Agentic Diagrammatica: Towards Autonomous Symbolic Computation in High Energy Physics

TL;DR

The paper introduces Diagrammatica, an extension enabling LLM agents to perform reliable symbolic calculations in high energy physics through tool-constrained computation and knowledge grounding.

Contribution

It presents a novel architecture combining symbolic computation tools with LLM agents for accurate theoretical calculations in physics.

Findings

Validated on decay width catalog and Standard Model checks.

Performed NDA sensitivity analysis for muon decay multiplicity.

Achieved reliable symbolic calculations with tool-constrained approach.

Abstract

We present Diagrammatica, a symbolic computation extension to the HEPTAPOD agentic framework, which enables LLM agents to plan and execute multi-step theoretical calculations. Symbolic computation poses a distinctive reliability challenge for LLM agents, as correctness is governed by implicit mathematical conventions that are not encoded in a form that can be easily checked in the computational backend. We identify two complementary remedies, tool-constrained computation and targeted knowledge grounding, and pursue the first as the primary architecture. Concretely, we concentrate the agent's action distribution onto tool calls with convention-fixing semantics, in which the agent specifies a compact, human-auditable diagram specification and a trusted backend performs the symbolic or numerical manipulations exactly. The toolkit provides two complementary calculation paths consuming a shared diagram specification: Naive Dimensional Analysis (NDA) for order-of-magnitude rate estimates and Exact Diagrammatic Analysis (EDA) for tree-level symbolic calculations via automatic FeynCalc code generation, both supplemented by automatic Feynman diagram enumeration and a navigable theory knowledge base. The architecture is validated on two benchmarks: (1) an exhaustive catalog of all tree-level, single-vertex $1\to 2$ partial decay widths across scalar, fermion, and vector parents, with complete massless and threshold limits and Standard Model validation; and (2) an NDA sensitivity study of the muon decay multiplicity $\mu^+ \to \nu_\mu\bar{\nu}_e + n(e^+e^-) + e^-$, determining the maximum observable $n$ at current and planned muon experiments.