Radiative corrections to axial anomaly

It is demonstrated that, contrary to the generally accepted viewpoint, the single-loop value is not the only one involved in the axial anomaly. Contributions which were not taken into account previously arise in diagrams for scattering of light by light (or gluons by gluons). The radiative corrections in quantum electrodynamics and in non-Abelian gauge theories are calculated. It is shown that in supersymmetric quantum electrodynamics the multi-loop contributions can explain the apparent contradiction between the axial anomaly and anomaly in the trace of the energy-momentum tensor. A complication arises in supersymmetric non-Abelian theories due to the dependence on the gauge in the matrix elements outside the mass surface