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LaMET-Agent: An Agent Framework for Large-Momentum Effective Theory Analysis

Jinchen He, Xiangyu Jiang, Fei Yao, Dian-Jun Zhao

arXiv:2609.32225v1hep-latcs.AIhep-ph

TL;DR

LaMET analysis is a mature but demanding multi-stage process that still relies on expert judgment and repeated implementation. lamet-agent organizes that work into an executable, inspectable pipeline, and its four end-to-end analyses reproduce published results. The present release focuses on collinear quark distributions.

  • Problem

    LaMET analyses require expert judgment and repeated implementation across stages, limiting efficiency, reproducibility, and broader adoption.

    Source: §I · p. 2

  • Method

    lamet-agent formalizes LaMET analysis as a manifest-declared workflow with bounded, validated LLM decisions and deterministic numerical tools.

    Source: §I · p. 2

  • Results

    Four representative analyses reproduce published results across two observables, two operator constructions, two renormalization schemes, and both single-ensemble and extrapolated workflows.

    Source: §V · p. 13

  • Takeaways & Limitations

    The present studies validate execution of expert-specified workflows across a broad range of LaMET analyses.

    Source: §V · p. 13

    The present release supports collinear quark distributions; TMDs, GPDs, and gluonic distributions are planned for subsequent releases.

    Source: §I · p. 3

Abstract

from arXiv · show

Large-momentum effective theory (LaMET) provides a first-principles framework for computing the $x$ dependence of light-cone parton distributions from lattice QCD. Over the past decade, theoretical and numerical advances have established a mature multi-stage workflow for systematic calculation of parton physics, although its implementation still requires expert judgment and substantial repeated effort. We present lamet-agent, an open-source large language model (LLM) agent framework that organizes this workflow into an executable, reproducible, and inspectable analysis pipeline. The present release supports collinear quark distributions and implements correlator analysis, renormalization, Fourier transformation, perturbative matching, continuum, physical pion mass and infinite-momentum extrapolations, and automated result review. We validate it on four end-to-end analyses: pion parton distribution functions in the gauge-invariant and Coulomb-gauge formulations, and pion and kaon distribution amplitudes, obtaining results consistent with the published calculations. Extensions to transverse-momentum-dependent distributions, generalized transverse-momentum-dependent distributions, and gluonic distribution functions are planned for subsequent releases.

I. INTRODUCTION

LaMET offers a first-principles route from lattice correlators to light-cone parton distributions, but its multi-stage analysis still depends on expert judgment and repeated implementation. lamet-agent packages domain practice as an inspectable workflow and validates it through four end-to-end analyses.

I. INTRODUCTION

  • LaMET relates finite, large-momentum spatial correlators to light-cone distributions through perturbative matching and a systematic large-momentum expansion.In the moderate-x region where these expansions are controlled, it permits a systematically improvable point-by-point determination.Source: §I · p. 1
  • Precision controls for renormalization, matching, resummation, and power corrections make LaMET mature enough for an executable workflow, while adding complexity.The conventional gauge-invariant construction uses Wilson lines with linear divergences; Coulomb-gauge quasi-observables avoid them and improve signal-to-noise ratio, especially at large transverse separation.Source: §I · pp. 1–2
  • LaMET analysis requires expert choices, including correlator fit windows, excited-state counts, model averaging, and extrapolation ansätze, alongside deterministic operations.This reliance on expert intervention and repeated implementation limits efficiency, reproducibility, and broader adoption.Source: §I · p. 2
  • The framework targets expert practice that is sparsely represented in public training corpora, rather than relying on general-model reasoning alone.The design principles call for balancing LLM agency with deterministic tools, end-to-end validation, transparent artifacts, extensibility, and researcher control over scientific judgments.Source: §I · p. 2
  • lamet-agent formalizes LaMET knowledge as an auditable workflow: a manifest defines stage jobs, while bounded LLM decisions are validated before use.Numerical evaluations are deterministic, and intermediate artifacts and reports preserve provenance independently of the agent.Source: §I · pp. 2–3
  • Four end-to-end analyses reproduce published results across pion PDFs in two formulations and pion and kaon DAs.The framework's scope includes correlator analysis, renormalization, Fourier transformation, perturbative matching, extrapolations, and automated result review.Source: §I · p. 3

II. LAMET ANALYSIS WORKFLOW

LaMET transforms Euclidean lattice correlators into light-cone parton observables through distinct analysis stages. Deterministic numerical operations are interleaved with data-dependent choices that require expert judgment.

