Anomalous part of baryon current in chiral effective field theory

Question

Let's assume QCD at high energies. It has $SU_{L}(3)\times SU_{R}(3)$ global symmetry. At $\Lambda_{\text{QCD}}$ scale this group is spontaneously broken to $SU_{f}(3)$. We can then extract Goldstone degrees of freedom from quark fields, $q \to Uq$, and replace $\bar{q}q$ term by vacuum expectation value. We will get chiral effective field theory in terms of $U$.

It can be shown that baryon current anomaly piece can be given in terms of $U$ as
$$
J^{\mu} = \frac{\epsilon^{\mu\nu\alpha\beta}}{24 \pi^{2}}\text{Tr}\left[U^{-1}\partial_{\nu}UU^{-1}\partial_{\alpha}UU^{-1}\partial_{\beta}U\right]
$$
How to derive this result?

Comments

How do you know that the formula is valid?

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It is represented in Witten's article (Eq. (2)), the reference of which you've given in your answer on my question about baryons as skyrmion solution.