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New $U(1)$ gauge theories involving Standard Model (SM) fermions typicallyrequire additional electroweak fermions for anomaly cancellation. We study thenon-decoupling properties of these new fermions, called anomalons, in the$Z-Z'-\gamma$ vertex function, reviewing the connection between the full modeland the effective Wess-Zumino operator. We calculate the exotic $Z \to Z'\gamma$ decay width in $U(1)_{B-L}$ and $U(1)_B$ models, where $B$ and $L$denote the SM baryon and lepton number symmetries. For $U(1)_{B-L}$ gaugesymmetry, each generation of SM fermions is anomaly free and the exotic $Z \toZ_{BL}' \gamma$ decay width is entirely induced by intragenerational masssplittings. In contrast, for $U(1)_B$ gauge symmetry, the existence of twodistinct sources of chiral symmetry breaking enables a heavy, anomaly-free setof fermions to have an irreducible contribution to the $Z \to Z_B' \gamma$decay width. We show that the current LEP limits on the exotic $Z \to Z'_B\gamma$ decay are weaker than previously estimated, and low-mass $Z'_B$ dijetresonance searches are currently more constraining. We present a summary of thecurrent collider bounds on $U(1)_B$ and a projection for a TeraZ factory on the$Z \to Z_B' \gamma$ exotic decay, and emphasize how the $Z \to Z' \gamma$ decayis emblematic of new anomalous $U(1)$ gauge symmetries.

Probing new $U(1)$ gauge symmetries via exotic $Z \to Z' \gamma$ decays