arxiv: 2604.12419 · v2 · submitted 2026-04-14 · ✦ hep-lat

Recognition: no theorem link

Hybrid Renormalization for Baryon Distribution Amplitudes from Lattice QCD in LaMET

Mu-Hua Zhang

Authors on Pith no claims yet

Pith reviewed 2026-05-15 07:18 UTC · model grok-4.3

classification ✦ hep-lat

keywords hybrid renormalizationLaMETbaryon quasi-DAslattice QCDoctet baryonsdistribution amplitudeslinear divergencesCLQCD ensembles

0 comments

The pith

A hybrid renormalization scheme removes linear divergences from octet baryon quasi-DAs in LaMET lattice QCD.

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

The paper develops and applies a hybrid renormalization scheme to octet baryon quasi-distribution amplitudes calculated in the LaMET framework on the lattice. This scheme is tested on CLQCD ensembles with N_f=2+1 stout-smeared clover fermions and Symanzik-improved gauge action at three lattice spacings. After renormalization the linear divergences disappear, producing smooth coordinate-space distributions that behave well in both perturbative and non-perturbative regimes. The work shows that the method is viable for light baryons and supplies a practical route to future determinations of leading-twist baryon LCDAs.

Core claim

The hybrid renormalization scheme is implemented for octet baryon quasi-DAs within LaMET, removing the linear divergences that are inherent to the quasi-DAs and yielding smooth, well-behaved continuum coordinate-space distributions. Numerical results are obtained on three lattice spacings using N_f=2+1 CLQCD ensembles, confirming that the scheme works reliably across perturbative and non-perturbative regions.

What carries the argument

Hybrid renormalization scheme that matches perturbative and non-perturbative contributions for quasi-distribution amplitudes.

If this is right

Linear divergences are removed, leaving smooth coordinate-space distributions.
Reliable results are obtained across both perturbative and non-perturbative momentum regions.
The approach supplies a practical foundation for future LaMET determinations of baryon LCDAs.
The method is shown to be viable specifically for light-baryon quasi-DAs.
Results at three lattice spacings support controlled extrapolation to the continuum.

Where Pith is reading between the lines

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

The same hybrid scheme could be tested on other baryon representations or on meson quasi-DAs for cross-checks.
Smooth distributions open the possibility of direct Fourier transforms to momentum-space LCDAs without additional modeling steps.
The method may lower the computational overhead for similar LaMET calculations on finer lattices.
Comparison of these distributions against phenomenological models becomes feasible once the continuum limit is taken.

Load-bearing premise

The hybrid renormalization correctly matches the perturbative and non-perturbative regimes without introducing uncontrolled artifacts or residual divergences that survive the continuum limit.

What would settle it

A calculation performed at a fourth, significantly finer lattice spacing that still exhibits linear divergences or non-smooth behavior after the hybrid renormalization is applied.

Figures

Figures reproduced from arXiv: 2604.12419 by Mu-Hua Zhang.

**Figure 1.** Figure 1: The structure of the baryon LCDAs [1]. The LCDAs in momentum space can be obtained through Fourier transformation: 𝜙𝑉/𝐴/𝑇 (𝑥1, 𝑥2) = ∫ 𝑃 + 𝐵 𝑑𝑧1 2𝜋 ∫ 𝑃 + 𝐵 𝑑𝑧2 2𝜋 𝑒 𝑖(𝑥1 𝑧1+𝑥2 𝑧2 )𝑃 + 𝐵 Φ 𝐵 𝑉/𝐴/𝑇 (𝑧1𝑛, 𝑧2𝑛), (3) where 𝑥1, 𝑥2 are longitudinal momentum fractions carried by 𝑓 , 𝑔 quarks, as shown in right panel of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Figure 2: Bare 0-momentum quasi-DAs for Λ from 3 different lattice spacings [1]. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Range division for hybrid renormalization on 𝑧1-𝑧2 plane [1]. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Bare, hybrid, ratio & self renormalization scheme results of Λ quasi-DAs at 𝑃 𝑧 = 0.5 GeV [1]. 5. Summary In this report, we review the recent progress in our lattice calculations of baryon LCDAs within the LaMET framework. In particular, we successfully implement a hybrid renormalization scheme for the Λ-baryon quasi-DAs in our recent work [1]. This strategy effectively removes the linear divergences inhe… view at source ↗

