A new connection between WIMP dark matter and the hierarchy problem

TL;DR

This paper links the hierarchy problem to WIMP dark matter, proposing that the Higgs mass is dynamically driven to the WIMP scale near a phase transition boundary, with testable implications for experiments.

Contribution

It introduces a novel scenario connecting the Higgs mass, WIMP dark matter, and vacuum stability through a critical boundary mechanism.

Findings

WIMP mass around the weak scale can explain dark matter abundance.

Observation of WIMP mass > 1.2 TeV constrains Higgs mass and new physics scale.

The scenario is testable via direct detection, astrophysics, and colliders.

Abstract

This work proposes a direct link between the hierarchy problem and Weakly Interacting Massive Particles (WIMPs): we suggest that the small mass of the Higgs boson arises from being dynamically driven to the scale of the WIMP. Such a special electroweak vacuum is singled out by lying close to the critical boundary of a phase transition, as recently explored in a new class of cosmological solutions to the hierarchy problem. They generically predict the Higgs potential to be destabilised just above the weak scale. Intriguingly, the requirement for new physics to achieve this coincides with two independently well-motivated expectations: a split spectrum of light fermions and heavy bosons, as anticipated from naturalness, and the so-called "WIMP miracle". A WIMP with mass around the weak scale not only happens to have the correct thermal relic abundance to be the dark matter (DM), it can also give rise to the necessary critical boundary at the TeV scale through its Yukawa couplings to the Higgs. We use a higgsino-like singlet-doublet model to illustrate our Higgs-DM criticality scenario and show that if this WIMP DM mass is observed to be greater than ~1.2 TeV then it necessarily implies a strong bound on the Higgs mass and an upper bound on the scale of heavy new physics that restores vacuum stability. It can be thoroughly probed in direct detection experiments, astrophysical signals and future collider searches, further motivating a comprehensive exploration of the remaining heavy WIMP parameter space.