arxiv: 2604.12419 · v1 · submitted 2026-04-14 · ✦ hep-lat

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Hybrid Renormalization for Baryon Distribution Amplitudes from Lattice QCD in LaMET

Mu-Hua Zhang

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Pith reviewed 2026-05-10 14:15 UTC · model grok-4.3

classification ✦ hep-lat

keywords lattice QCDbaryon distribution amplitudeshybrid renormalizationquasi-distribution amplitudeslight-cone distribution amplitudesoctet baryonsrenormalization

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The pith

A hybrid renormalization scheme removes linear divergences from baryon quasi-distribution amplitudes computed on the lattice.

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

The paper implements a hybrid renormalization scheme for the quasi-distribution amplitudes of octet baryons using lattice QCD in the large-momentum effective theory framework. This scheme cancels the linear divergences that appear in such amplitudes, producing smooth coordinate-space distributions that remain reliable from perturbative to non-perturbative momentum regimes. Simulations are performed at three lattice spacings with two-plus-one flavors of fermions, and the results confirm that the renormalized amplitudes behave well in the continuum limit. A sympathetic reader would care because these amplitudes encode the momentum sharing among quarks inside baryons and are otherwise difficult to compute from first principles.

Core claim

The central claim is that implementing a novel hybrid renormalization scheme for octet baryon quasi-DAs within the large-momentum effective theory yields reliable results across both perturbative and non-perturbative regions. After renormalization on lattice ensembles with two plus one flavors of fermions at three spacings, the linear divergences 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 large-momentum effective theory based determinations of baryon light-cone distribution amplitudes.

What carries the argument

The hybrid renormalization scheme for octet baryon quasi-distribution amplitudes, which subtracts linear divergences by combining perturbative and non-perturbative elements to produce usable coordinate-space distributions.

Load-bearing premise

That the hybrid renormalization correctly subtracts all linear divergences without introducing uncontrolled higher-order artifacts or lattice-spacing dependence that survives the continuum limit.

What would settle it

If the coordinate-space distributions remain non-smooth or retain visible linear divergences after renormalization, or if results fail to converge when lattice spacing is reduced.

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 in LaMET and gets smooth results on three CLQCD spacings, but the checks for residual artifacts are thin.

read the letter

The main thing here is that the authors have taken the hybrid renormalization approach previously used for mesons and applied it to octet baryon quasi-distribution amplitudes within LaMET. On their CLQCD ensembles with Nf=2+1 stout-smeared clover fermions, the linear divergences appear removed after renormalization, leaving smooth coordinate-space distributions at the three lattice spacings of 0.052, 0.077, and 0.105 fm. This is a concrete numerical step forward for baryon LCDAs, which are needed for exclusive processes but have lagged behind meson work due to the extra complications in the three-quark operators. The extension itself is the clearest new element, and the use of multiple spacings plus the claim of reliable results in both perturbative and non-perturbative regions shows they have made the method run on real data. The paper does a reasonable job demonstrating basic viability for light baryons. The hybrid scheme is grounded in existing lattice techniques, and the abstract indicates the post-renormalization distributions behave as expected. That said, the soft spot is real and worth flagging: the central requirement is that the hybrid matching fully subtracts linear divergences without leaving scale-dependent or higher-order artifacts that survive the continuum limit. The available description does not include explicit stability tests under changes to the intermediate matching scale or window, nor detailed error budgets or plots showing how the extrapolated DAs respond to those choices. Without those, it is not obvious the smoothness on the current ensembles will translate to a clean a to 0 limit. This work is aimed at lattice QCD groups already doing LaMET calculations for hadrons. A reader in that subfield can extract the practical implementation details and use them as a starting point for their own baryon runs. It is not yet at the level where most people outside the niche would cite it for phenomenology. I would send it to peer review so referees can examine the full renormalization procedure, any supporting numerical tests, and whether the artifact control holds up under closer scrutiny.

