Cosmological Bounds on Scotogenic Model with Asymmetric Mediator

We study cosmological constraints on the asymmetric mediator scenario, a variant of the scotogenic model that addresses the origins of neutrino masses, dark matter (DM), and the baryon asymmetry. An SU(2)$_L$ doublet scalar $η$ mediates between the visible and dark sectors, while a singlet scalar $σ$ serves as the DM candidate. We evaluate the DM relic abundance by solving the Boltzmann equations including $η$ decay and scattering processes prior to the freeze-out of the $η$ asymmetry, and show Big Bang nucleosynthesis constraints from late-time $η$ decays. Combining the DM abundance and BBN bounds, we find the favored parameter space of this model, for instance, the mediator masses of $m_η\lesssim \mathcal{O}(10)$ TeV.

💡 Research Summary

The paper investigates cosmological constraints on an extended scotogenic model that incorporates an “asymmetric mediator” η (an SU(2)ₗ doublet scalar) and a singlet scalar σ, which serves as the dark‑matter (DM) candidate. The model is built on the usual scotogenic framework with three Z₂‑odd right‑handed neutrinos Nᵢ, but adds a Z₂‑odd inert doublet η and a Z₂‑odd real singlet σ. The key idea is that CP‑violating decays of the heavy Majorana neutrinos generate simultaneously a lepton asymmetry n_ΔL and an η‑asymmetry n_Δη, with n_ΔL = n_Δη at the moment of generation. The η‑asymmetry is then transferred to the DM sector when η (and its antiparticle η*) annihilate via gauge interactions, depleting the symmetric component, and the remaining asymmetric η (or η*) later decays into σ plus Standard Model particles. Consequently the DM number density n_σ equals the original lepton asymmetry, automatically linking the observed DM abundance to the baryon asymmetry.

The authors perform a thorough quantitative analysis of this scenario. First, they write down the full Lagrangian, including the Yukawa term h_{αi} ℓ_α ˜η N_i, the Majorana mass term for N_i, and the scalar potential V(H, η, σ) containing mass parameters μ_H², μ_η², μ_σ², quartic couplings λ_i (i = 1…8) and a trilinear coupling μ (η† H)σ. They assume λ₆, λ₇ ≪ 1 to evade direct‑detection limits and keep σ out of thermal equilibrium, while λ₈ must be tiny (≲ 3.9 × 10⁻⁸ (m_η/GeV)) so that the wash‑out process η η ↔ HH remains slower than the Hubble expansion at all relevant temperatures. The mixing between the CP‑even component of η and σ is suppressed by taking μ ≪ v, leading to a DM mass m_σ≈1.784 GeV fixed by the measured ratio Ω_DM/Ω_B.

A central part of the work is the solution of coupled Boltzmann equations for the yields Y_η and Y_σ. The authors include all relevant decay channels of η⁺⁻ (η⁺⁻ → η⁰ W⁺⁻, η⁰ π⁺⁻, ℓ⁺ ν η⁰, σ W⁺⁻) and of the neutral components (η⁰_R → σ h, η⁰_I → σ Z). They also incorporate the dominant scattering processes: η η* ↔ GG′ (gauge boson pairs), η⁺ ℓ⁻ ↔ η⁰ ν, and top‑quark mediated η t ↔ σ t. Thermal averages of the cross sections are computed (details in Appendices). The Boltzmann system tracks the depletion of the symmetric η η* component, the survival of the asymmetric part, and the eventual production of σ from η decays.

The lifetime of the charged scalar η⁺⁻ is a crucial observable because late decays can disrupt Big Bang Nucleosynthesis (BBN). The authors plot τ(η⁺⁻) as a function of the mass splitting δm_η ≡ m_{η⁺} − m_{η⁰}. For δm_η ≥ 10 MeV, the two‑body decay η⁺⁻ → η⁰ W⁺⁻ dominates, giving τ ≲ 0.01 s, well before the onset of BBN, so no constraint arises. However, for δm_η < 10 MeV the three‑body decay η⁺⁻ → σ W⁺⁻ (controlled by the trilinear coupling μ) becomes dominant. With a benchmark μ = 10⁻⁹ GeV, τ falls in the range 0.1–1 s, which would inject energetic particles during or after BBN and alter the neutron‑to‑proton ratio or destroy light nuclei. Therefore, the parameter region with small δm_η requires either a larger μ (to shorten the lifetime) or a larger δm_η (to open the faster gauge‑mediated channel).

The relic‑density analysis shows that the η mass cannot be arbitrarily large. As m_η grows, the annihilation cross section ⟨σv⟩ ∝ 1/m_η² drops, leaving a larger asymmetric component that overproduces DM after η decays. By scanning the parameter space, the authors find that mediator masses up to O(10) TeV are compatible with both the observed DM abundance and BBN constraints, provided the mass splitting satisfies δm_η ≲ 10 MeV and the trilinear coupling lies around μ ≈ 10⁻⁹ GeV. This region also respects collider bounds: the charged component behaves like a long‑lived slepton, and LHC searches for heavy charged tracks set a lower bound m_{η⁺} ≳ 660 GeV, which the authors adopt as a minimal value in their analysis.

In summary, the paper demonstrates that the asymmetric‑mediator scotogenic model can simultaneously explain neutrino masses, the baryon asymmetry, and the dark‑matter relic density, while remaining consistent with BBN, collider limits, and direct‑detection constraints. The viable parameter space is characterized by (i) mediator masses m_η ≲ 10 TeV, (ii) a small mass splitting δm_η ≲ 10 MeV, and (iii) a modest trilinear coupling μ ≈ 10⁻⁹ GeV. The authors suggest that upcoming LHC searches for long‑lived charged scalars and future low‑threshold direct‑detection experiments could probe this region, offering a concrete pathway to test the model.