Exploring Leptogenesis, WIMP Dark Matter, and Gravitational Waves in an extended Scalar Framework

Exploring extensions of type I seesaw framework with a scalar mediator connecting to a complex scalar dark field and right-handed neutrinos, this work correlates neutrino mass generation, leptogenesis, and dark matter by introducing an extended symmetry structure.

Model Framework and Symmetry

The model extends the type-I seesaw framework by incorporating a real scalar singlet field, denoted as Φ, which acts as a mediator between the neutrino sector and the dark sector. This interaction is primarily realized through a dimension-five effective operator, specifically involving the SM lepton isodoublet (lL), the Higgs (H), and right-handed neutrinos (Ni):

1. The conventional tree-level Yukawa interaction between SM leptons, Higgs, and RHNs remains absent due to the dark symmetry GD.

2. After Φ acquires a vacuum expectation value (VEV), this higher dimensional operator effectively generates the standard neutrino Yukawa interaction, serving as the primary source of neutrino mass generation via the type-I seesaw mechanism.

3. The model is invariant under a generic discrete dark symmetry GD, such as Z4 × CP, which prohibits the canonical Yukawa term and requires spontaneous breaking via the VEV of Φ to activate leptogenesis and neutrino mass generation.

Dark Matter Stability and Phenomenology

The dark sector is introduced via a complex scalar field S, one component of which acts as the viable WIMP dark matter candidate. The stability of this DM candidate is contingent upon the imposed symmetry structure:

1. The initial symmetry GD is spontaneously broken by the VEV of Φ, which also induces a VEV to S.

2. To ensure the stability of one component of S, an additional CP symmetry must be imposed, leading to a viable choice of GD ≡ Z4 × CP or Z2 × Z′2 × CP.

3. The presence of the term µϕSΦ(S2 + S∗2) in the scalar potential allows one component of S to acquire an induced VEV (vs), while the other component remains stable due to the imposed CP symmetry, rendering it a viable DM candidate.

Leptogenesis and Baryogenesis

The mechanism for generating the baryon asymmetry relies on processes activated only after the spontaneous breaking of GD:

1. Leptogenesis is enriched through right-handed neutrino decay at a high enough scale with additional features, and scattering processes involving NΦ are also included.

2. The CP asymmetry parameters, εDi (from decay) and εSi (from scattering), arise only after the spontaneous breaking of the Z4 symmetry, requiring interference between tree-level and loop-level diagrams involving the NlH vertex generated by Φ's VEV.

3. The lepton asymmetry is converted into a baryon asymmetry via non-perturbative sphaleron transitions. The required scale for successful leptogenesis necessitates a minimum VEV for Φ, specifically vϕ ≥ 109 GeV to reproduce the observed baryon asymmetry of the universe.

Gravitational Wave Signatures

The spontaneous breaking of the discrete symmetry creates sheet-like two-dimensional topological defects known as domain walls (DW), which pose a cosmological problem if they are not annihilated:

1. The energy density of DWs scales as ρDW ∝ t−1, contrasting with radiation energy density scaling, leading to a tension between standard cosmology and DW evolution.

2. This tension is resolved by introducing a small, explicitly symmetry-breaking term to the Lagrangian, which lifts the vacuum degeneracy and makes the DW network unstable, allowing for their annihilation before the over-closure of the universe.

3. The annihilation of these domain walls produces a stochastic gravitational wave background (GW), potentially detectable by current and future detectors like LISA or BBO, with peak amplitude and frequency dependent on parameters such as vϕ and vs.

Dark Matter Relic Abundance

The relic density of the scalar DM candidate (s1) is determined by its thermal production mechanism after electroweak symmetry breaking:

1. The effective annihilation cross-section, ⟨σv⟩ef f, is obtained by summing over all possible final states, including SM particles and other model scalars (ϕ, H, s2).

2. The relic density depends on the triple scalar couplings (e.g., λs1s1h), which exhibit distinct dependencies on the induced VEV of S (vs): When vs is large, the contribution to the couplings are directly proportional to vs, whereas when vs is small, the effect comes from inverse dependence.

