Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.
S-bases as a tool to solve reduction problems for Feynman integrals
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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.
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On the spanning cuts consistency problem in the IBP reductions of Feynman integrals
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.