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Dynamical generation of the weak and Dark Matter scale

Thomas Hambye, Alessandro Strumia

TL;DR

The paper addresses the origin of the small weak and Dark Matter scales by adopting a finite naturalness viewpoint that ignores quadratic divergences and adding a minimal SM extension with an SU(2)_X gauge group and a scalar S. Through dimensional transmutation, the weak scale and a stable vector Dark Matter arise dynamically, with a single remaining free parameter governing collider and DM observables; the model predicts an extra scalar h_2, a DM vector with calculable relic density, and a first-order dark/electroweak phase transition capable of generating gravitational waves, while maintaining vacuum stability up to the Planck scale. RG running and phenomenology show the potential can be stable to high scales for representative couplings, and current experimental constraints delineate the viable parameter space. The framework yields testable predictions for collider searches, direct/indirect DM detection, and gravitational wave experiments, linking electroweak physics to Dark Matter in a tightly constrained, minimal setup.

Abstract

Assuming that naturalness should be modified by ignoring quadratic divergences, we propose a simple extension of the Standard Model where the weak scale is dynamically generated together with an automatically stable vector. Identifying it as thermal Dark Matter, the model has one free parameter. It predicts one extra scalar, detectable at colliders, which triggers a first-order dark/electroweak cosmological phase transition with production of gravitational waves. Vacuum stability holds up to the Planck scale.

Dynamical generation of the weak and Dark Matter scale

TL;DR

The paper addresses the origin of the small weak and Dark Matter scales by adopting a finite naturalness viewpoint that ignores quadratic divergences and adding a minimal SM extension with an SU(2)_X gauge group and a scalar S. Through dimensional transmutation, the weak scale and a stable vector Dark Matter arise dynamically, with a single remaining free parameter governing collider and DM observables; the model predicts an extra scalar h_2, a DM vector with calculable relic density, and a first-order dark/electroweak phase transition capable of generating gravitational waves, while maintaining vacuum stability up to the Planck scale. RG running and phenomenology show the potential can be stable to high scales for representative couplings, and current experimental constraints delineate the viable parameter space. The framework yields testable predictions for collider searches, direct/indirect DM detection, and gravitational wave experiments, linking electroweak physics to Dark Matter in a tightly constrained, minimal setup.

Abstract

Assuming that naturalness should be modified by ignoring quadratic divergences, we propose a simple extension of the Standard Model where the weak scale is dynamically generated together with an automatically stable vector. Identifying it as thermal Dark Matter, the model has one free parameter. It predicts one extra scalar, detectable at colliders, which triggers a first-order dark/electroweak cosmological phase transition with production of gravitational waves. Vacuum stability holds up to the Planck scale.

Paper Structure

This paper contains 5 sections, 22 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The model
  3. Phenomenological analysis
  4. Conclusions
  5. Acknowledgements

Figures (2)

  • Figure 1: Predicted cross sections for the extra scalar boson (left) and for DM direct detection (right) as function of the only free parameter of the model $\lambda_{HS}$, varied as shown in the colour legend.
  • Figure 2: Running of the model parameters up to the Planck scale for $g_X=1$.