Workflow overview

  • The workflow separates deterministic numerical operations from dataset-dependent decisions such as fit windows, model choices, and extrapolation ansätze.Researchers iteratively inspect fit diagnostics and revise choices because no universal default suits every dataset.Source: §II · p. 3

Correlator analysis

  • Ground-state matrix elements are extracted from two- and three-point correlators using ratio, Feynman–Hellmann, or combined analyses.Analysts select fit windows and excited-state counts, and may compare models through model averaging; Lanczos offers an alternative with its own truncation and stability choices.Source: §II · p. 3

Renormalization

  • Renormalization removes ultraviolet regulator dependence, with RI/MOM and ratio prescriptions determining the subtraction differently.Hybrid renormalization uses the ratio at short distances and explicit Wilson-line power-divergence subtraction at large distances; fit choices and switching distance affect the result.Source: §II · pp. 3–4

Fourier transformation

  • Finite-range correlators are completed with an asymptotic long-distance tail before Fourier transformation, while Coulomb-gauge momentum-space data can bypass both steps.The tail form depends on the observable; the Coulomb-gauge large-distance behavior is not yet explicitly known, so its ansatz includes a power-law factor.Source: §II · p. 5

Perturbative matching

  • Perturbative matching relates the quasi-distribution to the light-cone distribution using scheme-specific kernels, evaluated at NLO in this work.Resummation options include RGR, LRR, and threshold resummation; quoted results exclude endpoint regions where xPz or (1 − x)Pz are not well above ΛQCD.Source: §II · p. 5

Extrapolation

  • Extrapolation combines finite-spacing, pion-mass, and momentum results into a physical-point distribution, with fit forms reflecting expected discretization and finite-momentum powers.Statistical errors propagate sample-by-sample, while systematic variations probe analysis choices and are combined by source before independent components are combined in quadrature.Source: §II · pp. 5–6

Review and interfaces

  • The final review collects inputs, diagnostics, tables, figures, and analysis choices without changing numerical results.Stage interfaces pass resampled numerical data and metadata between independent jobs, while deterministic tools perform numerical operations.Source: §II · p. 6

III. EXECUTION MODEL

lamet-agent organizes LaMET analysis into preparation, numerical execution, and interpretation. It checks user-specified choices, runs calculations in dependency order, and can review results against relevant literature.

Execution model

  • The framework divides analysis into preparation, numerical job execution, and interpretation.The LLM helps translate physics objectives into analysis choices recorded in a manifest.Source: §III · p. 6
  • The agent checks the specification and executes calculations in their dependency order.Physical validation, systematic variations, and recorded numerical evidence support tracing how choices affect final results.Source: §III · p. 6
  • When requested, the agent reviews results in the context of relevant literature.The review is part of interpretation, following numerical job execution.Source: §III · p. 6

A. Plan Mode and Manifest

Plan Mode lets users discuss and revise an analysis, while the manifest records its settings and systematic variations. Validation checks the configuration before the jobs execute in dependency order.

Plan Mode

  • Users can discuss an existing analysis and request natural-language changes to its observable, numerical method, or uncertainty treatment.Plan Mode translates requested changes into manifest edits, with validation feedback guiding revisions and confirmation of defaults.Source: A. Plan Mode and Manifest · p. 6

Manifest

  • The manifest specifies the target observable, input data, conventions, stages, job settings, and optional systematic variations.A stage describes an analysis step, while each job applies that step with specified inputs and parameter choices.Source: A. Plan Mode and Manifest · pp. 6, 8
  • A contract validates supported options, required parameters, physical conditions, and compatibility before calculations begin.Validation errors explain the relevant physical or statistical reason and can guide further planning; the expanded job dependencies form a DAG executed in authored order consistent with those dependencies.Source: A. Plan Mode and Manifest · p. 8

B. Job Execution

Jobs load and check their inputs, run the selected workflow, and report results. Bounded LLM ask operations recommend data-dependent parameters, while systematic variations and deterministic numerical procedures support traceable, repeatable analyses.

