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arxiv: 2606.29597 · v1 · pith:WXABBTUWnew · submitted 2026-06-28 · ✦ hep-lat · hep-ph

Complete Access to Leading-Twist Λ-Baryon Light-Cone Distribution Amplitudes from Lattice QCD

Mu-Hua Zhang , Haoyang Bai , Min-Huan Chu , Jun Hua , Xiangdong Ji , Xiangyu Jiang , Jian Liang , Cai-Dian L\"u
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Andreas Sch\"afer Wei Wang Yi-Bo Yang Jian-Hui Zhang Jia-Lu Zhang Qi-An Zhang
This is my paper

Pith reviewed 2026-06-30 01:39 UTC · model grok-4.3

classification ✦ hep-lat hep-ph
keywords lattice QCDLambda baryonlight-cone distribution amplitudesLaMETleading twistvalence quark momentum fractionselectromagnetic form factor
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The pith

Lattice QCD yields the first complete leading-twist LCDAs for the Lambda baryon as full two-dimensional functions of valence quark momentum fractions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reports the first lattice-QCD calculation that determines the three leading-twist light-cone distribution amplitudes of the Lambda baryon as complete two-dimensional functions rather than moments or assumed shapes. It achieves this by computing equal-time three-quark matrix elements in boosted Lambda states and converting them to the light-cone limit through large-momentum effective theory, followed by hybrid renormalization, large-lambda extrapolation, and joint extrapolations to the continuum, physical pion mass, and infinite momentum. When these lattice LCDAs replace the asymptotic form in a calculation of the Lambda electromagnetic form factor, the result changes by roughly ten percent at perturbative scales. A reader would care because many baryon observables in high-energy processes depend on the detailed momentum sharing among the three valence quarks, and first-principles access to the full functions removes reliance on model assumptions.

Core claim

We report the first complete lattice-QCD determination of the leading-twist light-cone distribution amplitudes (LCDAs) of the λ baryon, obtained as full two-dimensional functions of the valence-quark momentum fractions. The calculation employs large-momentum effective theory to relate the light-cone amplitudes to equal-time nonlocal three-quark matrix elements of boosted λ baryons. Controlled physical extrapolations to the continuum, physical pion mass, and infinite momentum, together with hybrid renormalization, large-λ extrapolation, and perturbative matching, yield the three leading-twist LCDAs V, A, and T. Using the lattice-determined LCDAs in place of the asymptotic form, we find an O(1

What carries the argument

LaMET matching that converts equal-time nonlocal three-quark matrix elements of boosted Lambda baryons into light-cone distribution amplitudes, together with hybrid renormalization and simultaneous extrapolations in lattice spacing, pion mass, and momentum.

If this is right

  • The full two-dimensional LCDAs V, A, and T are now available from first principles and must replace asymptotic or moment-only approximations in precision baryon calculations.
  • The Lambda electromagnetic form factor receives an O(10%) correction at perturbative scales when the lattice LCDAs are used.
  • This calculation supplies the first benchmark complete x-dependent baryon LCDAs for use in other phenomenological applications.
  • The companion framework paper together with this work opens lattice access to multi-dimensional baryon structure functions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same LaMET-plus-extrapolation pipeline could be applied to obtain LCDAs for other octet or decuplet baryons.
  • Having the full two-dimensional functions allows direct computation of observables that integrate over specific momentum fractions, such as certain decay amplitudes or generalized parton distributions.
  • The ten-percent shift in the form factor indicates that similar corrections may appear in other baryon observables that currently rely on asymptotic LCDAs.

Load-bearing premise

The combination of LaMET matching, hybrid renormalization, large-lambda extrapolation, and simultaneous continuum, physical-pion-mass, and infinite-momentum extrapolations recovers the true light-cone amplitudes without large uncontrolled systematic errors.

What would settle it

An independent non-lattice determination or a precision measurement of the Lambda electromagnetic form factor that agrees with the asymptotic prediction but disagrees with the ten-percent shift obtained from the lattice LCDAs.

Figures

Figures reproduced from arXiv: 2606.29597 by Andreas Sch\"afer, Cai-Dian L\"u, Haoyang Bai, Jia-Lu Zhang, Jian-Hui Zhang, Jian Liang, Jun Hua, Min-Huan Chu, Mu-Hua Zhang, Qi-An Zhang, Wei Wang, Xiangdong Ji, Xiangyu Jiang, Yi-Bo Yang.

