  We discuss the BCF anomaly of massless QCD-like theories, first obtained by
Anber and Poppitz, from the viewpoint of the low energy effective theories. We
assume that the QCD-like theories exhibit spontaneous chiral symmetry breaking
due to a quark bilinear condensate. Using the 't Hooft anomaly matching
condition for the BCF anomaly, we find that the low energy effective action is
composed of a chiral Lagrangian and a Wess-Zumino-Witten term together with an
interaction term of the $\eta^\prime$ meson with the background gauge field for
a discrete one-form symmetry. It is shown that the low energy effective action
cancels the quantum inconsistencies associated with $\eta^\prime$ due to an
ambiguity of how to uplift the action to a five-dimensional spacetime with a
boundary. The $\eta^\prime$ term plays a substantial role in exploring the
emergent higher-group structure at low energies.