read the original abstract

In our recent work [1] on lattice QCD calculation of the baryon leading-twist LCDAs within the framework of LaMET, a novel hybrid renormalization scheme is implemented for octet baryon quasi-DAs, yielding reliable results across both perturbative and non-perturbative regions. The numerical simulations are performed using CLQCD ensembles with $N_f = 2+1$ stout-smeared clover fermions and a Symanzik-improved gauge action. Calculations are carried out at three lattice spacings, $a = {0.052, 0.077, 0.105}$ fm. After renormalization, the linear divergences inherent in quasi-DAs are effectively removed, leading to smooth and well-behaved continuum coordinate-space distributions. These results demonstrate the viability of hybrid renormalization frameworks for light-baryon quasi-DAs and provide a robust foundation for future LaMET-based determinations of baryon LCDAs.

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.

Desk Editor's Note private letter to a colleague

The paper applies hybrid renormalization to octet baryon quasi-DAs on three lattice spacings and gets smooth distributions, but the checks that linear divergences are fully gone in the continuum limit are still thin.

read the letter

The main advance is a concrete implementation of the hybrid renormalization scheme for baryon quasi-distribution amplitudes in LaMET. They use CLQCD Nf=2+1 stout-smeared clover ensembles at a=0.052, 0.077, and 0.105 fm, apply the hybrid procedure, and report that the linear divergences drop out, leaving well-behaved coordinate-space distributions across perturbative and non-perturbative regions. That is a useful step beyond their earlier work, because it shows the scheme can be carried through for octet baryons without immediate blow-ups on these volumes and spacings. The multi-spacing setup is a plus; it at least lets them see that the results do not jump around wildly with a. The numerics look stable enough that the method is worth trying on other baryon channels. The soft spot is the limited evidence that the hybrid cutoff truly removes all residual divergences once you take the continuum limit. The abstract calls the removal “effective,” but there is no reported variation of the matching scale in physical units, no explicit test that the extrapolated result is independent of that choice, and no error budget or comparison to known perturbative limits. With only three spacings it is possible that O(a) artifacts from the perturbative kernel are being absorbed into the smooth-looking curves rather than eliminated. This is the kind of technical lattice paper that lattice QCD groups working on nucleon structure or high-energy baryon processes will want to read. A reader who already knows LaMET and quasi-DAs will pick up the implementation details quickly. I would send it to peer review; the numerical demonstration is new enough that referees can ask for the missing continuum controls and decide how much weight to give the results.

Referee Report

2 major / 2 minor

Summary. The paper presents a lattice QCD study of leading-twist light-cone distribution amplitudes for octet baryons within the LaMET framework. It implements a novel hybrid renormalization scheme for quasi-DAs on CLQCD N_f=2+1 ensembles at three lattice spacings (a=0.052, 0.077, 0.105 fm), claiming that linear divergences are effectively removed to yield smooth continuum coordinate-space distributions.

Significance. If the hybrid scheme demonstrably eliminates linear divergences without residual scale-dependent artifacts, the work supplies a practical renormalization method for baryon quasi-DAs and a foundation for future LaMET extractions of baryon LCDAs. The multi-spacing setup is a necessary step toward controlling discretization effects.

major comments (2)

[Abstract] Abstract: the assertion that linear divergences are 'effectively removed' is presented without quantitative evidence, error budgets, or comparison to known limits; this claim is load-bearing for the reliability of the reported distributions.
[Results] Results and methods: with only three lattice spacings and no reported variation of the hybrid matching scale μ0 in physical units, there is no explicit check that the extrapolated continuum result is independent of the hybrid cutoff choice, leaving open the possibility of residual O(a) artifacts from the perturbative kernel.

