Large Language Model-Assisted Framework for BSM Model Building

Abstract: Recent advances in AI, particularly LLMs, have created new opportunities for natural-language interaction with scientific software, but reliable theoretical model building still requires deterministic symbolic calculations. We present \texttt{bsm_agent}, an open-source symbolic framework for beyond the Standard Model (BSM) model building that combines a deterministic physics backend with an LLM chat interface. Starting from the SM field content and a user-specified set of additional scalars and/or fermions, the package constructs renormalizable Lagrangian, performs gauge-anomaly checks, expands operators into component fields, and derives electroweak symmetry breaking stationary conditions and tree-level mass matrices. The key novelty of the framework is that all of these tasks are performed automatically once the user specifies the quantum numbers of the new fields through a natural-language interface, eliminating the need for manual model construction. The symbolic calculations are performed entirely by the Python backend to ensure the correctness and reproducibility of the physics results; the LLM is used only as an orchestration layer that interprets natural-language requests, manages confirmation steps for ambiguous inputs, triggers backend tools, and formats report-ready summaries. The package supports three provider classes: local Ollama inference, remote self-hosted model servers accessed through the implemented remote provider interface, and commercial hosted APIs via OpenAI and Anthropic. This separation between conversational control and deterministic computation preserves reproducibility while making interactive BSM model construction substantially more convenient.

• The paper presents a framework that automates BSM model building by integrating a deterministic symbolic backend with an LLM-driven interface.
• It systematically generates gauge-invariant operators, performs anomaly checks, and calculates mass matrices to streamline complex model prototyping.
• The study demonstrates practical, reproducible methods for constructing and expanding BSM models, enhancing accessibility for research and education.

LLM-Assisted Framework for BSM Model Building: Technical Review

Motivation and Context

The framework "bsm_agent" (2606.21316) addresses the computational and practical bottlenecks in constructing particle physics models beyond the Standard Model (BSM). Traditional BSM extension workflows require manual enumeration of gauge-invariant operators, anomaly checks, Lagrangian derivations, and mass matrix computations; the complexity and prevalence of higher representations make this process error-prone and inefficient. By integrating a deterministic symbolic backend with a LLM-controlled interface, the package aims to provide model-building rigor and reproducibility, while reducing technical barriers and increasing accessibility for both pedagogical and research applications.

System Architecture

Modular Design

The framework employs a layered architecture:

• Field/group layer: Encodes the Standard Model content and user-defined extensions via explicit SU(3), SU(2), and U(1) quantum numbers. Supports scalars and Weyl fermions with a broad set of representations, constrained primarily by computational scaling.
• Model-construction layer: Automates derivation of the complete set of renormalizable (dimension ≤ 4) gauge-invariant operators for specified field content, focusing on non-supersymmetric extensions within the SM gauge group.
• Expansion layer: Translates compact operator notation into explicit component-field expressions via group-theoretic contraction algorithms.
• EWSB/mass-matrix layer: Implements vacuum expectation value (VEV) shifts for all neutral scalar components and performs symbolic stationary conditions and mass matrix extraction.
• Report layer: Outputs both compact and expanded LaTeX representations suitable for further analysis or documentation.
• Agent layer: Orchestration layer managed by an LLM, responsible for interpreting natural-language requests, confirming ambiguous inputs, and calling deterministic tools.

LLM Integration

Critically, the LLM fulfills an interface-only role; it never generates operators or computes physical quantities. It translates user queries, triggers backend computations, manages conversational state, and formats results. This strict separation preserves the reproducibility and determinism demanded in physics workflows.

• Supported LLM backends: Local (e.g., Ollama models), remote self-hosted, and commercial APIs (OpenAI, Anthropic) are supported with backend-agnostic orchestration.
• Interaction workflow: Confirmation steps mitigate misinterpretation of field quantum numbers or types, a vital safeguard against invalid model definition.

