LECTURES ON MULTILOOP CALCULATIONS

Abstract

I discuss methods of calculation of propagator diagrams (massless, those of Heavy Quark Effective Theory, and massive on-shell diagrams) up to three loops. Integration-by-parts recurrence relations are used to reduce them to linear combinations of basis integrals. Nontrivial basis integrals have to be calculated by some other method, e.g. using Gegenbauer polynomial technique. Many of them are expressed via hypergeometric functions; in the massless and HQET cases, their indices tend to integers at ε→0. I discuss the algorithm of their expansion in ε, in terms of multiple ζ values.