minor comments (2)

[Methods] Clarify the precise definition of the hybrid matching kernel and the procedure used to combine perturbative and non-perturbative regimes.
[Results] Include explicit tables or plots showing the dependence (or lack thereof) on the intermediate scale μ0 before and after extrapolation.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, indicating where revisions have been made.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion that linear divergences are 'effectively removed' is presented without quantitative evidence, error budgets, or comparison to known limits; this claim is load-bearing for the reliability of the reported distributions.

Authors: We agree that the abstract claim requires supporting context from the main text. In the revised manuscript we have updated the abstract to reference the quantitative evidence: the suppression of linear divergences is demonstrated by the smooth, well-behaved coordinate-space distributions obtained after renormalization, their consistency across the three lattice spacings, and the associated error budgets presented in Section 4. A brief comparison to the expected perturbative behavior at short distances has also been added. revision: yes
Referee: [Results] Results and methods: with only three lattice spacings and no reported variation of the hybrid matching scale μ0 in physical units, there is no explicit check that the extrapolated continuum result is independent of the hybrid cutoff choice, leaving open the possibility of residual O(a) artifacts from the perturbative kernel.

Authors: We acknowledge the validity of this observation. Our hybrid scale μ0 was chosen once to ensure overlap between the perturbative and non-perturbative regimes. In the revision we have added a dedicated paragraph in the results section that quantifies the sensitivity of the continuum extrapolation to μ0 using perturbative estimates of the matching kernel; the residual O(a) effects are shown to lie within the quoted uncertainties. A systematic scan over multiple physical values of μ0 would require new ensembles and is left for future work. revision: partial

standing simulated objections not resolved

A complete numerical demonstration that the continuum limit is independent of the hybrid cutoff μ0 cannot be performed with the present set of three lattice spacings and fixed μ0 choice.

Circularity Check

0 steps flagged

Minor self-citation to prior work; central numerical results remain independent of fitted inputs

full rationale

The paper cites its own recent work [1] to introduce the hybrid renormalization scheme for quasi-DAs, but the abstract and described results focus on lattice simulations at three spacings with standard CLQCD ensembles. No equations are shown that define a parameter from the output data or rename a fit as a prediction. The claim that linear divergences are 'effectively removed' is presented as an empirical outcome of the renormalization procedure applied to the computed quasi-DAs, not as a self-definitional loop. The derivation chain relies on the LaMET framework and numerical data rather than reducing to tautological inputs or self-citation chains that force the final distributions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract provides no explicit free parameters or new entities; relies on standard lattice QCD assumptions.

axioms (1)

domain assumption Lattice QCD with Nf=2+1 stout-smeared clover fermions and Symanzik-improved gauge action correctly approximates continuum QCD at the simulated spacings.
Invoked by the choice of ensembles and action.

pith-pipeline@v0.9.0 · 5453 in / 1157 out tokens · 45051 ms · 2026-05-15T07:18:03.516564+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages · 9 internal anchors

[1]

Baiet al.[Lattice Parton Collaboration (LPC)], Phys

H. Baiet al.[Lattice Parton Collaboration (LPC)], Phys. Rev. D112(2025) no.11, 114515 doi:10.1103/rqmb-x9x8 [arXiv:2508.08971 [hep-lat]]

work page doi:10.1103/rqmb-x9x8 2025
[2]

R.Aaijetal.[LHCb],Nature643(2025)no.8074,1223-1228doi:10.1038/s41586-025-09119- 3 [arXiv:2503.16954 [hep-ex]]

work page doi:10.1038/s41586-025-09119- 2025
[3]

V. L. Chernyak and A. R. Zhitnitsky, Phys. Rept.112(1984), 173 doi:10.1016/0370- 1573(84)90126-1

work page doi:10.1016/0370- 1984
[4]

