Hadronic vacuum polarization and light-by-light scattering in representative infrared-improved soft-wall holographic QCD models

Abstract We investigate the hadronic contributions to the anomalous magnetic moment of the muon $$a_\mu $$ a μ in three representative infrared-improved soft-wall anti-de Sitter (AdS)/quantum chromodynamics (QCD) models, focusing on the leading-order hadronic vacuum polarization (LO-HVP) and hadronic light-by-light (HLbL) contributions. The model parameters are fixed by the ground-state $$\rho $$ ρ -meson mass, pion mass, and pion decay constant, with the low-lying excited spectrum used as an additional phenomenological constraint. We find that the LO-HVP contribution remains below dispersive determinations, mainly because the $$\rho $$ ρ -meson decay constant is underestimated. In the HLbL sector, the standard Chern–Simons term gives well-defined ground-state pseudoscalar-pole contributions but leads to divergent excited-state sums in soft-wall models. We therefore also adopt a scalar-extended Chern–Simons term motivated by brane–antibrane construction, which provides infrared suppression and allows finite estimates for pseudoscalar excitations and axial-vector mesons. The resulting HLbL predictions are internally convergent but still quantitatively model-dependent, showing that further refinement of the infrared completion and short-distance constraints is required.