2-LOOP CORRECTIONS TO THE ELECTROMAGNETIC VERTEX FOR ENERGIES CLOSE TO THRESHOLD

Two-loop contributions to the electromagnetic form factors are calcula ted in the kinematic regime close to the fermion-antifermion threshold . The results are presented in an expansion in the velocity beta of th e fermions in the c.m. frame up to next-to-next-to-leading order in be ta. The existence of a new Coulomb singularity logarithmic in beta, wh ich is closely related to the O(alpha(2)ln alpha) corrections known fr om positronium decays, is demonstrated. It is shown that due to this C oulomb singularity O(alpha(2)) relativistic corrections to the nonrela tivistic cross section of heavy-fermion-antifermion pair production in e(+)e(-) annihilation cannot be determined by means of conventional m ultiloop perturbation theory. [S0556-2821(97)05123-0].