Job workflow

  • Each job loads external data or upstream results, checks stage requirements, and runs the workflow selected by manifest parameters.Built-in or user-defined matching kernels are selected and checked against the input physics settings and required parameters.Source: B. Job Execution · p. 8

Ask operations

  • Ask operations request structured LLM recommendations for choices such as fitting ranges, then validate and apply the returned parameters.Users may instead provide supported values in the manifest; Fourier-tail recommendations are constrained by stage requirements and fit-quality checks.Source: B. Job Execution · p. 8

Systematics

  • Systematic variations expand central jobs into corresponding downstream jobs so each requested change propagates through later stages.At extrapolation, alternatives are grouped by source, combined into an uncertainty budget, and traced to the jobs that produced them.Source: B. Job Execution · p. 9

Results and reuse

  • Stage reports collect results, plots, metadata, and diagnostics, while saved intermediate outputs can be reused in later runs.EnsembleData retains labeled numerical samples and physical metadata used for compatibility checks and formula selection.Source: B. Job Execution · pp. 8–9

Reproducibility

  • Repeating a run with the same manifest, inputs, and environment reproduces numerical results, but an ask-operation choice must first be written into the manifest.Stage reports record recommended values to support reproduction.Source: B. Job Execution · p. 9

C. Review

Review assembles numerical results, diagnostics, uncertainty estimates, and relevant literature to interpret what a completed analysis establishes. It checks consistency and identifies conclusions that remain limited by unavailable information or unexamined sources.

C. Review

  • Review connects the final distribution to extraction, transformation, and matching choices, while discussing fit-diagnostic limitations and evaluated systematic variations.Its scope is set by the analysis manifest.Source: C. Review · p. 9
  • The agent checks consistency across the calculation chain and uses statistical errors and the declared systematic-error budget to discuss uncertainty.Incompatible physical metadata and conclusions that cannot be assessed with available information are identified.Source: C. Review · p. 9
  • Candidate references provide methodological context for interpreting similarities or differences, while numerical claims about the current calculation come from its recorded outputs.The report can judge whether further calculations or systematic variations are needed based on available information.Source: C. Review · p. 10

IV. CASE STUDY

Four end-to-end examples span representative collinear LaMET analyses, with a manifest specifying the workflow and parameters. The examples reproduce published results consistently, but not every intermediate prescription exactly.

IV. CASE STUDY

  • A manifest declares the job DAG and stage parameters; after validation, the agent executes stages and produces distributions, intermediate artifacts, reports, and a final review.It consults the LLM where parameter recommendations are required.Source: §IV · p. 10
  • The four examples span pion PDFs in Coulomb-gauge and gauge-invariant constructions, pion and kaon DAs, and single- and multi-ensemble workflows.The pion PDFs follow Ref. [137], while the DAs [123] combine three lattice spacings and three momenta for joint continuum and infinite-momentum extrapolation.Source: §IV · p. 10
  • The examples use updated asymptotic analysis and data-dependent correlator choices, so they are consistent reproductions rather than exact reproductions of every published prescription.The correlator fit windows and excited-state counts are not uniquely preferred; this motivates treating systematic-error estimation as integral to the workflow.Source: §IV · p. 10

A. Pion Parton Distribution Functions

The pion-PDF case study applies one analysis workflow to gauge-invariant and Coulomb-gauge constructions, which share a light-cone limit but require different renormalization and matching paths. The runs yield positive, smoothly decreasing valence-like matched PDFs, with finite-momentum and single-ensemble limitations on their reach.

