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

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

hep-latSep 26, 2026

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

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

Organizations: Fermi National Accelerator Laboratory, Batavia, IL 60510, USA · Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA · Physics Division, Argonne National Laboratory, Lemont, IL 60439, USA · Department of Physics, Indiana University, Bloomington, IN 47405, USA · Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA · School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, China

Abstract

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.

Figures & tables

Figure 1: Scientific workflow of a generic LaMET analysis. The upper row shows the intermediate objects, the lower row the stage that maps one into the next. The bar in each stage box indicates schematically the split between data-dependent decisions requiring expert judgment (orange) and deterministic operations (blue). The Fourier transform is bypassed when the quasi-observable is already defined in momentum space; the review below the frame collects the record of every stage without altering the results.

Figure 2: Execution model of lamet-agent . Plan Mode turns the user’s physics objective into a manifest, which is executed only once it satisfies the contract; validation errors return to Plan Mode. The validated manifest is expanded into a job DAG whose jobs the agent then executes in a single ordered pass consistent with that dependency order under deterministic numerical tools. One job (heavier outline) is expanded above as an example of how any job is organized: it loads external correlators or the results of preceding jobs, runs the stage workflow, and returns a result that is saved for dependent jobs and for later runs. The crossed dependencies in the first two columns indicate that a job may consume several upstream results; jobs labeled var are those generated for systematic variations. Dashed lines indicate the three points at which the LLM is used: the initial planning dialogue, ask operations within a stage workflow, and the final Review. The Review compares the recorded results with the literature, writing its recommendations without changing the manifest or any numerical artifact.

Figure 3: A conversation between the planner and the user asking for a change in the matrix elements extraction method from least-squares fitting to the Lanczos algorithm. The user asks questions and describes changes in natural language, and the planner answers the question or applies the revision to the manifest.

	Coulomb gauge	Gauge invariant
Momenta	$n_{z}=0$ / $n_{z}=5$ , $P_{z}=2.15~\mathrm{GeV}$	$n_{z}=0$ / $n_{z}=4$ , $P_{z}=1.72~\mathrm{GeV}$
Correlator fit	joint 2pt $+$ 3pt ratio, 2 states	joint 2pt $+$ 3pt ratio, 2 states
fit window	rest : $t\in[3,12)$ ; $t_{\mathrm{sep}}=\{8,10,12\}$ ; $\tau_{\mathrm{cut}}=3$ boosted : $t\in[3,12)$ ; $t_{\mathrm{sep}}=\{8,10,12\}$ ; $\tau_{\mathrm{cut}}=3$	rest: $t\in[5,12)$ ; $t_{\mathrm{sep}}=\{8,10\}$ ; $\tau_{\mathrm{cut}}=3$ boosted: $t\in[6,12)$ ; $t_{\mathrm{sep}}=\{8,10\}$ ; $\tau_{\mathrm{cut}}=3$
$\chi^{2}/\mathrm{dof}$	$0.070$ / $0.311$	$0.671$ / $0.208$
Renormalization	hybrid scheme with an external rest-frame denominator; $z_{s}=0.18~\mathrm{fm}$	hybrid scheme with an external rest-frame denominator; $z_{s}=0.18~\mathrm{fm}$
$\delta m$ , $m_{0}$	$0$ , $0$	$0.5207~\mathrm{GeV}$ , $0.1232~\mathrm{GeV}$

Table 1: Physical setup, resolved settings, and fit diagnostics for the Coulomb-gauge and gauge-invariant pion-PDF runs, as reconstructed from the resolved manifests and stage reports. Where a manifest declares several candidates, the entry below is the choice the agent returned; the GI two-point windows and Fourier interval are single authored values. The correlator-fit

\chi^{2}/\mathrm{dof}

is quoted separately for the rest-frame and boosted jobs of each run. The CG

z

candidates are spaced by the lattice spacing

a=0.06~\mathrm{fm}

. The setup is stated in physical terms and implementation identifiers are shown only for kernels.

Figure 4: Coulomb-gauge pion light-cone PDFs from lamet-agent compared with the published results of Ref. [ 97 ] , on the

a=0.06~\mathrm{fm}

ensemble at

n_{z}=5

(

P_{z}=2.15~\mathrm{GeV}

). The PDFs are matched at NLO. Shaded bands denote propagated statistical uncertainties. The gray regions indicate the estimated endpoint regions.

