Higgs Potential from Derivative Interactions

TL;DR

This paper explores a derivative interaction formulation of the Higgs potential, showing its equivalence to the standard model at the classical level and discussing its renormalization, including an extension with a dimension-six operator.

Contribution

It introduces a derivative interaction formulation of the Higgs sector, including a non power-counting renormalizable extension that maintains functional identities and is equivalent to an effective dimension-six operator.

Findings

Classical equivalence to the standard Higgs model.

A renormalization scheme for the derivative interaction formulation.

Extension with a dimension-six operator maintains physical equivalence.

Abstract

A formulation of the linear $\sigma$ model with derivative interactions is studied. The classical theory is on-shell equivalent to the $\sigma$ model with the standard quartic Higgs potential. The mass of the scalar mode only appears in the quadratic part and not in the interaction vertices, unlike in the ordinary formulation of the theory. Renormalization of the model is discussed. A non power-counting renormalizable extension, obeying the defining functional identities of the theory, is presented. This extension is physically equivalent to the tree-level inclusion of a dimension six effective operator $\partial_\mu (\Phi^\dagger \Phi) \partial^\mu (\Phi^\dagger \Phi)$. The resulting UV divergences are arranged in a perturbation series around the power-counting renormalizable theory. The application of the formalism to the Standard Model in the presence of the dimension-six operator $\partial_\mu (\Phi^\dagger \Phi) \partial^\mu (\Phi^\dagger \Phi)$ is discussed.