The Effective Potential in Fermi Gauges Beyond the Standard Model

TL;DR

This paper derives gauge-dependent field masses in Fermi gauges for scalar extensions of the Standard Model, introduces a computational tool, and discusses gauge dependence issues affecting the effective potential's global minimum.

Contribution

It provides a method to compute gauge-dependent masses and a Mathematica tool for analyzing effective potentials in models beyond the Standard Model.

Findings

Existence of points with discontinuous global minima in gauge parameter space.

The gauge dependence can influence the identification of the true vacuum.

The developed tool facilitates large-scale phenomenological studies.

Abstract

We derive the field-dependent masses in Fermi gauges for arbitrary scalar extensions of the Standard Model. These masses can be used to construct the effective potential for various models of new physics. We release a flexible $\texttt{Mathematica}$ notebook ($\texttt{VefFermi}$) which performs these calculations and renders large-scale phenomenological studies of various models possible. Motivated by the debate on the importance of gauge dependence, we show that, even in relatively simple models, there exist points where the global minimum is discontinuous in the gauge parameter. Such points require some care in discovering, indicating that a gauge-dependent treatment might still give reasonable results when examining the global features of a model.