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We calculate the anomalous part of the polarization tensor of Dirac fermionsin $2+1$ dimensions in the presence of impurities described by the scatteringrate $\Gamma$ for arbitrary external frequency and momenta. We consider twodifferent versions of the Pauli--Villars subtractions and discuss theirphysical consequences.

Parity anomaly with impurities and the Pauli--Villars subtraction