Figure 1
Figure 1. Figure 1: FIG. 1. Region partition in the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of the hybrid-renormalized quasi-DA [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Combined extrapolation of the Λ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Final results for the leading-twist Λ LCDAs. The upper row shows the two-dimensional distributions of the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

We report the first complete lattice-QCD determination of the leading-twist light-cone distribution amplitudes (LCDAs) of the $\Lambda$ baryon, obtained as full two-dimensional functions of the valence-quark momentum fractions. The calculation employs large-momentum effective theory to relate the light-cone amplitudes to equal-time nonlocal three-quark matrix elements of boosted $\Lambda$ baryons. Controlled physical extrapolations to the continuum, physical pion mass, and infinite momentum, together with hybrid renormalization, large-$\lambda$ extrapolation, and perturbative matching, yield the three leading-twist LCDAs $V$, $A$, and $T$. Using the lattice-determined LCDAs in place of the asymptotic form, we find an $\mathcal{O}(10\%)$ shift in the $\Lambda$ electromagnetic form factor at perturbative scales, demonstrating that the full two-dimensional LCDAs, rather than only their asymptotic shapes or lowest moments, are required for precision baryonic phenomenology. This work, together with the companion paper [1] detailing the baryon-LaMET framework, provides the first complete multi-dimensional $x$-dependent baryon LCDAs from first principles and establishes a benchmark for lattice access to multi-dimensional baryon structure.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper claims the first complete lattice-QCD determination of the leading-twist LCDAs (V, A, T) of the Λ baryon as full two-dimensional functions of valence-quark momentum fractions. It employs LaMET to relate these to equal-time nonlocal three-quark matrix elements on boosted baryons, combined with hybrid renormalization, large-λ extrapolation, perturbative matching, and simultaneous extrapolations to the continuum, physical pion mass, and infinite momentum. The resulting LCDAs are shown to produce an O(10%) shift in the Λ electromagnetic form factor relative to the asymptotic form, establishing a benchmark for multi-dimensional baryon structure from first principles.

Significance. If the multi-stage extrapolation and matching pipeline is under control, this constitutes a significant advance by delivering the first first-principles, x-dependent LCDAs for a baryon rather than moments or asymptotic forms. The explicit demonstration of the form-factor correction underscores the phenomenological necessity of the full distributions and provides a concrete benchmark against which future lattice and model calculations can be tested.

major comments (1)
  1. Abstract and extrapolation sections: the central claim that the combination of LaMET matching, hybrid renormalization, large-λ extrapolation, and simultaneous continuum/physical-pion/infinite-momentum extrapolations recovers the LCDAs without uncontrolled bias is load-bearing, yet the fit forms, covariance matrices, χ²/dof values, and stability tests under variations of the fit ansatz are not reproduced in sufficient detail to verify the asserted control.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment. We address the point below and will revise the manuscript to provide the requested details on the extrapolation procedures.

read point-by-point responses

  1. Referee: Abstract and extrapolation sections: the central claim that the combination of LaMET matching, hybrid renormalization, large-λ extrapolation, and simultaneous continuum/physical-pion/infinite-momentum extrapolations recovers the LCDAs without uncontrolled bias is load-bearing, yet the fit forms, covariance matrices, χ²/dof values, and stability tests under variations of the fit ansatz are not reproduced in sufficient detail to verify the asserted control.

    Authors: We agree that additional documentation of the fit forms, covariance matrices, χ²/dof values, and stability tests is needed to allow full verification of the extrapolation control. The companion paper provides the overall LaMET framework, but the current manuscript's extrapolation sections will be expanded in revision to include the explicit functional forms for the simultaneous continuum, physical-pion-mass, and infinite-momentum extrapolations, the covariance matrices, the χ²/dof for the primary fits, and results from variations of the fit ansatz demonstrating stability. These additions will be placed in the main text or a dedicated appendix. revision: yes

Circularity Check

0 steps flagged

No significant circularity; result extracted from lattice matrix elements

full rationale

The derivation chain starts from equal-time nonlocal three-quark matrix elements computed on the lattice, applies LaMET matching, hybrid renormalization, and simultaneous extrapolations in continuum, mπ, Pz, and λ to obtain the LCDAs V, A, T as two-dimensional functions. These steps are data-driven extractions rather than self-definitions or re-use of fitted parameters as predictions. The companion paper [1] supplies operator definitions and matching coefficients but does not make the final LCDAs tautological. No load-bearing step reduces by construction to its own inputs; the O(10%) form-factor shift is a downstream application of the extracted functions. This is the normal non-circular outcome for a first-principles lattice determination.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of LaMET for baryons, the correctness of the hybrid renormalization scheme, and the assumption that the chosen extrapolations capture all relevant systematics. No explicit free parameters or invented entities are named in the abstract.

