Pseudoscalar transition form factors and the hadronic light-by-light contribution to the anomalous magnetic moment of the muon from holographic QCD

Abstract

We revisit the predictions for the pseudoscalar-photon transition form factors in bottom-up and top-down holographic QCD models which only use the pion decay constant and the $\rho$ meson mass as input. We find remarkable agreement with the available experimental data for the single-virtual ${\pi }^0$ 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 ${\eta }^{\prime }$ form factor at large momenta as well as with a recent lattice extrapolation for the double-virtual ${\pi }^0$ 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_\mu^{\pi^0}=6.1(4)\cdot 10^{-10}, which is somewhat lower than estimated previously by approximating these holographic predictions through simple interpolators, and in remarkably good agreement with recent results based on a dispersive approach or lattice simulations.

Comments: 19 pages, 5 figures, 2 tables; v3: detailed comparison with dispersive approach added, one more figure and several more references; v4: typo in acknowledgments fixed; v5: extended discussion of eta' contribution (version to appear in PRD); v6: corrected $a_{\mu }$ results for the HW1 model (erratum to appear in PRD), which improves agreement with dispersive results - figures unaffected