AN ALGORITHM FOR SMALL MOMENTUM EXPANSION OF FEYNMAN DIAGRAMS

An algorithm for obtaining the Taylor coefficients of an expansion of Feynman diagrams is proposed. It is based on recurrence relations which can be applied to the propagator as well as to the vertex diagrams. As an application, several coefficients of the Taylor series expansion for the two-loop non-planar vertex and two-loop propagator diagrams are calculated. The results of the numerical evaluation of these diagrams using conformal mapping and Pade approximants are given. Recently a new method to calculate Feynman diagrams was proposed 1 . It is based on the small momentum expansion 2 , conformal mapping and construction of Pade approximants from several terms in the Taylor series of the diagram. The method was successfully applied to the evaluation of two- and three- loop diagrams 3 . As it was observed, a suitably accurate approximations to the integrals can be obtained with 20-30 coefficients in the Taylor series. The computation of two-loop vertex diagrams reveals the necessity of an efficient algorithm for the expansion of the diagrams w.r.t. external momenta. To outline the problem, let us shortly describe the existing approach to the small momentum expansion. At present the only method of expansion is based on differentiation of the diagram w.r.t. external momenta. For the propagator type integrals the prescription for the small momentum expansion was formulated in Ref. 2 . Any coefficient in the Taylor series w.r.t. the external momentum q 2 can be obtained by applying 2 = @ @qµ @ @qµ in an appropriate power to the diagram and