Understand
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.