Mass Hierarchy and Vacuum Energy

TL;DR

This paper explores how the small weak scale and vacuum energy are related, proposing mechanisms involving a scalar field to dynamically select the weak scale near vacuum energy maxima, with implications for naturalness and experimental predictions.

Contribution

It introduces a novel framework where a scalar field scans Higgs parameters and localizes at vacuum energy maxima, linking weak scale smallness to vacuum energy dynamics.

Findings

Vacuum energy boundaries correspond to near-criticality and fine-tuning.

Scalar field mechanisms can naturally select the weak scale.

Heavy states coupled to the Higgs are predicted to be a loop factor heavier.

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.