We revisit the predictions for the pseudoscalar-photon transition form factors in bottomup and top-down holographic QCD models which only use the pion decay constant and the ρ meson mass as input. We find remarkable agreement with the available experimental data for the single-virtual π 0 form factor that have recently been extended to lower momenta by BESIII, down to 0.3 GeV 2 . The bottom-up models moreover turn out to be roughly consistent with recent experimental results obtained by BaBar for the double-virtual η form factor at large momenta as well as with a recent lattice extrapolation for the double-virtual π 0 form factor. Calculating the pion pole contribution to the hadronic light-by-light scattering in the anomalous magnetic moment of the muon, we find that the bottom-up models in question span the range a π 0 µ = 5.9(2) · 10 −10 , which is about 10% lower than estimated previously by approximating these holographic predictions through simple interpolators.

We review the recent progress made in using holographic QCD to study hadronic contributions to the anomalous magnetic moment of the muon, in particular the hadronic light-by-light scattering contribution, where the short-distance constraints associated with the axial anomaly are notoriously difficult to satisfy in hadronic models. This requires the summation of an infinite tower of axial vector mesons, which is naturally present in holographic QCD models, and indeed takes care of the longitudinal short-distance constraint due to Melnikov and Vainshtein. Numerically the results of simple hard-wall holographic QCD models point to larger contributions from axial vector mesons than assumed previously, while the predicted contributions from pseudo-Goldstone bosons agree nicely with data-driven approaches.

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