Topological quantization of vector meson anomalous couplings

We identify an overlooked Wess--Zumino--Witten structure in the hidden-local-symmetry~(HLS) formulation of vector mesons. The newly identified term generically leads to the topological quantization of the vector-meson anomalous couplings. If confirmed experimentally, this structure would expose the gauge nature of vector mesons in the anomalous sector and single out HLS over matter-field descriptions. The observed success of vector-meson dominance in anomalous interactions can then be explained by topological-action saturation of the odd-intrinsic-parity processes. Precision measurements of $η^{(\prime)}\toπ^+π^-γ^*$ form factors at BESIII and the Super $τ$-Charm Facility can directly test this saturation picture.