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

Abstract

For a large class of two-loop selfenergy- 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 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.

LaTeX, 27 pages + 3 ps figures, uses axodraw.sty, some references revisted

References in corpus (6)

• Differential Equations for Feynman Graph Amplitudes
• QCD Effects in Higgs Physics
• Pole masses of quarks in dimensional reduction
• Asymptotic expansions of two-loop Feynman diagrams in the Sudakov limit
• The Differential equation method: calculation of vertex-type diagrams with one non-zero mass
• Compact analytical form for a class of three-loop vacuum Feynman diagrams

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