pith. sign in

arxiv: 2606.18777 · v1 · pith:L6W2XWPNnew · submitted 2026-06-17 · ✦ hep-lat

Hybrid renormalization in lattice calculation of baryon LCDAs

Mu-Hua Zhang This is my paper

Pith reviewed 2026-06-26 18:40 UTC · model grok-4.3

classification ✦ hep-lat
keywords lattice QCDbaryon LCDAsquasi-distribution amplitudeshybrid renormalizationLaMEToctet baryonslight-cone distribution amplitudesNf=2+1 ensembles
0
0 comments X

The pith

A hybrid renormalization scheme removes linear divergences from lattice matrix elements of baryon quasi-distribution amplitudes.

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

The work applies a hybrid renormalization scheme to octet baryons in lattice QCD calculations of quasi-distribution amplitudes. The scheme targets and cancels linear divergences that appear in the relevant matrix elements. Computations on Nf=2+1 ensembles at three lattice spacings produce smooth and internally consistent quasi-DAs. These results supply the necessary input for LaMET to convert quasi-DAs into physical light-cone distribution amplitudes. The approach is presented as preparation for forthcoming continuum-limit and physical-pion-mass results.

Core claim

The hybrid renormalization scheme removes linear divergences in lattice matrix elements for octet baryons and yields smooth, self-consistent quasi-distribution amplitudes at lattice spacings of 0.052, 0.077, and 0.105 fm on Nf=2+1 ensembles with stout-smeared clover fermions.

What carries the argument

The hybrid renormalization scheme, which cancels linear divergences in the lattice matrix elements used to define quasi-distribution amplitudes.

If this is right

  • Reliable determinations of quasi-DAs become available for octet baryons.
  • Quasi-DAs are smooth and self-consistent across the three lattice spacings.
  • The results supply a solid foundation for LaMET-based extractions of baryon LCDAs.
  • Continuum-limit and physical-pion-mass extractions can now proceed from these quasi-DAs.

Where Pith is reading between the lines

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

  • The same hybrid scheme may generalize to other baryon species or to meson LCDAs if the divergence structure is comparable.
  • Once continuum results exist, direct comparisons with phenomenological extractions of baryon LCDAs from experimental data become feasible.
  • The approach could shorten the path to precision lattice inputs for baryon structure observables that enter high-energy processes.

Load-bearing premise

The hybrid renormalization scheme is assumed to correctly cancel all linear divergences without introducing new uncontrolled systematics or distorting the quasi-DAs at the three lattice spacings employed.

What would settle it

Quasi-DAs that remain rough or fail to agree across the three spacings when the same hybrid scheme is reapplied, or that show large discrepancies with an independent renormalization method.

Figures

Figures reproduced from arXiv: 2606.18777 by Mu-Hua Zhang.

Figure 1
Figure 1. Figure 1: The structure of the baryon LCDAs [1]. 3. Lattice simulation 3.1. Lattice setup The calculation is carried out on 𝑁𝑓 = 2 + 1 ensem￾bles with stout-smeared clover fermions and a Symanzik￾improved gauge action generated by the CLQCD collabo￾ration [21]. Three lattice spacings are used to eliminate UV divergences and facilitate continuum extrapolation. Informa￾tion of ensembles are summarized in [PITH_FULL_I… view at source ↗
Figure 2
Figure 2. Figure 2: Bare 0-momentum quasi-DAs for Λ from 3 different lattice spacings [1]. effects of the bare matrix element as 𝑀̂ (𝑧1 , 𝑧2 , 𝑃 𝑧 , 𝑎) = exp [ 𝑘 𝑎 ln(𝑎ΛQCD) ̃𝑧 + 𝑔(𝑧1 , 𝑧2 , 𝑃 𝑧 ) + 𝑓(𝑧1 , 𝑧2 )𝑎 2 + 𝛾0 𝑏0 ln ln(1∕𝑎ΛQCD) ln(𝜇∕ΛMS) + ln ( 1 + 𝑑 ln(𝑎ΛQCD) )], (9) where 𝑘 characterizes the linear divergence and 𝑓(𝑧1 , 𝑧2 )𝑎 2 accounts for discretization effects. The function 𝑔(𝑧1 , 𝑧2 , 𝑃 𝑧 ) encodes nonperturbat… view at source ↗
Figure 3
Figure 3. Figure 3: Range division for hybrid renormalization [1]. scheme effectively removes UV divergences, yet develops singular behavior in the short-distance region. In contrast, the resulting hybrid scheme simultaneously: • eliminates linear divergences, • avoids short-distance singularities, • preserves smooth behavior across all regions. Numerical results demonstrate that this approach pro￾vides stable and consistent … view at source ↗
Figure 4
Figure 4. Figure 4: Bare, hybrid, ratio & self renormalization scheme results of Λ quasi-DAs at 𝑃 𝑧 = 0.5 GeV [1]. mass are currently being finalized and will be reported in the near future. References [1] H. Bai, et al. (Lattice Parton Collaboration (LPC)), Hybrid renormal￾ization for distribution amplitude of a light baryon in large momentum effective theory, Phys. Rev. D 112 (2025) 114515. [2] R. Aaij, et al. (LHCb), Obser… view at source ↗
read the original abstract

