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Despite recent developments, there are a number of conceptual issues on thehadronic light-by-light (HLbL) contribution to the muon $(g-2)$ which remainunresolved. One of the most controversial ones is the precise way in whichshort-distance constraints get saturated by resonance exchange, particularly inthe so-called Melnikov-Vainshtein (MV) limit. In this paper we address this andrelated issues from a novel perspective, employing a warped five-dimensionalmodel as a tool to generate a consistent realization of QCD in the large-$N_c$limit. This approach differs from previous ones in that we can work at thelevel of an effective action, which guarantees that unitarity is preserved andthe chiral anomaly is consistently implemented at the hadronic level. We usethe model to evaluate the inclusive contribution of Goldstone modes andaxial-vector mesons to the HLbL. We find that both anomaly matching and the MVconstraint cannot be fulfilled with a finite number of resonances (includingthe pion) and instead require an infinite number of axial-vector states. Ournumbers for the HLbL point at a non-negligible role of axial-vector mesons,which is closely linked to a correct implementation of QCD short-distanceconstraints.

On axials and pseudoscalars in the hadronic light-by-light contribution to the muon $(g-2)$