Mass Hierarchy and Vacuum Energy

Abstract

A hierarchically small weak scale does not generally coincide with enhanced symmetry, but it may still be exceptional with respect to vacuum energy. By analyzing the classical vacuum energy as a function of parameters such as the Higgs mass, we show how near-criticality, i.e. fine-tuning, corresponds universally to boundaries where the vacuum energy transitions from exactly flat to concave down. In the presence of quantum corrections, these boundary regions can easily be perturbed to become maxima of the vacuum energy. After introducing a dynamical scalar field $\phi$ which scans the Higgs sector parameters, we propose several possible mechanisms by which this field could be localized to the maximum. One possibility is that the $\phi$ potential has many vacua, with those near the maximum vacuum energy expanding faster during a long period of cosmic inflation and hence dominating the volume of the Universe. Alternately, we describe scenarios in which vacua near the maximum could be anthropically favored, due to selection of the late-time cosmological constant or dark matter density. Independent of these specific approaches, the physical value of the weak scale in our proposal is generated naturally and dynamically from loops of heavy states coupled to the Higgs. These states are predicted to be a loop factor heavier than in models without this mechanism, avoiding tension with experimental null results.