A. Pion Parton Distribution Functions

  • The CG and GI operators share the same infinite-boost light-cone limit but differ in ultraviolet structure, requiring distinct renormalization and matching paths.The GI Wilson line carries a linear divergence and associated renormalon, which the CG operator does not.Source: A. Pion Parton Distribution Functions · p. 10
  • The two runs use separate manifests and correlators from the same a = 0.06 fm ensemble, at nz = 5 (CG) and nz = 4 (GI), without extrapolation.They propagate 109 jackknife samples and compare at finite Pz with reference results at corresponding momenta.Source: A. Pion Parton Distribution Functions · p. 10
  • The agent selects correlator windows and Fourier-tail candidates using fit-quality gates, then holds the selected window, Fourier range, and tail model fixed across resamples.Correlator fits use Q ≥0.05; surviving Fourier candidates are ranked by Bayesian evidence.Source: A. Pion Parton Distribution Functions · p. 10
  • The CG and GI runs resolve different fit windows, Fourier ranges, and matching kernels, while both pass their fit-quality gates and finish with no consistency errors.The review reports one benign warning: the expected change of x grid between Fourier transformation and matching.Source: A. Pion Parton Distribution Functions · p. 11
  • Finite-momentum power corrections make endpoint regions less constrained; the shaded x < 0.1 and x > 0.9 boundaries are approximate guides, not precise reliability limits.The text estimates ΛQCD/Pz ∼0.1 and notes that even extrapolated results remain less constrained near endpoints.Source: A. Pion Parton Distribution Functions · p. 11
  • Both reviews report positive, smoothly decreasing valence-like matched PDFs and treat small χ2/dof as internal consistency, not external validation.The comparison is against published results of Ref. [137].Source: Figure 4 · p. 12, Figure 5 · p. 12, A. Pion Parton Distribution Functions · p. 12

B. Meson Distribution Amplitudes

The pion and kaon DA analyses reproduce published results in the interior region, while fit quality is substantially weaker for the kaon. The workflow uses self-renormalization, Fourier continuation, NLO matching, and joint continuum and infinite-momentum extrapolation.

B. Meson Distribution Amplitudes

  • The analyses use original gauge-invariant correlators and the aligned z = 0 slice as the qDA-ratio denominator across three HISQ lattice spacings and momenta.Each analysis propagates 100 bootstrap samples through the full pipeline.Source: B. Meson Distribution Amplitudes · p. 12
  • The kaon uses simultaneous fits to its nonlocal qDA correlator and z = 0 two-point correlator, while the pion uses one-state fits to the real and imaginary qDA-ratio components.The kaon fit choice was made to improve fit stability.Source: B. Meson Distribution Amplitudes · p. 12
  • The workflow carries finite-a results through Fourier transformation and matching before jointly extrapolating in x space, unlike Ref. [123], which extrapolates coordinate-space matrix elements before Fourier transformation.Source: B. Meson Distribution Amplitudes · p. 13
  • The analyses use ratio-scheme self-renormalization at µ = 2 GeV, NLO matching, and joint continuum and infinite-momentum extrapolation, with the same pion reference factor applied to kaon matrix elements.The shared factor is justified by state independence of ultraviolet renormalization for a common discretized operator and lattice action [123].Source: B. Meson Distribution Amplitudes · pp. 12–13
  • Kaon pointwise fits are poor over most of 0.1 ≲ x ≲ 0.9, whereas the pion fits remain uniformly acceptable.At x ≃ 0.3, 0.5, and 0.7, the pion χ2/dof values are 0.34, 0.43, and 0.34; the kaon values are 5.12, 5.51, and 0.78.Source: B. Meson Distribution Amplitudes · p. 13
  • The pion DA overlaps the Ref. [123] band through most of 0.1 ≲ x ≲ 0.9 and retains symmetry about x = 1/2; the kaon reproduces the published result within propagated systematic uncertainties over the interior region.Gray endpoint bands mark regions where quantitative comparison is not attempted.Source: B. Meson Distribution Amplitudes · p. 13

V. STATUS AND OUTLOOK

lamet-agent makes LaMET analyses executable through a declarative job-DAG manifest, with deterministic stage workflows and bounded, validated LLM decisions. The current validation and planned extensions define the framework’s scope, while several checks of its reliability remain open.

V. STATUS AND OUTLOOK

  • The declarative job-DAG manifest separates deterministic numerical execution from bounded, schema-validated data-dependent choices, and permits user intervention and partial workflows from external artifacts.Plan Mode prepares and validates specifications; qualifying manifests can proceed directly to execution, and terminal review is read-only.Source: §V · p. 13
  • Systematic-budget ansatz families and uncertainty coverage need testing beyond the variants exercised, while provider, expert-baseline, repeated-run, and human-in-the-loop studies remain open.The studies are intended to characterize decision stability and cost, and which choices can be safely delegated.Source: §V · p. 13
  • Figure 6 compares the agent’s joint a → 0 and Pz → ∞ extrapolation bands with Ref. [123], with endpoint regions shaded because large power corrections limit quantitative comparison.The agent-band uncertainties combine central statistical error with Fourier-range, matching-scale, and extrapolation-basis components.Source: Figure 6 · p. 14
  • Four planned extension areas include TMD and GTMD workflows, threshold-resummed matching, variational correlator methods, and current-current correlators, all within the declarative interface.Each extension is framed as a new stage contract, ask specification, or kernel.Source: §V · p. 14
  • The discussion presents inspectable provenance and deterministic tools as a basis for reducing duplicated implementation effort and lowering the barrier to reproducible use.Source: §V · p. 14

