Enterprise AI Analysis
Exploring Scotogenic Parameter Spaces and Mapping Uncharted Dark Matter Phenomenology with Multi-objective Search Algorithms
Authors: Fernando Abreu de Souza, Nuno Filipe Castro, Miguel Crispim Romão, Werner Porod
Abstract: We present a novel artificial intelligence approach to explore beyond Standard Model parameter spaces by leveraging a multi-objective optimisation algorithm. We apply this methodology to a non-minimal scotogenic model which is constrained by Higgs mass, anomalous magnetic moment of the muon, dark matter relic density, dark matter direct detection, neutrino masses and mixing, and lepton flavour violating processes. Our results successfully expand on the phenomenological realisations presented in previous work.
Executive Impact & AI-Driven Advantages
This research leverages cutting-edge AI optimization to accelerate the discovery of new physics, offering a robust framework for complex, high-dimensional parameter space exploration. Our methodology significantly enhances the efficiency and diversity of viable solution identification in Beyond Standard Model theories, critical for enterprise-scale scientific computing and strategic R&D.
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CMA-ES Convergence Improvement
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h-NSGA-III Successful Runs
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Max Parameter Dimensions Explored
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Pseudoscalar DM Discovery
Deep Analysis & Enterprise Applications
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The Scotogenic Model & Core Constraints
The scotogenic model extends the Standard Model with a scalar SU(2)L doublet (η) and three neutral fermions (Ψ1, Ψ2, F1, F2), plus a real singlet (S). All new states are odd under a postulated Z2 symmetry, ensuring a stable Dark Matter (DM) candidate and generating neutrino masses at the one-loop level.
Beyond Standard Model States:
| Field | SU(2)L | U(1)Y | Z2 Parity |
|---|---|---|---|
| Ψ1, Ψ2 | 2 | -1 | Odd |
| F1, F2 | 1 | 0 | Odd |
| η | 2 | 1 | Odd |
| S | 1 | 0 | Odd |
Key constraints driving our search include: Higgs mass, the anomalous magnetic moment of the muon (aμBSM), dark matter relic density (ΩDMh²), direct detection limits from LZ experiments, neutrino masses and mixing, and upper limits on lepton flavour violating (LFV) processes (e.g., μ → eγ).
AI-Driven Search Algorithms & Strategies
Our methodology employs black-box optimization, reframing the search for viable parameter space as a minimization problem for a constraint function C(O). We compared two state-of-the-art algorithms:
| Algorithm | Approach | Strengths | Weaknesses | Performance (with Hierarchy) |
|---|---|---|---|---|
| CMA-ES (Single-Objective) | Minimizes a single aggregated cost function C(θ) = ΣC(Ok). |
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Convergence rate improved from 10% to 40% with hierarchical constraints. |
| NSGA-III (Multi-Objective) | Optimizes multiple objectives (C(O1), C(O2), ...) simultaneously, generating a Pareto front. |
|
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Successful runs at ~50% with hierarchical constraints, significantly more efficient overall. |
To overcome tensions between constraints (e.g., aμBSM vs. LFV), we introduced Hierarchical Constraints, forcing the algorithms to satisfy critical constraints first. Additionally, Novelty Detection was integrated with CMA-ES to reward exploration of sparsely populated regions, enhancing the discovery of new phenomenological realisations.
Key Results: Novel Dark Matter Discoveries
Our AI-driven scans significantly expanded the known viable parameter space, revealing novel Dark Matter phenomenology:
- Fermionic DM Dominance: Fermionic DM (χ0) remains the most frequent candidate, found in ~90.6% (non-CI) and ~86.2% (CI) of valid points.
- DM Mass Ranges: Heavy fermionic DM (~1100 GeV without CI, ~250 GeV with CI) was frequently found. Scalar DM (Φ0) shows no strong mass preference but often lies between 500-1000 GeV.
- Novel Pseudoscalar DM: For the first time, a pseudoscalar DM candidate (A0) was discovered, albeit in a small fraction (0.001%) of solutions, with a mass around 1.2 TeV.
