Gauge hierarchy from electroweak vacuum metastability

TL;DR

This paper explores the idea that the gauge hierarchy problem may stem from the metastability of the electroweak vacuum, linking the small Higgs mass to vacuum stability and constraining new physics models.

Contribution

It proposes that electroweak vacuum metastability naturally leads to a small Higgs mass, providing new bounds on the instability scale in various extensions of the Standard Model.

Findings

In the Standard Model, the instability scale is around 10^11 GeV.

Extensions like the νMSM and composite Higgs models can lower the instability scale.

The bound on the Higgs mass can be reduced to approximately 10 TeV in some models.

Abstract

We consider the possibility that the gauge hierarchy is a byproduct of the metastability of the electroweak vacuum, i.e., that whatever mechanism is responsible for the latter also sets the running Higgs mass to a value smaller than its natural value by many orders of magnitude. This perspective is motivated by the early-time framework for eternal inflation put forth recently, which favors vacua that are relatively short-lived, but applies more generally to any theoretical approach predicting that our vacuum should be metastable. We find that the metastability of the electroweak vacuum, together with the requirement that such a non-trivial vacuum exists, requires the Higgs mass to be smaller than the instability scale by around one order of magnitude. While this bound is quite weak in the Standard Model (SM), as the instability scale is $\sim 10^{11}$ GeV, simple and well-motivated extensions of the SM - concretely, the $\nu$MSM with an approximate $B-\tilde{L}$ symmetry and the minimal SU(4)/Sp(4) composite Higgs model - can significantly tighten the bound by lowering the instability scale. We find that the bound can be brought down to $\simeq 10$ TeV where our perturbative treatment of the decay rate becomes unreliable. Our results imply that, assuming the SM symmetry breaking pattern, small running Higgs masses are a universal property of theories giving rise to metastability, suggesting a common origin of the two underlying fine-tunings and providing a strong constraint on any attempt to explain metastability.