Figure 5: Gauge-invariant pion light-cone PDFs from lamet-agent compared with the published results of Ref. [ 97 ] , on the same ensemble at

n_{z}=4

(

P_{z}=1.72~\mathrm{GeV}

). The PDFs are matched at NLO with LRR. Shaded bands denote propagated statistical uncertainties. The gray regions indicate the estimated endpoint regions.

Panel of Figure 6 — Figure 6: Final gauge-invariant comparison of pion and kaon DAs, obtained using the original correlators from Ref. [ 115 ] . The blue bands correspond to the lamet-agent joint extrapolation $a\to 0$ , $P_{z}\to\infty$ , with uncertainties combining the central statistical error and the Fourier-range, matching-scale, and extrapolation-basis components as specified in the manifests. The orange bands represent the results reported in Ref. [ 115 ] . The endpoint regions $x<0.1$ and $x>0.9$ are shaded in gray, where LaMET matching suffers large power corrections, hence a quantitative comparison is limited.

	Pion DA	Kaon DA
Momenta	$n_{z}=6,8,10$ ; $P_{z}$ = $(1.35,1.32,1.28)$ , $(1.80,1.76,1.70)$ , and $(2.25,2.20,2.13)~\mathrm{GeV}$	same momenta and ensembles
Correlator fit	one-state fits to the real and imaginary parts of the nonlocal-to-local qDA ratio	simultaneous fit to the nonlocal qDA correlator and its aligned $z=0$ two-point correlator
fit window	$n_{z}=6:\ [13,18),[8,13),[6,11)$ $n_{z}=8:\ [9,14),[6,11),[4,9)$ $n_{z}=10:\ [7,12),[5,8),[3,8)$	$n_{z}=6:\ [12,17),[8,12),[6,11)$ $n_{z}=8:\ [8,11),[6,9),[4,7)$ $n_{z}=10:\ [7,12),[5,8),[3,6)$
$\chi^{2}/\mathrm{dof}$	$n_{z}=6:\ (0.251,0.130,0.422)$ $n_{z}=8:\ (0.873,0.140,0.500)$ $n_{z}=10:\ (0.777,1.346,0.100)$	$n_{z}=6:\ (1.093,4.198,3.141)$ $n_{z}=8:\ (5.141,9.516,9.540)$ $n_{z}=10:\ (3.231,13.313,65.299)$
Renormalization	ratio scheme with self-renormalization; the common zero-momentum pion reference determines $z_{R}(z,a)$ ; $\mu=2~\mathrm{GeV}$	same reference and strategy applied to the kaon matrix elements
Asymptotic region	$n_{z}=6:\ (0.52\text{--}1.21),(0.53\text{--}1.50),(0.61\text{--}1.46)$ $n_{z}=8:\ (0.52\text{--}1.49),(0.53\text{--}1.50),(0.61\text{--}1.46)$ $n_{z}=10:\ (0.52\text{--}1.49),(0.53\text{--}1.50),(0.61\text{--}1.46)$	$n_{z}=6:\ (0.75\text{--}1.49),(0.62\text{--}1.50),(0.97\text{--}1.21)$ $n_{z}=8:\ (0.75\text{--}1.26),(0.62\text{--}0.97),(0.73\text{--}0.97)$ $n_{z}=10:\ (0.75\text{--}1.21),(0.79\text{--}0.97),(0.85\text{--}1.09)$

Table 2: Physical setup, agent-selected settings, and fit diagnostics for the gauge-invariant pion- and kaon-DA runs, as reconstructed from the resolved manifests and stage reports. Both use the

96^{3}\times 192

64^{3}\times 96

, and

48^{3}\times 64

ensembles at

a=0.0574

0.0882

, and

0.1213~\mathrm{fm}

, respectively. As in Table 1 , the setup is stated in physical terms and implementation identifiers are shown only for kernels. Systematic variants are propagated through all affected downstream stages.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

JSON field	Accepted value	Physical meaning or condition
run_id	string	Human-readable identifier for one analysis run and its artifacts.
root_directory	path string	Filesystem base used to resolve relative input paths.
artifacts_directory	path string	Directory receiving per-job outputs and diagnostics.
random_seed	nonnegative integer	Common seed for reproducible resampling and stochastic numerical procedures.
workers	positive integer	Run-wide limit on concurrent sample-wise calculations.
target_observable	pdf , da , or gpd	Physical distribution produced by the workflow; it activates observable-specific stage fields.

