Large mass expansion versus small momentum expansion of Feynman diagrams

The method of the large mass expansion (LME) has the technical advantage that two-loop integrals occur only as bubbles with large masses. In many cases only one large mass occurs. In such cases these integrals are expressible in terms of Γ-functions, i.e. they can be handled completely analytically avoiding even recursions and therefore this approach may find a wide field of application. We consider it necessary to investigate the precision of this method and test it for several two-loop vertex functions ocurring in the Z→bb̄ decay by comparing it with the small momentum expansion. It turns out that in general high order approximants have to be taken into account for a sufficient accuracy.