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_μ^{π^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.

arXiv comment19 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

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• The anomalous magnetic moment of the muon in the Standard Model: an update
• Axial vector transition form factors in holographic QCD and their contribution to the anomalous magnetic moment of the muon
• On axials and pseudoscalars in the hadronic light-by-light contribution to the muon $(g-2)$
• Effects of Longitudinal Short-Distance Constraints on the Hadronic Light-by-Light Contribution to the Muon $g-2$
• Hadronic light-by-light contribution to the muon $g-2$ from holographic QCD with solved $U(1{)}_A$ problem
• Hadronic light-by-light contribution to the muon $g-2$ from holographic QCD with massive pions
• On some properties of the fourth-rank hadronic vacuum polarization tensor and the anomalous magnetic moment of the muon
• Witten-Veneziano mechanism and pseudoscalar glueball-meson mixing in holographic QCD
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• Holographic QCD and the muon anomalous magnetic moment
• Central exclusive diffractive production of axial-vector $f_1(1285)$ and $f_1(1420)$ mesons in proton-proton collisions
• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Scalar resonances in the hadronic light-by-light contribution to the muon $(g-2)$
• ${\pi }^0,\eta ,{\eta }^{\prime }$ two-photon transition form factors in the holographic soft-wall model and contributions to $(g-2{)}_{\mu }$
• Hadronic vacuum polarization contribution to the muon $g-2$ in holographic QCD
• Divergences in the hadronic light-by-light amplitude of the holographic soft-wall model
• Axial vector transition form factors in holographic QCD and their contribution to the muon $g-2$