[Paper Review] Scalar Dark Matter and Electroweak Stability

D. Demir, Cem Salih Ün|arXiv (Cornell University)|May 7, 2020

Particle physics theoretical and experimental studies30 references4 citations

TL;DR

This paper proposes a mechanism—mass-degeneracy-driven unification (MDDU)—wherein a real singlet scalar dark matter candidate stabilizes the electroweak scale by ensuring quartic couplings unify when the scalar and Higgs boson masses are degenerate. Simulations show this framework satisfies collider and astrophysical constraints, enabling a viable dark matter candidate with suppressed Higgs invisible decays and testable direct/indirect detection signals.

ABSTRACT

The standard model of elementary particles (SM), despite experimental completion at the LHC, needs to be extended for various physical reasons, including the cold dark matter (DM). Each extension comes with its scale and mechanism, and typically lifts, at the loop level, the electroweak scale towards its high scale. The problem is to keep the electroweak scale stable while providing a room for the aforementioned heavy extensions. To this end, it turns out that the SM Higgs sector remains stable in the presence of a heavy scalar if their quartic couplings unify at a certain scale when their masses are degenerate. Under this mass-degeneracy-driven unification (MDDU), the scalar under concern is found to qualify as a viable DM candidate and to leave the electroweak scale stable. Our detailed simulation studies explicitly show that the MDDU parameter space agrees with current collider and astrophysical bounds. Our work can be extended to other relevant scalars (like flavons, inflaton and others) as a mechanism by which the electroweak scale is held stable.

Motivation & Objective

• To resolve the electroweak hierarchy problem by stabilizing the Higgs boson mass against UV corrections from heavy BSM sectors.
• To identify a viable scalar dark matter candidate that remains consistent with current experimental bounds on relic density, direct detection, and invisible Higgs decays.
• To demonstrate that mass degeneracy between the Higgs and a real singlet scalar leads to quartic coupling unification, suppressing destabilizing loop corrections.
• To show that the MDDU mechanism allows for hierarchically small SM-BSM couplings, avoiding the need for fine-tuning or traditional BSM symmetries.
• To explore the phenomenological viability of the model through constraints from LHC, LUX-Zeplin, and Fermi-LAT experiments.

Proposed method

• Imposes mass degeneracy between the SM Higgs and a real singlet scalar S to trigger quartic coupling unification at a high scale.
• Uses dimensional regularization and ${\overline{\text{MS}}}$ renormalization to compute loop corrections to the Higgs mass, showing $\delta m_H^2 \propto \lambda_{HS} m_S^2 \log(m_S^2/Q^2)$.
• Applies the MDDU condition to enforce $\lambda_{HS} \to 0$ as $m_S \to \infty$, creating a seesaw-like suppression of Higgs mass shifts.
• Performs a blind scan over parameter space to identify regions consistent with the observed dark matter relic density.
• Evaluates direct detection cross-sections via spin-independent scattering on nuclei, focusing on $SS \to bb$, $\tau\tau$, $WW$, $ZZ$, $hh$, and $tt$ channels.
• Analyzes indirect detection signals through $SS \to bb$, $\tau\tau$, and $WW$ annihilation, comparing predicted rates to Fermi-LAT data and projections.

Experimental results

Research questions

• RQ1 Can the electroweak scale remain stable in the presence of a heavy scalar BSM sector without requiring fine-tuning?
• RQ2 Under what conditions does a real singlet scalar qualify as a viable dark matter candidate while preserving electroweak stability?
• RQ3 How do invisible Higgs decays into $SS$ constrain the $\lambda_{HS}$ coupling, and can MDDU naturally satisfy these bounds?
• RQ4 What are the direct and indirect detection signals of the scalar dark matter candidate, and are they testable in current or future experiments?
• RQ5 Can the MDDU mechanism be generalized to other scalar fields such as inflatons or flavons, and what are the implications for BSM physics?

Key findings

• The MDDU mechanism stabilizes the Higgs boson mass by ensuring that the Higgs-singlet coupling $\lambda_{HS}$ decreases with increasing $m_S$, effectively suppressing UV corrections.
• When $m_S = 50$, $80$, or $300$ GeV, the model produces viable dark matter relic density consistent with Planck data, particularly in resonance regions near $m_h/2$.
• The invisible branching ratio of the Higgs boson is naturally suppressed below 10% due to the MDDU condition, without requiring external constraints.
• Spin-independent direct detection cross-sections are predicted to lie slightly below the current LUX-Zeplin exclusion curve, making them testable in upcoming runs.
• Annihilation into $WW$ final states dominates at $m_S \gtrsim 80$ GeV, contributing about 80% to the total rate, and is expected to be probed in future Fermi-LAT upgrades.
• The $SS \to bb$ and $SS \to \tau\tau$ channels yield average cross-sections slightly below current Fermi-LAT exclusion limits, with future 15-year projections potentially testing these signals.