Zero-threshold expansion of two-loop self-energy diagrams

Abstract An algorithm is constructed to derive a small-momentum expansion for two-loop two-point diagrams in all cases where, due to the presence of physical thresholds, there are singularities at zero external momentum. The coefficients of this “zero-threshold” expansion are calculated analytically for arbitrary masses. Numerical examples, using diagrams occurring in the Standard Model, illustrate the convergence of the expansion below the first non-zero threshold.