Renormalizable extension of the Abelian Higgs-Kibble model with a dimension-six operator

A deformation of the Abelian Higgs Kibble model induced by a dimension-six derivative operator is studied. A novel differential equation is established fixing the dependence of the vertex functional on the coupling 𝑧 of the dimension-six operator in terms of amplitudes at 𝑧 =0 (those of the power-counting renormalizable Higgs-Kibble model). The latter equation holds in a formalism where the physical mode is described by a gauge-invariant field. The functional identities of the theory in this formalism are studied. In particular, we show that the Slavnov-Taylor identities separately hold true at each order in the number of internal propagators of the gauge-invariant scalar. Despite being nonpower-counting renormalizable, the model at 𝑧 ≠0 depends on a finite number of physical parameters.