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Higgs Naturalness and Dark Matter Stability by Scale Invariance

Jun Guo, Zhaofeng Kang

TL;DR

Extending the Standard Model with classical scale invariance (SI) provides a path to addressing Higgs naturalness via SI anomaly and radiative electroweak symmetry breaking. The authors construct a minimal scale-invariant framework—2HDM+S—where a real singlet DM is stabilized accidentally and a second Higgs doublet drives EWSB through the Coleman-Weinberg mechanism, with DM dynamics governed by the extended Higgs sector. Radiative EWSB is analyzed using the Gilard-Weinberg approach, predicting a SM-like Higgs as a pseudo-Goldstone boson and a heavy Higgs spectrum around 380 GeV, constrained by Higgs decays and oblique parameters; a light CP-odd state A is required to avoid h→AA decays. The resulting DM phenomenology features viable annihilation channels near the Higgs pole or via AA with phase-space suppression, but stringent direct-detection bounds (e.g., LUX) strongly shape the allowed parameter space, making upcoming DM searches and LHC data decisive for testing the model.

Abstract

Extending the spacetime symmetries of standard model (SM) by scale invariance (SI) may address the Higgs naturalness problem. In this article we attempt to embed accidental dark matter (DM) into SISM, requiring that the symmetry protecting DM stability is accidental due to the model structure rather than imposed by hand. In this framework, if the light SM-like Higgs boson is the pseudo Goldstone boson of SI spontaneously breaking, we can even pine down the model, two-Higgs-doublets plus a real singlet: The singlet is the DM candidate and the extra Higgs doublet triggers electroweak symmetry breaking via the Coleman-Weinberg mechanism; Moreover, it dominates DM dynamics. We study spontaneously breaking of SI using the Gillard-Weinberg approach and find that the second doublet should acquire vacuum expectation value near the weak scale. Moreover, its components should acquire masses around 380 GeV except for a light CP-odd Higgs boson. Based on these features, we explore viable ways to achieve the correct relic density of DM, facing stringent constraints from direct detections of DM. For instance, DM annihilates into $b\bar b$ near the SM-like Higgs boson pole, or into a pair of CP-odd Higgs boson with mass above that pole.

Higgs Naturalness and Dark Matter Stability by Scale Invariance

TL;DR

Extending the Standard Model with classical scale invariance (SI) provides a path to addressing Higgs naturalness via SI anomaly and radiative electroweak symmetry breaking. The authors construct a minimal scale-invariant framework—2HDM+S—where a real singlet DM is stabilized accidentally and a second Higgs doublet drives EWSB through the Coleman-Weinberg mechanism, with DM dynamics governed by the extended Higgs sector. Radiative EWSB is analyzed using the Gilard-Weinberg approach, predicting a SM-like Higgs as a pseudo-Goldstone boson and a heavy Higgs spectrum around 380 GeV, constrained by Higgs decays and oblique parameters; a light CP-odd state A is required to avoid h→AA decays. The resulting DM phenomenology features viable annihilation channels near the Higgs pole or via AA with phase-space suppression, but stringent direct-detection bounds (e.g., LUX) strongly shape the allowed parameter space, making upcoming DM searches and LHC data decisive for testing the model.

Abstract

Extending the spacetime symmetries of standard model (SM) by scale invariance (SI) may address the Higgs naturalness problem. In this article we attempt to embed accidental dark matter (DM) into SISM, requiring that the symmetry protecting DM stability is accidental due to the model structure rather than imposed by hand. In this framework, if the light SM-like Higgs boson is the pseudo Goldstone boson of SI spontaneously breaking, we can even pine down the model, two-Higgs-doublets plus a real singlet: The singlet is the DM candidate and the extra Higgs doublet triggers electroweak symmetry breaking via the Coleman-Weinberg mechanism; Moreover, it dominates DM dynamics. We study spontaneously breaking of SI using the Gillard-Weinberg approach and find that the second doublet should acquire vacuum expectation value near the weak scale. Moreover, its components should acquire masses around 380 GeV except for a light CP-odd Higgs boson. Based on these features, we explore viable ways to achieve the correct relic density of DM, facing stringent constraints from direct detections of DM. For instance, DM annihilates into near the SM-like Higgs boson pole, or into a pair of CP-odd Higgs boson with mass above that pole.

Paper Structure

This paper contains 11 sections, 34 equations, 3 figures.

Table of Contents

  1. Introduction and motivation
  2. Classical Scale invariance and Higgs naturalness
  3. Classical Scale invariance and the hierarchy problem
  4. Classical SI anomaly and the origin of EW scale
  5. Accidental dark matter (aDM) by SI
  6. SISM with singlets: a toy model
  7. Pinning down aDM model
  8. Radiative EWSB via Gilard-Weinberg (GW) approach
  9. Saving the light accidental dark matter by a light $A$
  10. Conclusions
  11. Acknowledgements

Figures (3)

  • Figure 1: Given a smaller $\tan\beta$, DM direct detection bound (LUX, red line) allows for a heavier dark matter near 100 GeV in the $\Phi_1-$portal. The projected LUX-300 live days (black line) of WIMP search is able to fully cover the surviving parameter space.
  • Figure 2: Exclusion of the light aDM (green line) in the type-II 2HDM+$S$ on the $m_{S}(\rm GeV)-\sigma_{\rm SI}(\rm pb)$ plane. Constraints are from CDMSlite (black line), superCDMS (dashed orange line) and LUX (red line).
  • Figure 3: Scenario of forbidden annihilating channel $SS\rightarrow AA$. Left: Required $\eta_1$ for a given $m_A$; Right: The required mass degeneracy between $m_{\rm DM}$ and $m_A$.