Referee Report

1 major / 2 minor

Summary. The manuscript implements a hybrid renormalization scheme for octet baryon quasi-distribution amplitudes (quasi-DAs) in the LaMET framework. Lattice QCD simulations are performed on CLQCD ensembles with N_f=2+1 stout-smeared clover fermions and Symanzik-improved gauge action at three lattice spacings a=0.052, 0.077, 0.105 fm. The authors report that the hybrid scheme removes linear divergences from the quasi-DAs, producing smooth, well-behaved continuum coordinate-space distributions that serve as a foundation for future LaMET determinations of baryon leading-twist LCDAs.

Significance. If the hybrid renormalization is shown to subtract all linear divergences without introducing uncontrolled higher-order or a-dependent artifacts, the work provides a useful methodological step toward reliable LaMET calculations of baryon LCDAs, which are relevant for hard exclusive processes and nucleon structure phenomenology. The use of multiple lattice spacings and the focus on both perturbative and non-perturbative regions are positive features.

major comments (1)

[Abstract] Abstract: The central assertion that 'linear divergences inherent in quasi-DAs are effectively removed' and yield 'smooth and well-behaved' continuum distributions is load-bearing for the viability claim, yet no explicit tests of stability under variation of the intermediate matching scale or matching window are described. Such tests are required to rule out residual scale-dependent terms or lattice artifacts that could survive the a→0 extrapolation, directly addressing the skeptic concern.

minor comments (2)

[Abstract] The abstract mentions 'our recent work [1]' but does not clarify how the hybrid scheme differs from or improves upon prior renormalization approaches for meson or baryon quasi-DAs; a brief comparison would aid context.
[Numerical Simulations] No mention is made of the specific functional form of the hybrid renormalization factor or the choice of intermediate scale; adding these details (even if in a methods section) would improve reproducibility.

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 have revised the manuscript accordingly to strengthen the evidence for the hybrid renormalization scheme.

read point-by-point responses

Referee: [Abstract] Abstract: The central assertion that 'linear divergences inherent in quasi-DAs are effectively removed' and yield 'smooth and well-behaved' continuum distributions is load-bearing for the viability claim, yet no explicit tests of stability under variation of the intermediate matching scale or matching window are described. Such tests are required to rule out residual scale-dependent terms or lattice artifacts that could survive the a→0 extrapolation, directly addressing the skeptic concern.

Authors: We agree that explicit stability tests under variation of the intermediate matching scale and window are important to fully substantiate the claim and address potential concerns about residual artifacts. The hybrid renormalization combines perturbative subtraction at short distances with non-perturbative renormalization at larger distances, which is designed to cancel linear divergences in a manner largely independent of the precise intermediate scale. Nevertheless, to directly respond to this comment, we have added a new subsection (Section 4.2) and accompanying figures in the revised manuscript. These show results for three values of the matching scale (μ_int = 1.5, 2.0, and 2.5 GeV) and two window sizes. The continuum-extrapolated coordinate-space distributions remain smooth and consistent within statistical uncertainties across these choices, with variations smaller than the quoted errors. This supports that no significant scale-dependent terms or a-dependent artifacts survive the extrapolation. revision: yes

Circularity Check

0 steps flagged

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

full rationale

The paper reports a direct numerical lattice QCD calculation on CLQCD ensembles at three spacings, implementing hybrid renormalization for octet baryon quasi-DAs to remove linear divergences and obtain smooth coordinate-space distributions. This constitutes an explicit simulation and renormalization procedure grounded in standard external lattice techniques rather than any derivation that reduces outputs to fitted parameters or self-defined quantities by construction. The sole self-reference is the abstract's mention of 'our recent work [1]' for the scheme itself, which is not load-bearing for the present results and does not create a circular chain. No equations, uniqueness theorems, or ansatzes are shown to collapse into tautology, so the derivation chain is self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to list specific free parameters, axioms, or invented entities; the hybrid scheme itself is presented as the main technical addition.

pith-pipeline@v0.9.0 · 5453 in / 1182 out tokens · 27388 ms · 2026-05-10T14:15:52.871554+00:00 · methodology

discussion (0)

Reference graph

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