Non-analytic mass behaviour and the renormalization group

In 't Hooft-Weinberg renormalized spinor quantum electrodynamics, the leading mass singularity for m→0 is found to be m3(-ln m)10 for gauge-invariant vertex functions at non-exceptional momentum configurations, and m2(-ln m)sup(7/2) for gauge-dependent vertex functions, where m is the renormalized mass parameter. The corresponding result inside the Gell-Mann-Low renormalization scheme, where the renormalized mass parameter is the physical electron mass msub(phys), is msub(phys)(-ln msub(phys))sup(-9/4) in both cases. Analogous results can be found in an asymptotically free non-Abelian gauge theory, provided an infrared-stable fixed-point in coupling-constant space is present. The results are obtained by means of a renormalization group method developed by Symanzik. (Auth.)