IBP and Reduction to Master Integrals

Abstract

The next method in our list is based on integration by parts¹ (IBP) [66] within dimensional regularization, i.e. property (2.39). The idea is to write down various equations (2.39) for integrals of derivatives with respect to loop momenta and use this set of relations between Feynman integrals in order to solve the reduction problem, i.e. to find out how a general Feynman integral of the given class can be expressed linearly in terms of some master integrals. In contrast to the evaluation of the master integrals, which is performed, at a sufficiently high level of complexity, in a Laurent expansion in ε, the reduction problem is usually² solved at general d, and the expansion in ε does not provide simplifications here.