Axion Couplings in Gauged $U(1)'$ Extensions of the Standard Model

We explore the effective theory of an axion in a gauged baryon number symmetry extension of the Standard Model (SM), where the axion is realized from a Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model construction. Integrating out the anomalons realizes a pattern of effective Wilson coefficients reflecting the factorization between the anomalous Peccei-Quinn and gauged baryon number symmetries. We construct and analyze the chiral transformation invariance of the axion effective theory, accounting for possible flavor-violating axion couplings. We calculate and study the unique phenomenology of the axion and $Z'$ boson, and we present the current collider limits on these particles in the $\{m_{Z'}, g_B\}$, $\{m_a, G_{a \gamma \gamma} \}$, and $\{m_a, f_a^{-1}\}$ planes.