Appendix

Table 3: Manifest fields accepted in the metadata object.

JSON field	Accepted value	Physical meaning or condition
stages	nonempty ordered object	Ordered stage mapping defining the sequence of physical transformations.
stages.<stage>.defaults	object; optional	Authored common values inherited by jobs in that stage.
stages.<stage>.jobs	nonempty ordered list	Physical jobs retain authored order before systematic expansion.
jobs[].id	safe identifier string	Stable graph identifier used for dependencies and job artifacts.
jobs[].inputs	role-to-source object; default {}	Maps each physical input role to an upstream job, external file, or explicitly permitted source form.
jobs[].<stage parameter>	stage-specific value	Job-specific physical choice overriding the inherited stage default.

Appendix

Table 4: Generic manifest fields accepted for every numerical or review stage.

JSON field	Accepted value	Physical meaning or condition
inputs.correlators	nonempty list of descriptor records	Explicit ordered correlator selection; one descriptor may contain many records.
inputs.correlators[].json	string ending in .json	Descriptor containing the selected correlator’s data definition.
inputs.correlators[].id	nonempty string	Unique record identifier selecting one correlator from that descriptor.
analysis_method	lsqfit or lanczos ; default lsqfit	Uses sample-wise nonlinear least squares or a Lanczos extraction.
component	re , im , or both	Selects the real, imaginary, or both matrix-element channels.
nstate ( lsqfit )	object mapping each fit_scope atom to a nonempty list of positive integers	Per-correlator spectral truncations scanned by the fit; keys must be bare atoms, never joint + strings.

Appendix

Table 5: Manifest fields accepted by correlator_analysis . Lsqfit- and Lanczos-specific fields are active only for the corresponding analysis_method .

JSON field	Accepted value	Physical meaning or condition
strategy	external_denominator , self_renormalization	Uses a factor determined outside the workflow or extracts a reusable factor from reference matrix elements.
normalization	Boolean	If true, divides every sample by its unique $z=0$ value before renormalization.
scheme	ratio , hybrid , or msbar	Selects how the supplied or fitted factor enters; hybrid separates short- and long-distance prescriptions.
type	apply for external_denominator , fit / apply for self_renormalization	Fits a reusable $z_{R}$ from references or applies the selected prescription to a target; external factors are apply-only.
inputs.target	job id or file source	Bare matrix element to be renormalized.
inputs.denominator	job id or file source; a nonzero constant only where permitted	External factor dividing the target; hybrid use requires a coordinate-dependent source and also anchors continuity in self-hybrid application.

Appendix

Table 6: Manifest fields accepted by renormalization . The selected strategy , type , and scheme jointly determine which conditional fields and input roles are required.

JSON field	Accepted value	Physical meaning or condition
inputs.input	job id or file source	Renormalized coordinate-space matrix element.
inputs.hermitian_partner	job id or file source; default none	Exchanged-flow GPD partner with reversed source and sink momenta, supplying the negative- $z$ branch by Hermiticity.
quasi_y_ls	increasing list or {start,stop,num}	Dimensionless $y$ grid.
zmin_fm , zmax_fm	nonempty lists of nonnegative and positive numbers	Candidate lower/upper tail-fit boundaries; one common range is selected from sample-average data before resample fits.
tail_window_step_offset	integer; default 0	Shifts every $z_{\min}$ by the signed distance $na_{s}$ while holding $z_{\max}$ fixed; zero is the unshifted central job.
zmax_ext_fm	positive number	Requested maximum $\|z\|$ in the finite sum.

Appendix

Table 7: Manifest fields accepted by fourier_transform .