axioms (2)
  • domain assumption Large-momentum effective theory correctly relates equal-time lattice matrix elements of boosted baryons to light-cone distribution amplitudes after matching and extrapolation.
    Invoked in the abstract description of the calculation method.
  • domain assumption Hybrid renormalization and perturbative matching introduce no uncontrolled errors at the quoted precision.
    Stated as part of the procedure yielding the LCDAs.

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discussion (0)

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Reference graph

Works this paper leans on

42 extracted references

  1. [1]

    Companion Paper: Baryon Light- Cone Distribution Amplitudes from Lattice QCD: For- malism, Renormalization, Extrapolation, and Matching

    Mu-Hua Zhang et al. Companion Paper: Baryon Light- Cone Distribution Amplitudes from Lattice QCD: For- malism, Renormalization, Extrapolation, and Matching

  2. [2]

    Peter Lepage and Stanley J

    G. Peter Lepage and Stanley J. Brodsky. Exclusive Pro- cesses in Perturbative Quantum Chromodynamics.Phys. Rev. D, 22:2157, 1980

    1980

  3. [3]

    A. V. Efremov and A. V. Radyushkin. Asymptotical Behavior of Pion Electromagnetic Form-Factor in QCD. Theor. Math. Phys., 42:97–110, 1980

    1980

  4. [4]

    V. L. Chernyak, A. A. Ogloblin, and I. R. Zhitnitsky. Wave Functions of Octet Baryons.Yad. Fiz., 48:1410– 1422, 1988

    1988

  5. [5]

    Next-to-Leading-Order QCD Corrections to Nucleon Dirac Form Factors.Phys

    Long-Bin Chen, Wen Chen, Feng Feng, Siwei Hu, and Yu Jia. Next-to-Leading-Order QCD Corrections to Nucleon Dirac Form Factors.Phys. Rev. Lett., 135(13):131903, 2025

    2025

  6. [6]

    Next-to-Leading-Order QCD Predic- tions for the Nucleon Form Factors.Phys

    Yong-Kang Huang, Bo-Xuan Shi, Yu-Ming Wang, and Xue-Chen Zhao. Next-to-Leading-Order QCD Predic- tions for the Nucleon Form Factors.Phys. Rev. Lett., 135(6):061901, 2025

    2025

  7. [7]

    Observation of charge–parity symmetry breaking in baryon decays.Nature, 643(8074):1223–1228, 2025

    Roel Aaij et al. Observation of charge–parity symmetry breaking in baryon decays.Nature, 643(8074):1223–1228, 2025

    2025

  8. [8]

    Aaij et al

    R. Aaij et al. Study of Λb0 and Ξb0 Decays to Λh+h’- and Evidence for CP Violation in Λb0→ΛK+K- Decays. Phys. Rev. Lett., 134(10):101802, 2025

    2025

  9. [9]

    Establish- ing CP Violation in b-Baryon Decays.Phys

    Jia-Jie Han, Ji-Xin Yu, Ya Li, Hsiang-nan Li, Jian-Peng Wang, Zhen-Jun Xiao, and Fu-Sheng Yu. Establish- ing CP Violation in b-Baryon Decays.Phys. Rev. Lett., 134(22):221801, 2025

    2025

  10. [10]

    CP violation in two-body hadronic Λb decays in the PQCD approach

    Jia-Jie Han, Ji-Xin Yu, Ya Li, Hsiang-nan Li, Jian-Peng Wang, Zhen-Jun Xiao, and Fu-Sheng Yu. CP violation in two-body hadronic Λb decays in the PQCD approach. 9 Phys. Rev. D, 112(5):053007, 2025

    2025

  11. [11]

    Perturbative QCD Prediction of the Hyperon Electric Dipole Moment from CP-Violating Dipole Inter- actions.Phys

    Kai-Bao Chen, Xiao-Gang He, Jian-Ping Ma, and Xuan- Bo Tong. Perturbative QCD Prediction of the Hyperon Electric Dipole Moment from CP-Violating Dipole Inter- actions.Phys. Rev. Lett., 136(5):051902, 2026

    2026

  12. [12]

