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

Understand

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.