At the 2025 International Conference on the Structure of Baryons (Baryons 2025), I presented our recent progress in lattice calculations of baryon light-cone distribution amplitudes (LCDAs). In Ref.[1], we implemented a novel hybrid renormalization scheme for octet baryons, leading to reliable determinations of quasi-distribution amplitudes (quasi-DAs). The calculations were performed on $N_f=2+1$ ensembles with stout-smeared clover fermions and a Symanzik-improved gauge action at three lattice spacings, $a = 0.052,0.077,0.105$ fm. The hybrid renormalization removes linear divergences in lattice matrix elements and yields smooth, self-consistent quasi-DAs, providing a solid foundation for LaMET-based extractions of baryon LCDAs. Results at the continuum limit and physical pion mass will be reported in the near future.

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 manuscript reports progress on lattice calculations of baryon light-cone distribution amplitudes (LCDAs) for octet baryons. It describes the implementation of a novel hybrid renormalization scheme on Nf=2+1 ensembles with stout-smeared clover fermions and Symanzik-improved gauge action at three lattice spacings (a=0.052, 0.077, 0.105 fm). The central claim is that this scheme removes linear divergences from lattice matrix elements and produces smooth, self-consistent quasi-distribution amplitudes (quasi-DAs), providing a foundation for future LaMET-based extractions at the continuum limit and physical pion mass.

Significance. If validated with explicit results, a hybrid renormalization scheme that systematically removes linear divergences without introducing new uncontrolled systematics would represent a useful technical step toward reliable lattice determinations of baryon LCDAs via LaMET. However, the manuscript provides no supporting data, equations, or validation, so no assessment of significance is possible.

major comments (1)
  1. The entire manuscript is a high-level conference abstract with no operator definitions, renormalization factors, fitting procedures, numerical matrix elements, error analysis, or validation plots at the three lattice spacings. This absence makes it impossible to verify the claim that the hybrid scheme removes linear divergences and yields smooth quasi-DAs (Abstract).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for reviewing the manuscript. The submission is a brief conference report summarizing progress presented at Baryons 2025 rather than a full technical paper. We respond to the major comment below.

read point-by-point responses

  1. Referee: The entire manuscript is a high-level conference abstract with no operator definitions, renormalization factors, fitting procedures, numerical matrix elements, error analysis, or validation plots at the three lattice spacings. This absence makes it impossible to verify the claim that the hybrid scheme removes linear divergences and yields smooth quasi-DAs (Abstract).

    Authors: We agree that the manuscript, as written, is a concise conference abstract and does not contain operator definitions, renormalization factors, fitting procedures, numerical matrix elements, error analysis, or validation plots. This is by design for the conference format, which limits length and emphasizes the overall approach and outlook. The hybrid renormalization scheme and resulting quasi-DAs are described at a summary level, with the supporting technical details and data reserved for a separate, forthcoming publication. Consequently, independent verification of the specific claims cannot be performed from the current text alone. revision: no