JSON field	Accepted value	Physical meaning or condition
inputs.quasi	job id or file source	One quasi-distribution whose attributes supply $P_{z}$ , the hybrid $z_{s}$ , and the parton, observable, gauge, operator, scheme, and component provenance fixing the kernel.
order	nlo	Only next-to-leading-order matching kernels are currently available.
resummation	"" , rgr , or lrr ; default ""	Empty selects fixed order; rgr resums the running coupling and takes its real/imaginary kernel suffix from the upstream source component; lrr resums the leading renormalon.
mu	positive number in GeV	$\overline{\mathrm{MS}}$ light-cone scale entering the coefficient function through $\ln(4y^2P_z^2/\mu^2)$ .
lc_x_ls	increasing list or {start,stop}	Exact output grid, or a closed window selecting existing quasi-grid points without interpolation.
kernel_parameters	object; default {}	Overrides checked against the selected kernel signature; every kernel accepts the plus-prescription regulator eps , and RGR kernels add kappa and mu_min_gev , which set $x_{\min}=\mu_{\min}/(2\kappa P_{z})$ and keep $\mu_{0}$ above the Landau pole. The grids and $z_{s}$ cannot be overridden.

Appendix

Table 8: Manifest fields accepted by perturbative_matching . The kernel filename is derived from these fields and the quasi-input provenance.

JSON field	Accepted value	Physical meaning or condition
operation	fit or systematics_budget ; default fit	Fits $h_{0}(x)$ where the selected correction bases vanish, or performs no refit and assembles statistical and systematic errors.
inputs.distributions	nonempty ordered list of job ids/file sources	Matched finite-parameter distributions for the scaling fit, or indexed central and variant distributions for the budget.
x_independent_terms	unique list; default []	Bases in $h=h_{0}(x)+\sum_{t}c_{t}B_{t}$ with one correction coefficient shared over all $x$ .
x_dependent_terms	unique list; default []	Bases with independent $c_{t}(x)$ , allowing cutoff, momentum, mass, or volume effects to distort the shape; disjoint from the shared list.
Supported term identifiers	a , a2 , a4 , ap2 , ap4 , exp_mpi_L , exp_sqrt2_mpi_L , mpi2 , mpi4_log_mpi2 , inv_p2 , inv_p4	Implement $a_{s}^{1,2,4}$ , raw $(a_{s}P)^{2,4}$ , finite-volume exponentials, physical-point-subtracted pion-mass terms, and higher-twist terms $P^{-2,-4}$ .
priors	exactly {mean,sdev} ; default {0,3}	Common numerical Gaussian prior for $h_{0}$ and all correction coefficients in their native units.

Appendix

Table 9: Manifest fields accepted by extrapolation . Fit-only and budget-only fields are selected by operation .

JSON field	Accepted value	Physical meaning or condition
inputs.results	nonempty ordered list of job ids/file sources	Explicit, ordered prior results defining the evidence available to review.
catalog	string	Selects the built-in catalog or a literature catalog resolved relative to the run root.
max_papers	positive integer	Bounds the number of selected full-text papers exposed to the reviewer.
report_language	en or ch	Generates the review prose directly in English or Chinese.
checks	nonempty list drawn from identity , units , kinematics , schemes , grids , resampling , extrapolation	Explicit controlled set of cross-result consistency checks requested from review.

Appendix

Table 10: Manifest fields accepted by review .

JSON field	Accepted value	Physical meaning or condition
systematics.<stage>	object keyed by fourier_transform , perturbative_matching , or extrapolation	Adds uncertainty variants only to a stage already present in the central workflow.
defaults	object; default {}	Common values inherited by variants before explicit overrides; central jobs are unchanged.
fourier_transform.variants[].id	safe lowercase identifier	Stable suffix and provenance label for one Fourier-tail variation.
fourier_transform.variants[]. tail_window_step_offset	nonzero integer	Moves every $z_{\min}$ by the signed distance $na_{s}$ , leaving $z_{\max}$ and other Fourier settings fixed.
perturbative_matching.variants[].id	safe lowercase identifier	Stable suffix and provenance label for one matching-scale variation.
perturbative_matching.variants[]. mu_factor	positive number other than 1	Multiplies the central $\mu$ , conventionally by $1/\sqrt{2}$ or $\sqrt{2}$ , for the matching-scale uncertainty.

Appendix

Table 11: Manifest fields accepted under the systematics object. No stage-local systematics contract is currently defined for correlator analysis or renormalization.

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