    V. L. Chernyak and I. R. Zhitnitsky. Nucleon Wave Func- tion and Nucleon Form-Factors in QCD.Nucl. Phys. B, 246:52–74, 1984

    1984

  13. [13]

    I. D. King and Christopher T. Sachrajda. Nucleon Wave Functions and QCD Sum Rules.Nucl. Phys. B, 279:785– 803, 1987

    1987

  14. [14]

    Higher order light-cone distribution amplitudes of the Lambda baryon.Eur

    Yong-Lu Liu, Chun-Yu Cui, and Ming-Qiu Huang. Higher order light-cone distribution amplitudes of the Lambda baryon.Eur. Phys. J. C, 74:3041, 2014

    2014

  15. [15]

    V. M. Braun, A. Lenz, and M. Wittmann. Nucleon Form Factors in QCD.Phys. Rev. D, 73:094019, 2006

    2006

  16. [16]

    Bali et al

    Gunnar S. Bali et al. Light-cone distribution amplitudes of the baryon octet.JHEP, 02:070, 2016

    2016

  17. [17]

    Bali et al

    Gunnar S. Bali et al. Light-cone distribution amplitudes of octet baryons from lattice QCD.Eur. Phys. J. A, 55(7):116, 2019

    2019

  18. [18]

    G. S. Bali, V. M. Braun, S. B¨ urger, M. G¨ ockeler, M. Gru- ber, F. Kaiser, B. A. Kniehl, O. L. Veretin, and P. Wein. Updated determination of light-cone distribution ampli- tudes of octet baryons in lattice QCD.Phys. Rev. D, 111(9):094517, 2025

    2025

  19. [19]

    Parton Physics on a Euclidean Lattice

    Xiangdong Ji. Parton Physics on a Euclidean Lattice. Phys. Rev. Lett., 110:262002, 2013

    2013

  20. [20]

    Large-momentum effective the- ory.Rev

    Xiangdong Ji, Yu-Sheng Liu, Yizhuang Liu, Jian-Hui Zhang, and Yong Zhao. Large-momentum effective the- ory.Rev. Mod. Phys., 93(3):035005, 2021

    2021

  21. [21]

    Light-cone distribution amplitudes of a light baryon in large-momentum effective theory.JHEP, 07:191, 2023

    Zhi-Fu Deng, Chao Han, Wei Wang, Jun Zeng, and Jia-Lu Zhang. Light-cone distribution amplitudes of a light baryon in large-momentum effective theory.JHEP, 07:191, 2023

    2023

  22. [22]

    Hybrid renormalization for quasi distribution amplitudes of a light baryon.JHEP, 12:044, 2023

    Chao Han, Yushan Su, Wei Wang, and Jia-Lu Zhang. Hybrid renormalization for quasi distribution amplitudes of a light baryon.JHEP, 12:044, 2023

    2023

  23. [23]

    Lightcone and quasi distribution amplitudes for light octet and decuplet baryons.JHEP, 07:019, 2024

    Chao Han, Wei Wang, Jun Zeng, and Jia-Lu Zhang. Lightcone and quasi distribution amplitudes for light octet and decuplet baryons.JHEP, 07:019, 2024

    2024

  24. [24]

    Hybrid renormaliza- tion with gradient flow for baryon quasidistribution am- plitudes.Phys

    Jia-lu Zhang and Mu-Hua Zhang. Hybrid renormaliza- tion with gradient flow for baryon quasidistribution am- plitudes.Phys. Rev. D, 113(1):014501, 2026

    2026

  25. [25]

    Light cone distribution ampli- tude for the Λ baryon from lattice QCD.Phys

    Min-Huan Chu et al. Light cone distribution ampli- tude for the Λ baryon from lattice QCD.Phys. Rev. D, 111(3):034510, 2025

    2025

  26. [26]

    Hybrid renormalization for distri- bution amplitude of a light baryon in large momentum effective theory.Phys

    Haoyang Bai et al. Hybrid renormalization for distri- bution amplitude of a light baryon in large momentum effective theory.Phys. Rev. D, 112(11):114515, 2025

    2025

  27. [27]

    Braun, Sergey E

    Vladimir M. Braun, Sergey E. Derkachov, G. P. Ko- rchemsky, and A. N. Manashov. Baryon distribution am- plitudes in QCD.Nucl. Phys. B, 553:355–426, 1999

    1999

  28. [28]