Symbolic Algorithmic Details

Operator Generation and Representation Handling

• Field definitions: Users specify fields by name, nature (scalar/fermion), SU(3), SU(2), U(1) assignments, and reality. Deduplication and canonical ordering ensure stability.
• Operator basis: The generator exhaustively enumerates all renormalizable invariants (up to quartic scalar terms, fermion masses, and Yukawa couplings), deduplicates Hermitian conjugates, and indexes multiple contraction possibilities.
• Supported representations: SU(2): up to septuplet scalars; SU(3): up to octet fields; computational scaling mitigated by specialized optimizations for common multiplet and contraction structures.
• Anomaly checks: Automated calculation of the five standard anomaly coefficients (SU(3)$^3$, SU(2)$^2$U(1), SU(3)$^2$U(1), Gravity-U(1), U(1)$^3$) is performed, with suggestions for conjugate fields where necessary.

Expansion and EWSB

• Component field expansion: Employs explicit Clebsch–Gordan and color-singlet basis construction to contract operator tensors, yielding explicit component expressions; basis, normalization, and phase conventions are made explicit, aiding cross-package comparisons.
• VEV insertion and mass matrix computation: All neutral scalar components receive VEVs, stationary conditions are computed symbolically, and tree-level mass matrices for scalars and fermions are automatically derived in real/complex basis conventions.

Computational Performance

Construction and expansion times scale with tensor-product space size; large multiplets (e.g., color octets, electroweak septuplets) are computationally intensive, but representation-aware optimizations and canonical pruning ensure tractability for most phenomenologically relevant scenarios.

User Workflow and Practical Features

Natural Language-Driven Model Construction

The user operates via a conversational interface, specifying models and extensions through plain language. The workflow supports incremental model building, modification, and deletion, with real-time feedback, summary, and validation at each stage.

• Incremental extension: Fields can be added sequentially to an existing model context.
• Ambiguity resolution: Automated queries resolve missing field details (e.g., scalar vs. fermion, real vs. complex).
• Export: Compact and fully expanded LaTeX/PDF reports are generated, structured by sector and conventions.

Complex Model Case Studies

Detailed examples include automated construction and full expansion of leptoquark models comprising multiple scalars with non-trivial representations. The framework identifies more than 100 independent Lagrangian terms, expands all operator classes, and computes mass matrices, all within seconds to minutes. Explicit mappings between the package conventions and external references are provided to facilitate interoperability and validation.

Basis and Convention Mapping

Expanded representations are fully documented by basis choice and normalization. Off-diagonal operator duplication is suppressed; cross-comparison with user-defined conventions is enabled through linear mapping of index sets and phase definitions.

Implications and Outlook

Practical Impact

The framework streamlines the pre-implementation stage of BSM modeling. Users are relieved from enumerating gauge invariants, anomaly checks, and symbolic expansion, with deterministic outputs that are directly usable in subsequent phenomenological or simulation workflows (e.g., FeynRules/SARAH compatibility). This paradigm is particularly effective for rapid prototyping and educational contexts, as well as for researchers requiring reproducible, extensible, and transparent model definitions.

Integration with AI for Science

The strict role separation for LLMs demonstrates a scientifically robust template for agentic AI integration in computational physics. By maintaining determinism, traceability, and modularity, it establishes a functional blueprint for advancing agent-driven scientific workflows without sacrificing rigor. Such designs are increasingly found in high-energy physics agentic packages (Plehn et al., 28 Jan 2026, Moreno et al., 20 Mar 2026, Faroughy et al., 13 May 2026, Agrawal et al., 23 Mar 2026, Wang, 17 Jun 2026).

Future Directions

Further development targets inclusion of higher SU(2)/SU(3) representations, support for extended gauge structures (Pati–Salam, SU(5), SO(10)), discrete and global symmetries, supersymmetry, and higher-dimensional operators. Automation of downstream phenomenological analysis is a logical extension. The paradigmatic separation between conversational orchestration and deterministic computation is likely to be adopted in broader agentic scientific software.

Conclusion

"bsm_agent" systematically automates the symbolic construction of renormalizable BSM models from natural-language field specifications, retaining reproducibility and rigor through deterministic computation while leveraging LLMs as orchestration layers. Explicit conventions, comprehensive operator generation, anomaly validation, expansion, and mass matrix extraction are performed algorithmically, enabling efficient exploration of complex BSM extensions. The framework is poised for significant utility in both pedagogical and research contexts and sets a rigorous standard for agent-assisted scientific modeling in high-energy physics.