Circularity Check

0 steps flagged

No significant circularity

full rationale

The supplied text is a short conference progress report that asserts implementation of a hybrid renormalization scheme on specific lattice ensembles and references prior work in Ref.[1] for the scheme itself. No equations, operator definitions, renormalization factors, fitting procedures, or derivation steps are presented that could reduce a claimed prediction or result to its own inputs by construction. The self-citation is not load-bearing for any mathematical claim within this document, and the central statements remain descriptive rather than deductive. This is the most common honest finding for high-level method summaries without internal derivations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are identifiable from the abstract alone; the text does not specify any fitted quantities or new postulated objects.

pith-pipeline@v0.9.1-grok · 5673 in / 1050 out tokens · 31383 ms · 2026-06-26T18:40:51.033776+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

34 extracted references · 1 linked inside Pith

  1. [1]

    H.Bai,etal.(LatticePartonCollaboration(LPC)), Hybridrenormal- izationfordistributionamplitudeofalightbaryoninlargemomentum effective theory, Phys. Rev. D 112 (2025) 114515

    2025

  2. [2]

    Aaij, et al

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

    2025

  3. [3]

    V. L. Chernyak, A. R. Zhitnitsky, Asymptotic Behavior of Exclusive Processes in QCD, Phys. Rept. 112 (1984) 173

    1984

  4. [4]

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

    1988

  5. [5]

    V. M. Braun, S. E. Derkachov, G. P. Korchemsky, A. N. Manashov, Baryon distribution amplitudes in QCD, Nucl. Phys. B 553 (1999) 355–426

    1999

  6. [6]

    Braun, R

    V. Braun, R. J. Fries, N. Mahnke, E. Stein, Higher twist distribution amplitudes of the nucleon in QCD, Nucl. Phys. B 589 (2000) 381–

    2000

  7. [7]

    [Erratum: Nucl.Phys.B 607, 433–433 (2001)]

    2001

  8. [8]

    P. Wein, A. Schäfer, Model-independent calculation of SU(3) 𝑓 violation in baryon octet light-cone distribution amplitudes, JHEP 05 (2015) 073

    2015

  9. [9]

    G. S. Bali, et al., Light-cone distribution amplitudes of the baryon octet, JHEP 02 (2016) 070

    2016

  10. [10]

    G.S.Bali,etal.(RQCD), Light-conedistributionamplitudesofoctet baryons from lattice QCD, Eur. Phys. J. A 55 (2019) 116

    2019

  11. [11]

    G.S.Bali,V.M.Braun,S.Bürger,M.Göckeler,M.Gruber,F.Kaiser, B.A.Kniehl,O.L.Veretin,P.Wein(RQCD), Updateddetermination oflight-conedistributionamplitudesofoctetbaryonsinlatticeQCD, Phys. Rev. D 111 (2025) 094517

    2025

  12. [12]

    Ji, Parton Physics on a Euclidean Lattice, Phys

    X. Ji, Parton Physics on a Euclidean Lattice, Phys. Rev. Lett. 110 (2013) 262002

    2013

  13. [13]

    China Phys

    X.Ji, PartonPhysicsfromLarge-MomentumEffectiveFieldTheory, Sci. China Phys. Mech. Astron. 57 (2014) 1407–1412

    2014

  14. [14]

    Hua, M.-H

    J. Hua, M.-H. Chu, P. Sun, W. Wang, J. Xu, Y.-B. Yang, J.-H. Zhang, Q.-A. Zhang (Lattice Parton), Distribution Amplitudes of K* and𝜙 at the Physical Pion Mass from Lattice QCD, Phys. Rev. Lett. 127 (2021) 062002

    2021

  15. [15]

    J.Hua,etal.(LatticeParton), PionandKaonDistributionAmplitudes from Lattice QCD, Phys. Rev. Lett. 129 (2022) 132001

    2022

  16. [16]

    Han, et al

    X.-Y. Han, et al. (Lattice Parton), Calculation of heavy meson light- cone distribution amplitudes from lattice QCD, Phys. Rev. D 111 (2025) 034503

    2025

  17. [17]

    Chu, et al

    M.-H. Chu, et al. (Lattice Parton), Light cone distribution amplitude fortheΛbaryonfromlatticeQCD, Phys.Rev.D111(2025)034510

    2025

  18. [18]

    C. Han, W. Wang, J. Zeng, J.-L. Zhang, Lightcone and quasi distribution amplitudes for light octet and decuplet baryons, JHEP 07 (2024) 019