V. L. Chernyak, A. A. Ogloblin and I. R. Zhitnitsky, Yad. Fiz.48(1988), 1410-1422 doi:10.1007/BF01557663

work page doi:10.1007/bf01557663 1988
[5]

Light-cone distribution amplitudes of the baryon octet

G.S.Bali,V.M.Braun,M.Göckeler,M.Gruber,F.Hutzler,A.Schäfer,R.W.Schiel,J.Simeth, W. Söldner and A. Sternbeck,et al.JHEP02(2016), 070 doi:10.1007/JHEP02(2016)070 [arXiv:1512.02050 [hep-lat]]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep02(2016)070 2016
[6]

G.S.Balietal.[RQCD],Eur.Phys.J.A55(2019)no.7,116doi:10.1140/epja/i2019-12803-6 [arXiv:1903.12590 [hep-lat]]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epja/i2019-12803-6 2019
[7]

G. S. Baliet al.[RQCD], Phys. Rev. D111(2025) no.9, 094517 doi:10.1103/PhysRevD.111.094517 [arXiv:2411.19091 [hep-lat]]

work page doi:10.1103/physrevd.111.094517 2025
[8]

Parton Physics on Euclidean Lattice

X. Ji, Phys. Rev. Lett.110(2013), 262002 doi:10.1103/PhysRevLett.110.262002 [arXiv:1305.1539 [hep-ph]]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.110.262002 2013
[9]

X. Ji, Sci. China Phys. Mech. Astron.57(2014), 1407-1412 doi:10.1007/s11433-014-5492-3 [arXiv:1404.6680 [hep-ph]]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s11433-014-5492-3 2014
[10]

Q. A. Zhanget al.[Lattice Parton], Phys. Rev. Lett.125(2020) no.19, 192001 doi:10.22323/1.396.0477 [arXiv:2005.14572 [hep-lat]]

work page doi:10.22323/1.396.0477 2020
[11]

Huaet al.[Lattice Parton], Phys

J. Huaet al.[Lattice Parton], Phys. Rev. Lett.127(2021) no.6, 062002 doi:10.1103/PhysRevLett.127.062002 [arXiv:2011.09788 [hep-lat]]

work page doi:10.1103/physrevlett.127.062002 2021
[12]

Huaet al.[Lattice Parton], Phys

J. Huaet al.[Lattice Parton], Phys. Rev. Lett.129(2022) no.13, 132001 doi:10.1103/PhysRevLett.129.132001 [arXiv:2201.09173 [hep-lat]]

work page doi:10.1103/physrevlett.129.132001 2022
[13]

M. H. Chuet al.[Lattice Parton (LPC)], Phys. Rev. D106(2022) no.3, 034509 doi:10.1103/PhysRevD.106.034509 [arXiv:2204.00200 [hep-lat]]

work page doi:10.1103/physrevd.106.034509 2022
[14]

X. Y. Hanet al.[Lattice Parton], Phys. Rev. D111(2025) no.3, 034503 doi:10.1103/PhysRevD.111.034503 [arXiv:2410.18654 [hep-lat]]

work page doi:10.1103/physrevd.111.034503 2025
[15]

J. X. Tan, Z. C. Gong, J. Hua, X. Ji, X. Jiang, H. Liu, A. Schäfer, Y. Su, H. Z. Wang and W. Wang,et al.[arXiv:2511.22547 [hep-lat]]

work page arXiv
[16]

M. H. Chuet al.[Lattice Parton], Phys. Rev. D111(2025) no.3, 034510 doi:10.1103/PhysRevD.111.034510 [arXiv:2411.12554 [hep-lat]]. 7 Hybrid Renormalization for Baryon Distribution Amplitudes from Lattice QCD in LaMETMu-Hua Zhang

work page doi:10.1103/physrevd.111.034510 2025
[17]

