Axial vector transition form factors in holographic QCD and their contribution to the anomalous magnetic moment of the muon

We evaluate axial vector transition form factors in holographic QCD models that have been shown to reproduce well recent experimental and theoretical results for the pion transition form factor. Comparing with L3 data on $f_1\to\gamma\gamma^*$ we find remarkable agreement regarding the shape of single-virtual form factors. In the double-virtual case, the holographic results differ strongly from a simple dipole form, and this has an important impact on the corresponding estimate of the axial vector contribution to the anomalous magnetic moment of the muon $a_\mu$ through hadronic light-by-light scattering. We demonstrate that hard-wall models satisfy the Melnikov-Vainshtein short-distance constraint for the latter, if and only if the infinite tower of axial vector states is included. The results for $a_\mu$, however, are strongly dominated by the first few resonances. Numerically, these results turn out to be surprisingly large: (2.9 - 4.1)$\times 10^{-10}$ in the hard-wall models, 57-58% of which are due to the longitudinal contribution, which is the one responsible for the Melnikov-Vainshtein short-distance constraint. Rescaling the holographic result to obtain an optimal fit of L3 data, but then matching only 52% of the asymptotic constraint, the result is reduced to $2.2(5)\times 10^{-10}$, which is still significantly larger than most previous phenomenological estimates of the axial vector exchange contribution.
Comment: 23 pages, 5 figures, 4 tables; v3: more details on the MV SDC, slightly improved numerics (HW1), slightly extended summary; v4: typos corrected, summary table IV corrected by revised results of 1906.11795; v5: small corrections in appendix B