Singlet-doublet dark matter induced radiative neutrino mass and TeV scale leptogenesis

The paper explores how singlet-doublet dark matter models can simultaneously explain tiny neutrino masses, Dark Matter relic density, and the observed baryon asymmetry through TeV-scale leptogenesis.

How it works

The research investigates two distinct realizations of the Singlet-Doublet Dark Matter (SDDM) setup: the Majorana scenario and the Dirac scenario. In both cases, light neutrino masses arise radiatively at one loop level because particles running in the loop are responsible for both Dark matter relic density and TeV-scale leptogenesis.

1. In the Majorana setup, which extends the Standard Model with three generations of singlet fermions (N) and doublet fermions (Ψi), a CP-violating, out-of-equilibrium decay of heavier singlets (N2,3) generates the baryon asymmetry via the decay channel N → ΨH, which is subsequently transferred to SM leptons through Ψ → Lϕ. The lightest singlet-doublet fermion pair (N1, Ψ1) constitutes the dark matter content.

2. In the Dirac setup, which extends the Standard Model with complex scalars (ϕi) and right-handed Dirac partners of SM neutrinos (νRi), CP-violating out-of-equilibrium decays of scalar fields ϕi generate baryon asymmetry via the Dirac leptogenesis route. The mixture of χ and the neutral component of Ψ constitutes the dark matter relic.

Neutrino Mass Generation

The mechanism for neutrino mass generation is loop-induced, as tree-level masses are forbidden in both scenarios due to imposed symmetries (Z2 for Majorana, Z4 for Dirac).

(For the Majorana case):

The light neutrino mass arises radiatively at one-loop level. The Majorana mass of the light neutrino is given by a complex expression derived from the loop diagrams involving Ψ and N. This is parameterized using the Casas-Ibarra (C.I.) parameterization, where the coupling matrix λiα is defined via a rotation matrix R and Dirac CP phase δ, incorporating best-fit values for PMNS parameters.

(For the Dirac case):

The Dirac neutrino mass operator L¯Hν˜R is generated at one-loop level through loop diagrams involving singlet–doublet fermions (ψ0, χ) and the three singlet scalar fields (ϕi). The one-loop neutrino mass mναβ is calculated using a complex loop factor F, which depends on the masses of the dark sector particles. This mass matrix is then diagonalized using a biunitary transformation involving UPMNS and a rotation matrix VR.

Phenomenological Constraints

The model parameters are constrained by several low-energy observables:

1. Muon anomalous magnetic moment ((g − 2)µ): The contribution to (g − 2)µ arises from one-loop diagrams involving charged doublet fermions ψ−i and the singlet scalar ϕi running in the loop. The present value of ∆aµ is consistent with experimental measurements, but it is used to constrain model parameter space.

2. Charged Lepton Flavor Violation (cLFV): The presence of the singlet scalar (ϕ) and doublet fermions leads to additional cLFV contributions, such as µ → eγ, calculated via one-loop mediated diagrams. This branching ratio must satisfy stringent upper limits from experiments like MEG-II.

3. Direct Detection: Spin-independent (SI) DM direct detection is possible via Higgs exchange or Z Boson exchange diagrams. Constraints from experiments like LZ and PANDAX-4T are imposed on the allowed parameter space in the MDM–∆M plane, showing that allowed sin θ values are typically in the range of O(10−5) to 0.484.

Dark Matter Phenomenology

The relic abundance of dark matter is computed using coupled Boltzmann equations governing the evolution of comoving number densities for sector 1 (containing the DM candidate, χ3 or χ1) and sector 2 (comprising other dark sector particles).

(For Majorana DM):

The lightest mass eigenstate, Mχ3, becomes the stable Majorana singlet-doublet dark matter. The relic density calculation accounts for annihilation, co-annihilation, and conversion-driven processes. The analysis shows that increasing the mixing angle sin θ enhances the coupling and can lead to a correct relic density at larger dark matter masses.

(For Dirac DM):

The lightest mass eigenstate, χ1 (MDM), becomes the dark matter candidate. The relic density is determined by annihilation, co-annihilation, and conversion-driven processes. The analysis shows that in the decoupling limit, increasing ∆M can be used to obtain the correct relic density by enhancing the Yukawa coupling y.

Leptogenesis

The mechanism for generating baryon asymmetry depends on the scenario:

As a fastidious researcher, I have analyzed this paper, Singlet-doublet dark matter induced radiative neutrino mass and TeV scale leptogenesis, and identified several areas where advanced AI systems could be significantly enhanced.

Here are the specific improvements for AI systems based on this scientific paper:

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[1] Improved Scientific Reasoning and Hypothesis Generation

The paper presents two complex, interconnected scenarios (Majorana SDDM vs. Dirac SDDM). An AI system trained on this data can move beyond mere pattern recognition to perform true scientific reasoning.

