Nonintegrable threshold singularities of two-point functions in perturbation theory

In perturbation theory, the spectral densities of two-point functions develop non-integrable threshold singularities at higher orders. In QCD, such singularities emerge when calculating the diagrams in terms of the pole quark mass, and they become stronger when one rearranges the perturbative expansion in terms of the running quark mass. In this paper we discuss the proper way to handle such singularities.
Comment: 7 pages, Extended version, Proof by induction is given in Appendices A and B, Conclusions remain unchanged