Progress in Evaluating Some Complicated Types of Feynman Diagrams with Two (and More) Loops

Abstract

Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large external momentum are considered. The coefficients of the expansions are calculated analytically. Comparison with numerical results shows good agreement below the first threshold and above the last threshold of the diagram. An approach to evaluating three- and four-point ladder diagrams with massless internal particles and off-shell external momenta is presented. Exact results for an arbitrary number of loops are obtained. Evaluating non-planar diagrams is also discussed.