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

TL;DR

This paper introduces a renormalizable extension of the Abelian Higgs-Kibble model by adding a dimension 6 operator, establishing a differential equation for the vertex functional, and demonstrating the model's dependence on finite physical parameters despite non-power-counting renormalizability.

Contribution

It develops a novel formalism for the Abelian Higgs-Kibble model with a dimension 6 operator, deriving a differential equation for its vertex functional and analyzing its renormalization properties.

Findings

The differential equation relates the vertex functional dependence on the dimension 6 coupling to amplitudes at zero coupling.

The Slavnov-Taylor identities hold at each order in the number of internal propagators.

The model depends on a finite number of physical parameters despite being non-power-counting renormalizable.

Abstract

A deformation of the Abelian Higgs Kibble model induced by a dimension 6 derivative operator is studied. A novel differential equation is established fixing the dependence of the vertex functional on the coupling $z$ of the dim.6 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 non-power-counting renormalizable, the model at $z \neq 0$ depends on a finite number of physical parameters.