Stuckelberg axions and the effective action of anomalous abelian models 1.: A unitary analysis of the Higgs-axion mixing

We analyze the quantam consistency of anomalous abelian models and of their effective field theories, rended anomaly-free by a Wess-Zumino term, in the case of multiple abelian symmetries. These models involve the combined Higgs-Stuckelberg mechanism and predict a pseudoscalar axion-like field that mixes with the goldstones of the ordinary Higgs sector. We focus our study on the issue of unitarity of these models both before and after spontaneous symmentry breaking and detail the set of Ward identities and the organization of the loop expansion in the effective theory. The analysis is performed on simple models where we show, in general, the emergence of new effective vertices determined by certain anomalous interactions.