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 $ρ$-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 $ρ$-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 meson spectra and reproduce the expected asymptotic behavior, their hadronic light-by-light predictions exhibit sizable differences, reflecting significant variations in the transition form factor at low momentum transfer $Q^{2}$.

Figures (4)

• Figure 1: The integrand $f(Q^2)\Pi^{\text{had}}_{\text{em}}(Q^2)$ as a function of $Q^2$ computed in different models: SW1 (orange solid line), SW2 (purple solid line), SW3 (blue solid line), the hard-wall model (black dashed line), the original soft-wall model (green dashed line), and the tachyon condensation model (magenta and red dashed lines).
• Figure 2: Comparison of the $Q^2$ dependence of $F(Q^2,0)$ computed in various holographic models with experimental data from CELLO, CLEO, and BESIII Danilkin:2019mhd.
• Figure 3: The singly-virtual form factor $Q^2F(Q^2,0)$ calculated in the holographic models, compared with the experimental data CELLO:1990klcCLEO:1997fhoBaBar:2009rrjBelle:2012wwz.
• Figure 4: The $Q^{2}$ dependence of the diagonal form factor $Q^2F(Q^2,Q^2)$ in the low-$Q^{2}$ region, where the light-red error band denotes the result obtained from the dispersive approach Hoferichter:2018kwz.