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Automated Extraction of Collins-Soper Kernel from Lattice QCD using An Autonomous AI Physicist System

Jin-Xin Tan, Ting-Jia Miao, Mu-Hua Zhang, Xiang-He Pang, Ze-Xi Liu, Lin-Feng Zhang, Si-Heng Chen, Wei Wang

Abstract

We employ {PhysMaster}, an autonomous agentic AI system integrating theoretical reasoning, numerical computation, and exploitation strategies towards ultra-long horizon automation, to tackle long-standing challenges in non-perturbative lattice analyzes, including low signal-to-noise ratio at large transverse separation, complex systematic uncertainties, and labor-intensive manual workflows. Using the extraction of the CS kernel from quasi-transverse-momentum-dependent wave functions (quasi-TMDWFs) via large-momentum effective theory (LaMET) as a showcase, we demonstrate that \textsc{PhysMaster} automates high-dimensional fitting, renormalization, continuum-chiral extrapolation, and non-perturbative reconstruction in a fully autonomous manner. This framework drastically reduces the duration of the workflow from months to hours without compromising precision, stabilizes signals in the large-$b_\perp$ region to $1~\rm fm$, and produces results consistent with perturbative QCD and state-of-the-art traditional lattice calculations. This work validates the effectiveness of physicist-AI collaboration for first-principles QCD research and establishes a generalizable, reproducible paradigm for automated studies of parton structure and other non-perturbative observables from lattice QCD.

Automated Extraction of Collins-Soper Kernel from Lattice QCD using An Autonomous AI Physicist System

Abstract

We employ {PhysMaster}, an autonomous agentic AI system integrating theoretical reasoning, numerical computation, and exploitation strategies towards ultra-long horizon automation, to tackle long-standing challenges in non-perturbative lattice analyzes, including low signal-to-noise ratio at large transverse separation, complex systematic uncertainties, and labor-intensive manual workflows. Using the extraction of the CS kernel from quasi-transverse-momentum-dependent wave functions (quasi-TMDWFs) via large-momentum effective theory (LaMET) as a showcase, we demonstrate that \textsc{PhysMaster} automates high-dimensional fitting, renormalization, continuum-chiral extrapolation, and non-perturbative reconstruction in a fully autonomous manner. This framework drastically reduces the duration of the workflow from months to hours without compromising precision, stabilizes signals in the large- region to , and produces results consistent with perturbative QCD and state-of-the-art traditional lattice calculations. This work validates the effectiveness of physicist-AI collaboration for first-principles QCD research and establishes a generalizable, reproducible paradigm for automated studies of parton structure and other non-perturbative observables from lattice QCD.
Paper Structure (9 sections, 9 equations, 6 figures)

This paper contains 9 sections, 9 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Theoretical and Methodological Framework
  3. Determining CS kernel within LaMET
  4. Agent-automated Reconstruction Strategy
  5. Lattice QCD Calculation and PhysMaster Results
  6. Long-chain Analysis as Automated Lattice Workflow
  7. $b_{\perp}$ Parametrization and Extracted CS Kernel
  8. Discussion and Prospect
  9. The Architecture of PhysMaster

Figures (6)

  • Figure 1: PhysMaster workflow for CS kernel extraction. The framework integrates literature retrieval, MCTS-driven exploration, hierarchical agent collaboration, and result validation.
  • Figure 2: Automated long‑chain analysis workflow executed by PhysMaster for CS kernel extraction. Starting from raw lattice two‑point correlators and Wilson loop data, the agent performs correlator ratioing, plateau fitting, renormalization, tail stabilization, Fourier transformation, and final CS kernel extraction in a fully automated manner.
  • Figure 3: Renormalized quasi‑TMD wave function (quasi‑TMDWF) at longitudinal momentum $P^z=1.47$ GeV. Real and imaginary parts are shown as functions of the momentum fraction $x$, demonstrating stable behavior enforced by PhysMaster’s physics‑motivated parametrization.
  • Figure 4: Collins–Soper kernel $K(b_\perp, \mu=2{\rm GeV})$ extracted by PhysMaster. Results provide robust nonperturbative constraints up to $b_\perp \sim 1$ fm with improved stability relative to traditional lattice extraction Tan:2025ofx.
  • Figure 5: Structure of the LANDAU layered academic data universe, consisting of literature library, validated methodologies, and high-confidence physics priors to support reliable AI-automated theoretical and computational physics research.
  • ...and 1 more figures