Higgs Vacuum Stability in a Mass-Dependent Renormalisation Scheme

TL;DR

This paper employs a mass-dependent renormalisation scheme to precisely analyze Higgs vacuum stability, concluding that the electroweak vacuum is not absolutely stable and likely too short-lived to survive cosmic inflation.

Contribution

It introduces a mass-dependent renormalisation scheme for the Higgs quartic coupling, improving stability analysis accuracy and conclusively determining the vacuum's instability at high confidence.

Findings

Absolute stability of the Higgs vacuum is excluded at 99.98% C.L.

The electroweak vacuum lifetime is too short to survive inflation.

Refined error in the top quark mass required for stability is 0.28 GeV.

Abstract

Using a physical renormalisation scheme we derive mass-dependent renormalisation group equations for the running of the Higgs quartic coupling within the Standard Model. Subsequently, we accurately take into account weak scale thresholds, resulting in a reduction of the error in the determination of the maximum $M_t$ required for absolute stability of the vacuum to 0.28 GeV. For the first time, we conclusively establish the fate of the electroweak vacuum, finding that absolute stability of the Higgs vacuum state is excluded at 99.98% C.L. We also discuss the consequences when this new result is combined with the BICEP Collaboration's recent observation of B-mode polarisation in the cosmic microwave background, finding the Standard Model electroweak vacuum lifetime to be too short to have survived inflation. The implications for inflationary and new physics models are also discussed.