Hadronic Contributions to the Muon $g-2$ in Improved Holographic QCD Models

Abstract

We present a systematic study of the hadronic contributions to the muon anomalous magnetic moment within several infrared-improved AdS/QCD models. The models are constrained by the pion decay constant and the $\rho$-meson mass and are shown to reproduce phenomenologically reasonable low-energy hadron spectra. Within a unified holographic framework, we evaluate both the leading-order hadronic vacuum polarization contribution and the pseudoscalar-pole contribution to hadronic light-by-light scattering. The holographic predictions for the hadronic vacuum polarization contribution are found to be systematically lower than recent dispersive determinations, and we demonstrate that this discrepancy is closely correlated with an underestimation of the $\rho$-meson decay constant in the models. We further compute the pion transition form factor and the corresponding pseudoscalar-pole hadronic light-by-light contribution. Although the models yield similar pion mass spectra and reproduce the expected asymptotic behavior, their predictions for the hadronic light-by-light contribution exhibit sizable variations, driven by differences in the transition form factor in the low momentum transfer $Q^{2}$ region.