Solving Recurrence Relations for Multi-Loop Feynman Integrals

Details Solving Recurrence Relations for Multi-Loop Feynman Integrals Solving Recurrence Relations for Multi-Loop Feynman Integrals

2003-07-07

arxiv.org/abs/hep-ph/0307088v2

Nucl.Phys. B672 (2003) 199-221

Physics

High Energy Physics

High Energy Physics - Phenomenology

24 pages, 5 ps figures, references added, minor modifications, published version

Scientific paper

We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, {\it i.e.}, the problem of expressing any Feynman integral from this class as a linear combination of master integrals. We show how the parametric representation invented by Baikov can be used to characterize the master integrals and to construct an algorithm for evaluating the corresponding coefficient functions. To illustrate this procedure we use simple one-loop examples as well as the class of diagrams appearing in the calculation of the two-loop heavy quark potential.

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