- Diverse DM Mixing: We identified scenarios with high mixing between singlet and doublet states for fermionic DM, offering new implications for DM annihilation.
- Expanded Direct Detection Landscape: Novelty detection allowed us to map fermionic DM spin-independent cross-sections between the LZ experimental upper bound and the neutrino floor, a region previously unexplored in this model.
Pseudoscalar DM
A novel Dark Matter candidate identified through AI exploration.
LHC Phenomenology & Future Search Potential
The discovered phenomenological realisations present diverse implications for LHC searches:
- Fermionic DM Production: Main production channels are Drell-Yan processes via the SU(2)L components of the new fermions. Cross-sections can be substantial; for MΨ = 800 GeV, total cross section is ~4.26 fb at 13.6 TeV.
- Doublet-like Fermionic DM: Small mass splitting leads to soft decay products (e.g., χ+ → π+χ0), making detection challenging, similar to higgsino dark matter.
- Singlet-like Fermionic DM:
- Heavy DM (>700 GeV): Mass differences to charged fermions can range from a few GeV to 200 GeV, leading to decays into off-shell W/Z bosons or via neutral scalars (e.g., χ+ → lνχ0, χ0 → hχ0).
- Light DM (<500 GeV): Phenomenology depends on whether additional scalars are heavier or lighter than doublet-like fermions, involving various decay chains (e.g., χ+ → η+ν, χ+ → Φ0l+).
- Pseudoscalar DM at LHC: With masses generally above 500 GeV and smaller cross-sections than fermionic DM, these scenarios are typically not sensitive to current LHC searches. However, scenarios involving long-lived charged particles might be discoverable in future searches.
Our findings suggest the need for reinterpretation of existing LHC analyses, especially for regions of parameter space with high mixing and specific mass splittings, to fully probe these novel DM realisations.
Enterprise Process Flow
Define Parameter Space
→
Formulate Constraint Function C(O)
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Apply AI Optimisation (CMA-ES/NSGA-III)
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Introduce Hierarchical Constraints
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Leverage Novelty Detection
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Discover New Phenomenology
Case Study: Mitigating Constraint Tension with Hierarchical Optimization
A significant challenge in exploring the scotogenic model is the inherent tension between explaining the muon's anomalous magnetic moment (aμBSM), fitting neutrino data, and adhering to strict lepton flavour violation (LFV) bounds. Standard optimization methods often get stuck in local minima, failing to satisfy all critical constraints simultaneously.
Our solution: the Hierarchical Constraint Methodology. By explicitly prioritizing the aμBSM constraint and setting other constraints to a "numerical infinity" until aμBSM is met, we guided the algorithms out of these local traps. This strategy drastically improved the convergence rate and allowed for the discovery of previously overlooked phenomenological regions. While recent updates to the SM prediction for muon g-2 [68] somewhat mitigate this specific tension, our hierarchical approach remains a powerful, generalizable tool for any BSM model facing conflicting, high-dimensional constraints.
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Your AI Implementation Roadmap
A typical phased approach to integrating advanced AI optimization into your enterprise R&D, tailored for maximum impact and minimal disruption.
Phase 1: Discovery & Strategy
Initial consultation to understand your current R&D challenges, existing computational infrastructure, and specific objectives. Define key performance indicators (KPIs) and tailor an AI strategy document.
Phase 2: Data & Model Integration
Work with your teams to integrate your complex scientific models and data into our AI optimization framework. This includes defining parameter spaces, constraints, and objective functions.
Phase 3: AI Algorithm Deployment & Customization
Deploy and fine-tune multi-objective and hierarchical optimization algorithms (like NSGA-III and h-CMA-ES) on your specific problems. Implement novelty detection to ensure comprehensive exploration.
Phase 4: Validation & Iteration
Validate AI-generated solutions against experimental data or simulations. Establish iterative feedback loops to continuously improve algorithm performance and model accuracy, driving faster discovery cycles.
Phase 5: Knowledge Transfer & Scaling
Train your internal teams on AI methodology and tools. Develop a roadmap for scaling AI optimization across multiple research projects and departments, establishing an internal AI R&D center of excellence.
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