Absence of Second-Order Correction to the Triangle Anomaly in Quantum Electrodynamics

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Abstract
We report on the investigation of possible ambiguities involved in calculating the second-order correction to the axial-vector anomaly. The testing ground is finite-mass quantum electrodynamics where the anomaly is defined using Pauli-Villars regularization. The result supports Adler's previous conclusion that there exist no such corrections. Furthermore, the mass renormalization is explicitly shown to be consistent in this order.