Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision

TL;DR

This paper provides a comprehensive, gauge-independent analysis of the Standard Model's vacuum stability, incorporating advanced multi-loop calculations to refine the upper bound on the top quark mass for stability up to the Planck scale.

Contribution

It introduces a gauge-invariant method for analyzing vacuum stability with high-precision calculations, improving the accuracy of the top quark mass bound.

Findings

Derived an upper bound on the top quark pole mass consistent with experimental measurements.

Performed a high-precision, gauge-independent analysis including multi-loop corrections.

Estimated the theoretical uncertainty in the stability bound.

Abstract

We perform a manifestly gauge-independent analysis of the vacuum stability in the Standard Model (SM) including two-loop matching, three-loop renormalization group evolution, and pure QCD corrections through four loops. All these ingredients are exact, except that light-fermion masses are neglected. We in turn apply the criterion of nullifying the $\overline{\mathrm{MS}}$ Higgs self-coupling and its beta function and a recently proposed consistent method for determining the true minimum of the effective Higgs potential that also avoids gauge dependence. Exploiting our knowledge of the Higgs-boson mass, we derive an upper bound on the pole mass of the top quark by requiring that the SM be stable all the way up to the Planck mass scale and conservatively estimate the theoretical uncertainty. This bound is compatible with Monte Carlo mass quoted by the Particle Data Group at the $1.3\sigma$ level.