Two-loop chiral anomaly as an infrared phenomenon

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Abstract
We consider a two-loop chiral anomaly within the dispersion approach to matrix elements of the axial-vector current. The anomaly is known to be ultraviolet ambiguous to this order and our goal is to trace the ambiguity in terms of imaginary parts of the matrix elements which are "observable." We find that the matrix elements depend crucially on details of infrared regularization which is needed to specify the imaginary part. In particular, if one sets the masses of the particles inside the loop equal to zero first while letting the virtuality of external particles go to zero next then the anomaly does not receive a two-loop contribution. If the limiting procedure is reversed then one reconstructs the so-called supersymmetric current which acts as a partner of the energy-momentum tensor in the supermultiplet of currents. The results are applied to the problem of renormalization of topological charges.