Hadronic light-by-light contribution to the muon $g-2$ from holographic QCD with massive pions

We extend our previous calculations of the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment in holographic QCD to models with finite quark masses and a tower of massive pions. Analysing the role of the latter in the Wess-Zumino-Witten action, we show that the Melnikov-Vainshtein short-distance constraint is satisfied solely by the summation of contributions from the infinite tower of axial vector meson contributions. There is also an enhancement of the asymptotic behavior of pseudoscalar contributions when their infinite tower of excitations is summed, but this leads only to subleading contributions for the short-distance constraints on light-by-light scattering. We also refine our numerical evaluations, particularly in the pion and $a_1$ sector, which corroborates our previous findings of contributions from axial vector mesons that are significantly larger than those adopted for the effects of axials and short-distance constraints in the recent White Paper on the Standard Model prediction for $(g-2)_\mu$.