Renormalizable Extension of the Abelian Higgs-Kibble Model with a Dim.6 Derivative Operator

TL;DR

This paper introduces a novel method for renormalizing a non-power-counting renormalizable extension of the Abelian Higgs-Kibble model with a dimension-6 derivative operator, using gauge-invariant variables and a differential equation approach.

Contribution

It develops a consistent subtraction scheme for a non-renormalizable Higgs model extension, enabling finite parameter renormalization and potential applications to Higgs physics at the LHC.

Findings

Formulation of a differential equation controlling $z$-dependence.

Finite parameter subtraction in a non-power-counting renormalizable model.

Potential relevance to Higgs potential studies at the LHC.

Abstract

We present a new approach to the consistent subtraction of a non power-counting renormalizable extension of the Abelian Higgs-Kibble (HK) model supplemented by a dim.6 derivative-dependent operator controlled by the parameter $z$. A field-theoretic representation of the physical Higgs scalar by a gauge-invariant variable is used in order to formulate the theory by exploiting a novel differential equation, controlling the dependence of the quantized theory on $z$. These results pave the way to the consistent subtraction by a finite number of physical parameters of some non-power-counting renormalizable models possibly of direct relevance to the study of the Higgs potential at the LHC.