Appendix A: Parameters Manual

  • Appendix A’s parameters manual lists only manifest-authored JSON fields and summarizes each field’s principal physical action and activation condition.Stage-level defaults may be overridden by job-level values.Source: Appendix A · p. 23

1. Metadata

The metadata object carries shared run identity, physical parameters, and execution and resampling context. The stages mapping and job dependencies define the analysis DAG and support traceable complete or partial workflows.

1. Metadata

  • Metadata defines run identity, directory, physical parameters, and shared execution and resampling context inherited by all jobs.Observable and parton labels activate conditional contracts; stage-specific fitting, renormalization, and matching choices are excluded.Source: §1 · p. 23, Table III · p. 23

2. Stages

  • The ordered stages mapping and globally unique job identifiers define the analysis DAG, while role-named inputs declare upstream dependencies and external artifacts.Stage defaults can be overridden by individual jobs, and declared intermediate files allow partial workflows to resume.Source: §2 · p. 23

a. Correlator Analysis

Correlator fit scope determines the observable and spectral information entering the analysis, with fit choices affecting excited-state contamination and stability. Renormalization, Fourier transformation, and matching each have stage-specific inputs and constraints.

a. Correlator Analysis

  • Correlator fit scope sets the observable and spectral treatment; joined atoms share a correlated likelihood, successive entries chain posteriors, and omitting the 2pt atom gives an independent ratio fit.Candidate windows and models are assessed on sample-average data before being fixed across resamples; the Lanczos path uses nested-bootstrap Ritz extraction.Source: a. Correlator Analysis · pp. 23–24, Table IV · p. 24

b. Renormalization

  • Renormalization either consumes an external factor directly or fits reusable zR(z, a) from reference matrix elements before applying it to targets.Ratio, MS, and hybrid schemes activate different conversion, linear-mass, and switching-distance terms.Source: b. Renormalization · p. 24

c. Fourier Transform

  • Fourier transformation maps finite resampled coordinate-space matrix elements to a quasidistribution, with range, tail continuation, negative-z completion, and phase convention among its physical choices.Range and tail candidates are assessed on sample-average data; the selected range is fixed, and evidence-weighted means combine resampled tail results when model averaging is enabled.Source: c. Fourier Transform · p. 24

d. Perturbative Matching

  • Perturbative matching applies a deterministic kernel to convert a finite-momentum quasi-distribution into its light-cone counterpart, deriving kernel identity from authored settings and quasi-input provenance.Validation checks convention, grid, and provenance consistency rather than fitting.Source: d. Perturbative Matching · p. 24

e. Extrapolation

Extrapolation fits matched distributions for h0(x), while review checks selected cross-stage evidence and systematics propagate explicitly configured variants through downstream jobs.

e. Extrapolation

  • Extrapolation fits matched distributions for h0(x) after accounting for lattice artifacts, finite-momentum effects, unphysical quark-mass effects, and finite-volume corrections.Correction coefficients may be shared across the x grid or fitted independently at each point.Source: e. Extrapolation · pp. 24–25

f. Review

  • Review deterministically checks selected cross-stage identities, units, kinematics, schemes, grids, resampling, and extrapolation metadata, then recommends changes without modifying the manifest or numerical artifacts.Its ordered inputs bound the available results; optional literature can provide context but cannot supply missing run values or override diagnostics.Source: f. Review · p. 26

3. Systematics

  • Systematic variants are configured as branches from the nominal job graph, each changing one supported parameter and propagating it through downstream jobs before budget combination.No stage-local systematics contract is currently defined for correlator analysis or renormalization.Source: §3 · p. 26, Table XI · p. 29

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