[Paper Review] Scale-Invariant Two Component Dark Matter

Seyed Yaser Ayazi, Ahmad Mohamadnejad|arXiv (Cornell University)|Aug 27, 2018

Dark Matter and Cosmic Phenomena27 references4 citations

TL;DR

This paper proposes a scale-invariant two-component dark matter model within a classically scale-invariant extension of the Standard Model, featuring a scalar and a spinor dark matter particle mediated by a scalon field. It demonstrates that the spinor component dominates the observed relic density, while constraints from direct detection, invisible Higgs decays, and self-interactions help rule out parts of the parameter space, offering a minimal framework with reduced free parameters.

ABSTRACT

We study a scale invariant extension of the standard model which can explain simultaneously dark matter and the hierarchy problem. In our set-up, we introduce a scalar and a spinor as two-component dark matter in addition to scalon field as a mediator. Interesting point about our model is that due to scale invariant conditions, compared to other two-component dark matter models, it has lower independent parameters. Possible astrophysical and laboratory signatures of two-component dark matter candidate are explored and it is shown that the most contribution of observed relic density of dark matter can be determined by spinor dark matter. Detectability of these dark matter particles is studied and the direct and invisible Higgs decay experiments are used to rule out part of the parameter space of the model. In addition, the dark matter self-interactions are considered and shown that their contribution saturate this constraint in the resonant regions.

Motivation & Objective

• To address the hierarchy problem and dark matter relic abundance within a single, minimal framework based on classical scale invariance.
• To propose a two-component dark matter scenario with a scalar and a spinor field, both odd under a Z₂ symmetry for stability.
• To reduce the number of independent parameters by enforcing scale invariance, enhancing model predictability.
• To explore astrophysical and laboratory constraints, including direct detection, invisible Higgs decays, and self-interactions.
• To determine the dominant contribution to the observed dark matter relic density and assess detectability across experimental probes.

Proposed method

• Introduce a scale-invariant extension of the Standard Model by removing the Higgs mass term and adding a scalar singlet (S), a spinor singlet (χ), and a scalon field (ϕ), all singlets under SM gauge symmetry.
• Implement a Z₂ symmetry under which S and χ are odd, ensuring stability of the lightest odd particles, while ϕ and all SM fields are even.
• Construct a renormalizable, scale-invariant potential involving Higgs, ϕ, S, and their interactions: λ_H(H†H)² + λ_ϕϕ⁴/4! + λ_sS⁴/4! + λ_ϕHϕ²H†H + λ_sH S²H†H + λ_ϕsϕ²S².
• Include a spinor sector with a Yukawa coupling: ℒ_spinor = χ̄(iγᵘ∂ᵤ - gϕ)χ, allowing χ to interact with the scalon field.
• Use the Coleman-Weinberg mechanism for radiative symmetry breaking, generating masses for all fields after electroweak symmetry breaking.
• Derive cross sections and decay rates for DM self-interactions and invisible Higgs decays using non-relativistic quantum field theory and propagator poles, including resonant contributions from heavy Higgs states H₁ and H₂.

Experimental results

Research questions

• RQ1 Can a scale-invariant two-component dark matter model simultaneously resolve the hierarchy problem and reproduce the observed dark matter relic density?
• RQ2 Which component—scalar or spinor—dominates the relic density in this model, and what determines its dominance?
• RQ3 How do direct detection experiments and invisible Higgs decay searches constrain the parameter space of the model?
• RQ4 What are the implications of DM self-interactions, particularly in resonant regions, for cosmological and astrophysical observations?
• RQ5 To what extent does scale invariance reduce the number of independent parameters compared to other two-component dark matter models?

Key findings

• The spinor dark matter component is the dominant contributor to the observed dark matter relic density, with the scalar component playing a subdominant role.
• The model's parameter space is significantly constrained by invisible Higgs decay searches, particularly for Higgs boson decays into DM pairs, ruling out large regions of the parameter space.
• Direct detection constraints are effective in excluding large portions of the parameter space, especially for the scalar DM component due to its coupling to the scalon.
• DM self-interactions are enhanced in resonant regions, and their cross sections saturate the upper bounds from cosmological observations, particularly for χχ → χχ and SS → SS processes.
• The model achieves a minimal number of independent parameters due to scale invariance, making it more predictive than non-scale-invariant two-component DM models.
• The self-interaction cross sections for Sχ → Sχ are sensitive to the momentum transfer and the presence of resonant Higgs states H₁ and H₂, with explicit formulas derived for all relevant processes.