Gauge-Independent Scales Related to the Standard Model Vacuum Instability

TL;DR

This paper identifies gauge-invariant scales associated with the Standard Model vacuum instability, overcoming gauge dependence issues in the conventional instability scale, through various physical probes and questions.

Contribution

It introduces gauge-invariant measures of the Higgs potential instability by analyzing the system under different physical conditions and probes.

Findings

Established gauge-invariant instability scales.

Demonstrated gauge dependence of the conventional instability scale.

Provided physical interpretations of the instability in different scenarios.

Abstract

The measured (central) values of the Higgs and top quark masses indicate that the Standard Model (SM) effective potential develops an instability at high field values. The scale of this instability, determined as the Higgs field value at which the potential drops below the electroweak minimum, is about $10^{11}$ GeV. However, such a scale is unphysical as it is not gauge-invariant and suffers from a gauge-fixing uncertainty of up to two orders of magnitude. Subjecting our system, the SM, to several probes of the instability (adding higher order operators to the potential; letting the vacuum decay through critical bubbles; heating up the system to very high temperature; inflating it) and asking in each case physical questions, we are able to provide several gauge-invariant scales related with the Higgs potential instability.