    Asymp- totic Long-Distance Expansion of Euclidean Correlators in Lattice Parton Applications

    Xiangdong Ji, Yizhuang Liu, and Yushan Su. Asymp- totic Long-Distance Expansion of Euclidean Correlators in Lattice Parton Applications. 1 2026

    2026

  29. [29]

    Quark masses and low-energy con- stants in the continuum from the tadpole-improved clover ensembles.Phys

    Zhi-Cheng Hu et al. Quark masses and low-energy con- stants in the continuum from the tadpole-improved clover ensembles.Phys. Rev. D, 109(5):054507, 2024

    2024

  30. [30]

    Charmed meson masses and decay constants in the continuum limit from the tadpole im- proved clover ensembles.Phys

    Hai-Yang Du et al. Charmed meson masses and decay constants in the continuum limit from the tadpole im- proved clover ensembles.Phys. Rev. D, 111(5):054504, 2025

    2025

  31. [31]

    Bali, Bernhard Lang, Bernhard U

    Gunnar S. Bali, Bernhard Lang, Bernhard U. Musch, and Andreas Sch¨ afer. Novel quark smearing for hadrons with high momenta in lattice QCD.Phys. Rev. D, 93(9):094515, 2016

    2016

  32. [32]

    Flavor sym- metry and the static potential with hypercubic blocking

    Anna Hasenfratz and Francesco Knechtli. Flavor sym- metry and the static potential with hypercubic blocking. Phys. Rev. D, 64:034504, 2001

    2001

  33. [33]

    DeGrand, Anna Hasenfratz, and Tamas G

    Thomas A. DeGrand, Anna Hasenfratz, and Tamas G. Kovacs. Improving the chiral properties of lattice fermions.Phys. Rev. D, 67:054501, 2003

    2003

  34. [34]

    Grebe, Daniel C

    Rui Zhang, Anthony V. Grebe, Daniel C. Hackett, Michael L. Wagman, and Yong Zhao. Kinematically enhanced interpolating operators for boosted hadrons. Phys. Rev. D, 112(5):L051502, 2025

    2025

  35. [35]

    Kinematic enhancement for nu- cleon interpolators

    Daniel Reitinger, Tobias Sizmann, Andreas Sch¨ afer, Rui Zhang, and Yong Zhao. Kinematic enhancement for nu- cleon interpolators. 6 2026

    2026

  36. [36]

    V. M. Braun, A. N. Manashov, and J. Rohrwild. Baryon Operators of Higher Twist in QCD and Nucleon Distri- bution Amplitudes.Nucl. Phys. B, 807:89–137, 2009

    2009

  37. [37]

    Two-Loop Renormalization-Group Evolution for the Nucleon Distribution Amplitude

    Yong-Kang Huang, Yao Ji, Bo-Xuan Shi, and Yu-Ming Wang. Two-Loop Renormalization-Group Evolution for the Nucleon Distribution Amplitude. 12 2025. [38]Supplemental Material

    2025

  38. [38]

    Use QUDA for lattice QCD calculation with Python

    Xiangyu Jiang, Chunjiang Shi, Ying Chen, Ming Gong, and Yi-Bo Yang. Use QUDA for lattice QCD calculation with Python. 11 2024

    2024

  39. [39]

    M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi. Solving Lattice QCD systems of equations using mixed precision solvers on GPUs.Comput. Phys. Commun., 181:1517–1528, 2010

    2010

  40. [40]

    Babich, M

    R. Babich, M. A. Clark, B. Joo, G. Shi, R. C. Brower, and S. Gottlieb. Scaling lattice QCD beyond 100 GPUs. InInternational Conference for High Performance Com- puting, Networking, Storage and Analysis, 9 2011

    2011

  41. [41]

    M. A. Clark, B´ alint Jo´ o, Alexei Strelchenko, Michael Cheng, Arjun Gambhir, and Richard. C. Brower. Ac- celerating lattice QCD multigrid on GPUs using fine- grained parallelization. InInternational Conference for High Performance Computing, Networking, Storage and Analysis, 12 2016

    2016

  42. [42]

    Lattice QCD pack- age GWU-code and QUDA with HIP.PoS, LAT- TICE2019:286, 2020

    Yu-Jiang Bi, Yi Xiao, Wei-Yi Guo, Ming Gong, Peng Sun, Shun Xu, and Yi-Bo Yang. Lattice QCD pack- age GWU-code and QUDA with HIP.PoS, LAT- TICE2019:286, 2020

    2020