Multiloop calculations in HQET

Abstract

Recently, algorithms for calculation of 3-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. These algorithms (based on integration by parts recurrence relations) reduce an arbitrary diagram to a combination of a finite number of basis integrals. Here I discuss various ways to calculate non-trivial bases integrals, either exactly or as expansions in epsilon. Some integrals of these two classes are related to each other by inversion, which provides a useful cross-check.