  New $U(1)$ gauge theories involving Standard Model (SM) fermions typically
require additional electroweak fermions for anomaly cancellation. We study the
non-decoupling properties of these new fermions, called anomalons, in the
$Z-Z'-\gamma$ vertex function, reviewing the connection between the full model
and 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 $U(1)_{B-L}$ gauge
symmetry, each generation of SM fermions is anomaly free and the exotic $Z \to
Z_{BL}' \gamma$ decay width is entirely induced by intragenerational mass
splittings. In contrast, for $U(1)_B$ gauge symmetry, the existence of two
distinct sources of chiral symmetry breaking enables a heavy, anomaly-free set
of 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 $Z'_B$ dijet
resonance searches are currently more constraining. We present a summary of the
current 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 $Z \to Z' \gamma$ decay
is emblematic of new anomalous $U(1)$ gauge symmetries.
