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Physical Naturalness and Dynamical Breaking of Classical Scale Invariance

Matti Heikinheimo, Antonio Racioppi, Martti Raidal, Christian Spethmann, Kimmo Tuominen

TL;DR

The paper confronts the hierarchy problem under the premise of physical naturalness and classical scale invariance, arguing that UV scales should not couple to the Higgs in a way that generates large radiative corrections. It advocates a classically scale-invariant SM extended by a confining dark sector (dark technicolor) connected through a Higgs portal, where the dark dynamics dynamically generate the electroweak scale and provide dark matter candidates. An explicit model is developed, detailing the dark sector, the Higgs-portal interactions, and the resulting low-energy spectrum and DM phenomenology, including relic-density considerations and mass hierarchies. The work highlights potential experimental signatures through Higgs portal effects and notes open questions about flavor structure and UV completion, framing a path for testing classically conformal UV theories that realize physical naturalness.

Abstract

We propose a model of a confining dark sector, dark technicolor, that communicates with the Standard Model through the Higgs portal. In this model electroweak symmetry breaking and dark matter share a common origin, and the electroweak scale is generated dynamically. Our motivation to suggest this model is the absense of evidence for new physics from recent LHC data. Although the conclusion is far from certain at this point, this lack of evidence may suggest that no mechanism exists at the electroweak scale to stabilise the Higgs mass against radiative corrections from UV physics. The usual reaction to this puzzling situation is to conclude that the stabilising new physics is either hidden from us by accident, or that it appears at energies that are currently inaccessible, such that nature is indeed fine-tuned. In order to re-examine the arguments that have lead to this dichotomy, we review the concept of naturalness in effective field theories, discussing in particular the role of quadratic divergences in relation to different energy scales. This leads us to suggest classical scale invariance as a guidline for model building, implying that explicit mass scales are absent in the underlying theory.

Physical Naturalness and Dynamical Breaking of Classical Scale Invariance

TL;DR

The paper confronts the hierarchy problem under the premise of physical naturalness and classical scale invariance, arguing that UV scales should not couple to the Higgs in a way that generates large radiative corrections. It advocates a classically scale-invariant SM extended by a confining dark sector (dark technicolor) connected through a Higgs portal, where the dark dynamics dynamically generate the electroweak scale and provide dark matter candidates. An explicit model is developed, detailing the dark sector, the Higgs-portal interactions, and the resulting low-energy spectrum and DM phenomenology, including relic-density considerations and mass hierarchies. The work highlights potential experimental signatures through Higgs portal effects and notes open questions about flavor structure and UV completion, framing a path for testing classically conformal UV theories that realize physical naturalness.

Abstract

We propose a model of a confining dark sector, dark technicolor, that communicates with the Standard Model through the Higgs portal. In this model electroweak symmetry breaking and dark matter share a common origin, and the electroweak scale is generated dynamically. Our motivation to suggest this model is the absense of evidence for new physics from recent LHC data. Although the conclusion is far from certain at this point, this lack of evidence may suggest that no mechanism exists at the electroweak scale to stabilise the Higgs mass against radiative corrections from UV physics. The usual reaction to this puzzling situation is to conclude that the stabilising new physics is either hidden from us by accident, or that it appears at energies that are currently inaccessible, such that nature is indeed fine-tuned. In order to re-examine the arguments that have lead to this dichotomy, we review the concept of naturalness in effective field theories, discussing in particular the role of quadratic divergences in relation to different energy scales. This leads us to suggest classical scale invariance as a guidline for model building, implying that explicit mass scales are absent in the underlying theory.

Paper Structure

This paper contains 11 sections, 20 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Naturalness - General Considerations
  3. The standard model
  4. Physics beyond the standard model
  5. Renormalizability and Classical Scale Invariance
  6. Renormalizability of effective field theories
  7. Classical scale invariance
  8. An Explicit Model: EW Symmetry Breaking from Dark Technicolor
  9. The dark technicolor model
  10. Low energy phenomenology
  11. Discussion and Conclusions

Figures (1)

  • Figure 1: The $5\sigma$-allowed region for the relic density of DM, for $g_h\alpha=0.3$ (green), $g_h\alpha=0.1$ (red) and $g_h\alpha=0.01$ (blue). The mass of the messenger scalar is plotted on the $x$-axis, and the $y$-axis shows $\Delta m=m_s-2m_\pi$.