Light vectors coupled to anomalous currents with harmless Wess-Zumino terms

We reconsider the case of light vectors coupled to anomalous fermionic currents, focusing on the interplay between ultraviolet and infrared dynamics. Taking as a general framework the gauging of the Standard Model accidental symmetries, we show that it is possible to devise an anomaly-free ultraviolet completion with mostly chiral heavy fermions such that anomalous Wess-Zumino terms are suppressed in the infrared, thus relaxing would-be strong bounds from the longitudinal emission of light vectors coupled to nonconserved currents. We classify such scenarios and show that they will be extensively probed at the high-luminosity phase of the LHC via the measurement of the h -> Z gamma rate and the direct search for nondecoupling charged leptons.