Three-loop results in HQET

Two-loop HQET propagator diagrams were reduced [1] to two master integrals, using integration by parts [2] identities. There are 10 generic topologies of three-loop HQET propagator diagrams (Fig. 1). They can be reduced [3], using integration by parts relations, to 8 master integrals (Fig. 2). The algorithm has been constructed by hand, and implemented as a REDUCE package Grinder [3]. It is analogous to the massless package Mincer [4]. The first 5 master integrals can be easily expressed via Γ functions. The next two ones are two-loop integrals with a single d-dependent index. The last one is truly three-loop.