeynCalc to FIRE and Package-X
• FIRE 6.5: Feynman Integral Reduction with New Simplification Library
• Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme
• Decoupling of heavy quarks in HQET
• Evaluating the three-loop static quark potential
• Feynman integral reduction using Gröbner bases
• A new method for finding more symmetry relations of Feynman integrals
• IBP reduction via Gröbner bases in a rational double-shift algebra