Gauge hierarchy from electroweak vacuum metastability

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. We find that the metastability of the electroweak vacuum, together with the requirement that such a nontrivial vacuum exists, requires the Higgs mass to be smaller than the instability scale by around 1 order of magnitude. While this bound is quite weak in the Standard Model (SM), as the instability scale is ∼1011 GeV, simple and well-motivated extensions of the SM significantly tighten the bound by lowering the instability scale. We first consider the effect of right-handed neutrinos in the νMSM with approximate B-L symmetry, which allows for masses of order TeV for the right-handed neutrinos and O(1) Yukawa couplings. We find that right-handed neutrinos cannot by themselves fully explain the gauge hierarchy, as the tightest upper bound compatible with current experimental constraints is ∼108 GeV. As we demonstrate on the example of the minimal SU(4)/Sp(4) composite Higgs model, this bound can be lowered significantly through the interplay of the neutrinos and a dimension-six operator. In this scenario, the bound can be brought down considerably, with the smallest value accessible by our perturbative treatment being of order ≃10 TeV, and consistently several orders of magnitude below its natural value. While this is insufficient to fully solve the gauge hierarchy problem, 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.