In trying to better understand the chiral-anomaly WZW-term interaction of the heavy vector mesons, I have trouble finding much relevant literature, but maybe I am looking in the wrong place.

One useful article I found is this one:

In equation (3) they state a WZW summand proportional to this term:

$$ A \wedge d K^+ \wedge d K^- \wedge d \pi^0 \phantom{AAAAAAAA} (3) $$

Then they mumble something about

$K^*$ could be regarded as a pair of $K$ and $\pi$

and then they list electromagnetic interactions, of which their equation (9) is the term proportional to this term:

$$ d A \wedge \big( d K^+ \wedge {K^*}^- - d K^- \wedge {K^*}^+ \big) \phantom{AAAAAAA} (9) $$

Please bear with my ignorance:

Question 1: Is (9) supposed to be the result of (3) after "regarding $K^*$ as a pair of $K$ and $\pi$" (and then doing an integration by parts)?

Question 2: No citation for any of these interaction terms is given in the above article. What would be a source with more details?

Question 3: Do we expect terms directly analogous to (3) and/or (9) for the D- and B-mesons?

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    $\begingroup$ Shouldn't $\pi^0$ come with a $d$ since in their paper it comes with a derivative? Also, how should we interpret the pair here? Are we supposed to add $K$ and $\pi$ or wedge them? $\endgroup$ Apr 11 '20 at 16:19
  • $\begingroup$ Regarding the missing $d$: yes thanks, fixed now. Regarding the pairing: that's part of my question, so I don't know. $\endgroup$ Apr 11 '20 at 16:35
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    $\begingroup$ Indeed, the bulk of the decays of K* go through $K\partial_m \pi$. Have you looked at similar anomalous vertices involving a ρ and a π ? $\endgroup$ May 1 '21 at 17:00
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    $\begingroup$ Just a thought. $\endgroup$ May 1 '21 at 17:44
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    $\begingroup$ These come near incorporating vector mesons into WZW: 1; Hashimoto, M. (1996). Hidden local symmetry for anomalous processes with isospin-and SU (3)-breaking effects. Physical Review D, 54(9), 5611; and appendix in 3. $\endgroup$ May 1 '21 at 19:39

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