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 ε. Some integrals of these two classes are related to each other by inversion, which provides a useful cross-check.

Laurent series expansion of sunrise-type diagrams using configuration space techniques

“…Using the integration-by-parts technique, many diagrams are reduced to simplified subsets of master integrals (see e.g. [6,7,8,9,10,11,12,13,14]).…”