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arXiv · 2002.01191

The fate of the axial anomaly in a finite field theory

Pierre Grangé·Jean-François Mathiot·Ernst Werner
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Abstract

The conservation of the vector current and the axial anomaly responsible for the $\pi_0 \to \gamma \gamma$ 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 $4$-dimensional space-time, with no restrictions whatsoever on the four-momentum of the internal loop, and without the need to introduce any additional non physical degrees of freedom like Pauli-Villars fields. We comment on the similar contributions responsible for the decay of the Higgs boson into two photons.

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Pierre Grangé, Jean-François Mathiot, Ernst Werner. 2020-02-04. The fate of the axial anomaly in a finite field theory. https://doi.org/10.1142/s0217751x20500256

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