Why, Where and How to Expand

Abstract

Suppose that we have to analytically evaluate a two-loop Feynman diagram which depends on two parameters, e.g. a mass squared and a momentum squared. This is generally a rather complicated problem. It usually happens, however, that the parameters involved differ in scale so that it is reasonable to expand the diagram in their small ratio. We shall see in this book that an asymptotic expansion in an arbitrary limit with two scales can be written explicitly as an infinite series of products of certain one-scale Feynman integrals, with a power and logarithmic dependence on the expansion parameter, which can be evaluated analytically much more easily than the initial two-scale integral. The original Feynman integral can then be replaced by a sufficiently large number of terms of its expansion.