On the gauge dependence of the Standard Model vacuum instability scale

TL;DR

This paper examines how the gauge choice affects the calculation of the Standard Model vacuum instability scale, revealing significant gauge dependence and uncertainty in the predicted instability point.

Contribution

It demonstrates that while the electroweak vacuum stability bound is gauge independent, the instability scale is gauge dependent, introducing substantial theoretical uncertainty.

Findings

The instability scale varies by at least two orders of magnitude with gauge choice.

Electroweak vacuum stability bound remains gauge independent.

Gauge fixing parameters significantly influence the instability scale calculation.

Abstract

After reviewing the calculation of the Standard Model one-loop effective potential in a class of linear gauges, we discuss the physical observables entering the vacuum stability analysis. While the electroweak-vacuum-stability bound on the Higgs boson mass can be formally proven to be gauge independent, the field value at which the effective potential turns negative (the so-called instability scale) is a gauge dependent quantity. By varying the gauge-fixing scheme and the gauge-fixing parameters in their perturbative domain, we find an irreducible theoretical uncertainty of at least two orders of magnitude on the scale at which the Standard Model vacuum becomes unstable.