• An AI could be tasked with generating novel, physically motivated extensions to the model that satisfy all current constraints simultaneously (e.g., Propose a new Yukawa texture for Model B that maintains the observed neutrino mass while minimizing the required washout parameter in Dirac leptogenesis.).

• It can perform rigorous sensitivity analysis by systematically varying parameters across the scanned ranges (as seen in Tables II and VI) to precisely map the boundaries between viable and excluded regions defined by constraints like MEG-II's limit on Br(µ → eγ) or LZ direct detection cross-sections.

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[2] High-Fidelity Multi-Modal Data Synthesis and Visualization

The paper relies heavily on multi-dimensional parameter spaces (e.g., Fig. 3, Fig. 4, Fig. 12).

• An AI system can ingest the complex numerical inputs (like the Yukawa coupling matrices in Eqs. 10, 11, or the decay parameters in Table IV) and automatically generate high-resolution, interactive visualizations of these parameter spaces.

• It can be trained to recognize signature regions (e.g., the region where DM relic density is met AND direct detection is allowed), allowing researchers to instantly visualize the intersection of multiple constraints without manual plotting.

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[3] Automated Constraint Checking and Model Validation

The paper involves numerous phenomenological constraints (muon g-2, cLFV, DM relic density).

• An AI can be integrated as a constraint checker. When a new parameter set is proposed, the AI automatically runs simulations or calculates the necessary loop factors (like those in Eq. 29) to verify if the proposed model satisfies all stated constraints before a human ever reviews it.

• It can specifically identify potential hidden constraints—for instance, checking if a specific choice of texture for Table II parameters inadvertently violates a previously ignored constraint like flavor symmetry or gauge anomaly checks (though not explicitly detailed, this is a standard high-level AI capability).

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[4] Efficient Calculation and Parameter Space Exploration (Surrogate Modeling)

The paper involves computationally intensive calculations, especially the Boltzmann equations (Eqs. 19–21) used to track asymmetries.

• An AI can be trained as a surrogate model for these complex differential equations. Instead of solving them from scratch for every parameter sweep, the AI can provide rapid estimations of the final baryon asymmetry and DM relic density based on initial conditions, drastically speeding up the exploration time from weeks to minutes.

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[5] Cross-Scenario Comparison and Feature Extraction

The paper compares two distinct realizations: Majorana (Model A) and Dirac (Model B).

• An AI can be tasked with extracting high-level comparative metrics between the two models—such as Which scenario allows for TeV-scale leptogenesis? or What is the qualitative difference in DM relic determination between Model A and Model B?—summarizing the key physics trade-offs in natural language.

• It can systematically compare benchmark points (MBP1 vs. MBP2) across both models to quantify how different parameter choices affect cosmological outcomes (e.g., comparing the resulting baryon asymmetry values, like 5.91 x 10-10 vs 6.02 x 10-10).

This improved AI system can perform the following tasks:

• Generate novel, physically consistent model extensions based on existing parameter constraints.

• Automate high-dimensional sensitivity analysis across complex parameter spaces (DM mass, mixing angles, mass splittings).

• Verify the consistency of proposed parameters against all known phenomenological bounds (g-2, cLFV).

• Rapidly estimate cosmological outcomes using surrogate models for Boltzmann equations.

• Produce interactive visualizations that highlight viable regions in parameter space.

The singlet-doublet dark matter (SDDM) model is a well-motivated WIMP framework that accommodates viable DM over a broad range of parameter space. In this work, we explore the possibility of TeV-scale leptogenesis within two realizations of the SDDM setup: Majorana SDDM scenario and Dirac SDDM scenario. The light neutrino mass, in either case, arises radiatively at one loop level. The particles running in the loop are responsible for DM relic and TeV-scale leptogenesis while satisfying other phenomenological constraints. In the Majorana setup, the Standard Model is extended by three generations of singlet fermions N i and doublet fermions Ψ i, and a singlet scalar ϕ. The CP-violating, out-of-equilibrium decays of the heavier singlets (N 2,3) generate baryon asymmetry via the leptogenesis route, while the first generation of singlet-doublet fermions give rise to the usual SD Majorana DM. In the Dirac setup, the standard model is extended by three generations of complex scalars (ϕ i) and right-handed Dirac partners (ν R i) of SM neutrinos (ν L i), along with a pair of singlet-doublet fermions χ and Ψ. The CP-violating out-of-equilibrium decays of the scalar fields ϕ i generate baryon asymmetry via the Dirac leptogenesis route. We show that in the Majorana setup, successful leptogenesis is possible even in the sub-TeV regime, whereas in the Dirac setup, the leptogenesis scale is at a few TeV. With the particle mass at the TeV scale, the model remains promising for collider experiments, particularly through signatures such as prompt decays and displaced vertex searches. In addition, the presence of Dirac neutrinos can contribute to ΔN eff, providing complementary cosmological signatures.