    2024

  19. [19]

    Z.-F. Deng, C. Han, W. Wang, J. Zeng, J.-L. Zhang, Light-cone distributionamplitudesofalightbaryoninlarge-momentumeffective theory, JHEP 07 (2023) 191

    2023

  20. [20]

    Zeng, Light-Cone Distribution Amplitudes of Light Baryons in Large-momentum Effective Theory, PoS QCHSC24 (2025) 097

    J. Zeng, Light-Cone Distribution Amplitudes of Light Baryons in Large-momentum Effective Theory, PoS QCHSC24 (2025) 097

    2025

  21. [21]

    Y.-J. Shi, J. Zeng, Factorization formula connecting theΛ𝑏 LCDA in QCD and boosted HQET, JHEP 05 (2026) 212

    2026

  22. [22]

    Hu, et al

    Z.-C. Hu, et al. (CLQCD), Quark masses and low-energy constants inthecontinuumfromthetadpole-improvedcloverensembles, Phys. Rev. D 109 (2024) 054507

    2024

  23. [23]

    Zhang, A

    R. Zhang, A. V. Grebe, D. C. Hackett, M. L. Wagman, Y. Zhao, Kinematically enhanced interpolating operators for boosted hadrons, Phys. Rev. D 112 (2025) L051502

    2025

  24. [24]

    G. S. Bali, B. Lang, B. U. Musch, A. Schäfer, Novel quark smearing for hadrons with high momenta in lattice QCD, Phys. Rev. D 93 (2016) 094515. M.-H. Zhang:Preprint submitted to ElsevierPage 4 of 5 Hybrid renormalization in lattice calculation of baryon LCDAs

    2016

  25. [25]

    Hasenfratz, F

    A. Hasenfratz, F. Knechtli, Flavor symmetry and the static potential with hypercubic blocking, Phys. Rev. D 64 (2001) 034504

    2001

  26. [26]

    T. A. DeGrand, A. Hasenfratz, T. G. Kovacs, Improving the chiral properties of lattice fermions, Phys. Rev. D 67 (2003) 054501

    2003

  27. [27]

    W. I. Jay, E. T. Neil, Bayesian model averaging for analysis of lattice field theory results, Phys. Rev. D 103 (2021) 114502

    2021

  28. [28]

    Huo, et al

    Y.-K. Huo, et al. (Lattice Parton (LPC)), Self-renormalization of quasi-light-front correlators on the lattice, Nucl. Phys. B 969 (2021) 115443

    2021

  29. [29]

    Ji, Matching perturbative and nonperturbative physics with power accuracy in heavy quark effective theory (1995)

    X.-D. Ji, Matching perturbative and nonperturbative physics with power accuracy in heavy quark effective theory (1995)

    1995

  30. [30]

    R.Zhang,J.Holligan,X.Ji,Y.Su, Leadingpoweraccuracyinlattice calculationsofpartondistributions, Phys.Lett.B844(2023)138081

    2023

  31. [31]

    C. Han, Y. Su, W. Wang, J.-L. Zhang, Hybrid renormalization for quasi distribution amplitudes of a light baryon, JHEP 12 (2023) 044

    2023

  32. [32]

    X.Ji,Y.Liu,A.Schäfer,W.Wang,Y.-B.Yang,J.-H.Zhang,Y.Zhao, A Hybrid Renormalization Scheme for Quasi Light-Front Correla- tionsinLarge-MomentumEffectiveTheory,Nucl.Phys.B964(2021) 115311

    2021

  33. [33]

    Zhang, Hybrid Renormalization for Baryon Distribution Amplitudes from Lattice QCD in LaMET, in: 26th International Symposium on Spin Physics, 2026.arXiv:2604.12419

    M.-H. Zhang, Hybrid Renormalization for Baryon Distribution Amplitudes from Lattice QCD in LaMET, in: 26th International Symposium on Spin Physics, 2026.arXiv:2604.12419

    Pith/arXiv arXiv 2026

  34. [34]

    J.-l.Zhang,M.-H.Zhang, Hybridrenormalizationwithgradientflow for baryon quasidistribution amplitudes, Phys. Rev. D 113 (2026) 014501. M.-H. Zhang:Preprint submitted to ElsevierPage 5 of 5

    2026