Abstract
The conservation of the vector current and the axial anomaly responsible for the π0 → γγ decay amplitude are obtained in leading order within the Taylor–Lagrange formulation of fields considered as operator-valued distributions. As for gauge theories, where this formulation eliminates all divergences and preserves gauge symmetry, it is shown that the different contributions can be evaluated directly in four-dimensional space–time, with no restrictions whatsoever on the four-momentum of the internal loop, and without the need to introduce any additional nonphysical degrees of freedom like Pauli–Villars fields. We comment on the similar contributions responsible for the decay of the Higgs boson into two photons.