V. M. Braun, S. E. Derkachov, G. P. Korchemsky and A. N. Manashov, Nucl. Phys. B553 (1999), 355-426 doi:10.1016/S0550-3213(99)00265-5 [arXiv:hep-ph/9902375 [hep-ph]]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0550-3213(99)00265-5 1999
[18]

C. Han, W. Wang, J. Zeng and J. L. Zhang, JHEP07(2024), 019 doi:10.1007/JHEP07(2024)019 [arXiv:2404.04855 [hep-ph]]

work page doi:10.1007/jhep07(2024)019 2024
[19]

Z. C. Huet al.[CLQCD], Phys. Rev. D109(2024) no.5, 054507 doi:10.1103/PhysRevD.109.054507 [arXiv:2310.00814 [hep-lat]]

work page doi:10.1103/physrevd.109.054507 2024
[20]

Zhang, A

R. Zhang, A. V. Grebe, D. C. Hackett, M. L. Wagman and Y. Zhao, Phys. Rev. D112(2025) no.5, L051502 doi:10.1103/6dh4-6k4t [arXiv:2501.00729 [hep-lat]]

work page doi:10.1103/6dh4-6k4t 2025
[21]

G. S. Bali, B. Lang, B. U. Musch and A. Schäfer, Phys. Rev. D93(2016) no.9, 094515 doi:10.1103/PhysRevD.93.094515 [arXiv:1602.05525 [hep-lat]]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.93.094515 2016
[22]

Flavor Symmetry and the Static Potential with Hypercubic Blocking

A. Hasenfratz and F. Knechtli, Phys. Rev. D64(2001), 034504 doi:10.1103/PhysRevD.64.034504 [arXiv:hep-lat/0103029 [hep-lat]]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.64.034504 2001
[23]

T. A. DeGrand, A. Hasenfratz and T. G. Kovacs, Phys. Rev. D67(2003), 054501 doi:10.1103/PhysRevD.67.054501 [arXiv:hep-lat/0211006 [hep-lat]]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.67.054501 2003
[24]

W.I.JayandE.T.Neil,Phys.Rev.D103(2021),114502doi:10.1103/PhysRevD.103.114502 [arXiv:2008.01069 [stat.ME]]

work page doi:10.1103/physrevd.103.114502 2021
[25]

Y. K. Huoet al.[Lattice Parton (LPC)], Nucl. Phys. B969(2021), 115443 doi:10.1016/j.nuclphysb.2021.115443 [arXiv:2103.02965 [hep-lat]]

work page doi:10.1016/j.nuclphysb.2021.115443 2021
[26]

C.Han,Y.Su,W.WangandJ.L.Zhang,JHEP12(2023),044doi:10.1007/JHEP12(2023)044 [arXiv:2308.16793 [hep-ph]]

work page doi:10.1007/jhep12(2023)044 2023
[27]

X. D. Ji, [arXiv:hep-ph/9507322 [hep-ph]]

work page internal anchor Pith review Pith/arXiv arXiv
[28]

Zhang, J

R. Zhang, J. Holligan, X. Ji and Y. Su, Phys. Lett. B844(2023), 138081 doi:10.1016/j.physletb.2023.138081 [arXiv:2305.05212 [hep-lat]]

work page doi:10.1016/j.physletb.2023.138081 2023
[29]

X. Ji, Y. Liu, A. Schäfer, W. Wang, Y. B. Yang, J. H. Zhang and Y. Zhao, Nucl. Phys. B964 (2021), 115311 doi:10.1016/j.nuclphysb.2021.115311 [arXiv:2008.03886 [hep-ph]]

work page doi:10.1016/j.nuclphysb.2021.115311 2021
[30]

J. l. Zhang and M. H. Zhang, Phys. Rev. D113(2026) no.1, 014501 doi:10.1103/rm4s-wlfq [arXiv:2510.14325 [hep-ph]]. 8

work page doi:10.1103/rm4s-wlfq 2026