Mass Hierarchy and Vacuum Energy

Understand

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.