The Fujikawa method to find the chiral anomaly allows us to find for the axial current $$\partial_\mu j^\mu=-\frac{g^2}{16\pi^2}\epsilon^{\mu\nu\rho\sigma} Tr F_{\mu\nu}F_{\rho\sigma},$$ which is the usual gauge-covariant form of the chiral anomaly. This is done for example in Srednicki ch. 77, or Weinberg ch. 22.
Gauge anomalies can in principle also be understood as a variation of the fermionic measure under a gauge transformation, so the Fujikawa method should also work. In this case we should however get the consistent form of the anomaly, at least if the current is defined as coming from an effective action. In Srednicki's notation this is $$D_\mu^{ab}j^{b\mu}=\frac{g^2}{24\pi^2}\epsilon^{\mu\nu\rho\sigma}\partial_\mu Tr \left(T^a (A_\nu\partial_\rho A_\sigma-\frac{i}{2}gA_\nu A_\rho A_\sigma)\right),$$ which Srednicki mentions can also be obtained from the Fujikawa method, albeit with a more involved analysis.
Does any one know what changes must be made to the derivation when dealing with gauge variations, leading to the consistent form? Or a good source for this?
