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A deformation of the Abelian Higgs Kibble model induced by a dimension 6derivative operator is studied. A novel differential equation is establishedfixing the dependence of the vertex functional on the coupling $z$ of the dim.6operator in terms of amplitudes at $z = 0$ (those of the power-countingrenormalizable Higgs-Kibble model). The latter equation holds in a formalismwhere the physical mode is described by a gauge-invariant field. The functionalidentities of the theory in this formalism are studied. In particular we showthat the Slavnov-Taylor identities separately hold true at each order in thenumber of internal propagators of the gauge-invariant scalar. Despite beingnon-power-counting renormalizable, the model at $z \neq 0$ depends on a finitenumber of physical parameters.

Renormalizable Extension of the Abelian Higgs-Kibble Model with a dimension 6 operator