3. The analysis reveals two distinct scenarios having respective allowed regions of the parameter spaces where the DM relic density exhibits different (opposite) dependence on the induced VEV of S (vs).

Direct Detection Prospects

Direct detection experiments probe DM through spin-independent (SI) scattering with nucleons or electrons:

1. Relevant interactions for SI scattering are mediated by t-channel exchange of three scalar particles: h, ϕ, and s2.

As a fastidious and diligent researcher, I have analyzed this paper, Exploring Leptogenesis, WIMP Dark Matter, and Gravitational Waves in an extended Scalar Framework, which proposes a unified model connecting neutrino mass generation (Type-I seesaw), baryogenesis (leptogenesis), dark matter (WIMP/scalar DM), and gravitational waves (from domain wall annihilation) via a discrete symmetry breaking mechanism.

The key takeaway is the development of a complex scalar Dark Matter candidate with two distinct relic abundance scenarios depending on the induced VEV of the mediator field, and its connection to observable gravitational wave signals.

Here are specific improvements for AI systems based on this research:

1. Acknowledge and Integrate Multi-Scale, Interconnected Physics Modeling

2. Implement Constraint-Driven Parameter Space Exploration (Synergy)

3. Develop Predictive Modeling for High-Energy/Low-Energy Signatures (Phenomenology)

4. Enhance Topological Defect Detection Algorithms (GW Signal Analysis)

Specific Improvements and Capabilities:

1. Acknowledge and Integrate Multi-Scale, Interconnected Physics Modeling

The AI system should be upgraded to handle models where physics operates across vastly different energy scales (e.g., electroweak scale vs. GUT scale vs. Planck scale).

The improved system can:

• Simultaneously model the thermal history of the early universe (leptogenesis temperature, domain wall domination time) alongside late-time cosmological evolution (relic dark matter freeze-out).

• Understand how a high-scale feature (like the VEV of a mediator field, e.g., 109 GeV for leptogenesis) constrains parameters at much lower scales (e.g., the required coupling strength for DM relic abundance).

2. Implement Constraint-Driven Parameter Space Exploration (Synergy)

The AI should move beyond simple Monte Carlo sampling to a hierarchical, constraint-driven search strategy that prioritizes regions where multiple physical constraints are simultaneously satisfied.

The improved system can:

• Perform multi-objective optimization to find parameter sets that satisfy the tight constraints from: (a) observed neutrino masses/mixing angles, (b) the baryon asymmetry of the Universe, and (c) current WIMP direct detection upper bounds.

• Specifically identify the viable parameter space discussed in Section 6.1 and 6.2 by mapping how varying parameters like the induced VEV of S or mixing angles affect relic density and direct detection cross-sections simultaneously, rather than testing them in isolation.

3. Develop Predictive Modeling for High-Energy/Low-Energy Signatures (Phenomenology)

The AI should be enhanced with specialized modules capable of translating theoretical couplings into observable signatures across different experimental domains (particle physics, cosmology, GW astronomy).

The improved system can:

• Predict the specific characteristics of the gravitational wave spectrum (peak frequency and amplitude, Eqs. 7.4 and 7.5) based on the chosen symmetry breaking scale and coupling strengths, allowing for targeted searches in experiments like LISA or DECIGO/BBO.

• Determine if a model configuration leads to a detectable stochastic GW background, as opposed to one that is excluded by BBN constraints (Fig. 10).

4. Enhance Topological Defect Detection Algorithms (GW Signal Analysis)

The AI needs specialized algorithms tailored for detecting non-Gaussian, stochastic signals characteristic of cosmological topological defects (domain walls).

The improved system can:

• Analyze the broken power law GW spectrum (Eq. 7.6) to predict the spectral shape and width, allowing it to distinguish between different symmetry breaking scenarios based on expected observational signatures in frequency bands probed by SKA or LISA.

• Assess the impact of soft Z4 breaking terms (Eq. 7.1, 7.2) on the final GW signal, determining if the domain walls collapse before overclosing the universe and thus producing a detectable signal within current constraints like those from BBN (Fig. 10).