Analytic two-loop results for self-energy- and vertex-type diagrams with one non-zero mass

Abstract

For a large class of two-loop self-energy- and vertex-type diagrams with only one non-zero mass ( m) and the vertices also with only one non-zero external momentum squared ( q 2) the first few expansion coefficients are calculated by the large mass expansion. This allows us to ‘guess’ the general structure of these coefficients and to verify them in terms of certain classes of ‘basis elements’, which are essentially harmonic sums. Since for this case with only one non-zero mass the large mass expansion and the Taylor series in terms of q 2 are identical, this approach yields analytic expressions of the Taylor coefficients, from which the diagram can be easily evaluated numerically in a large domain of the complex q 2-plane by well known methods. It is also possible to sum the Taylor series and present the results in terms of polylogarithms.