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arxiv: 2606.30387 · v1 · pith:SQPX36V3new · submitted 2026-06-29 · ✦ hep-lat · hep-ph

Baryon Light-Cone Distribution Amplitudes from Lattice QCD: Formalism, Renormalization, Extrapolation, and Matching

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 03:10 UTC · model grok-4.3

classification ✦ hep-lat hep-ph
keywords baryon light-cone distribution amplitudeslattice QCDlarge-momentum effective theoryquasi-distribution amplitudeshybrid renormalizationLambda baryonleading-twist amplitudes
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The pith

A complete lattice framework converts equal-time quasi-DAs into physical baryon light-cone distribution amplitudes.

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

Baryon light-cone distribution amplitudes are parametrized by two independent momentum fractions, which makes their first-principles calculation harder than for mesons. The paper supplies an end-to-end large-momentum effective theory pipeline that starts from equal-time three-quark quasi-distribution amplitudes computed on the lattice and produces the physical leading-twist LCDAs after renormalization and matching. Key technical steps include a hybrid renormalization scheme on the two-dimensional coordinate plane, a large-distance extrapolation based on the asymptotic fall-off of Euclidean correlators, and the corresponding one-loop matching kernels. The full procedure is demonstrated on the A-structure amplitude of the Lambda baryon using multiple lattice ensembles, with explicit control of continuum, pion-mass, and infinite-momentum extrapolations. The resulting infrastructure enables systematic, x-dependent determinations of baryon LCDAs.

Core claim

We present a systematic large-momentum effective theory framework for determining baryon leading-twist LCDAs from lattice QCD that covers the complete path from equal-time three-quark quasi-distribution amplitudes to physical baryon LCDAs, including formulation of the V, A, and T quasi-DAs, hybrid renormalization, large-λ extrapolation, and one-loop matching, as demonstrated on the Lambda-baryon A-structure.

What carries the argument

The large-momentum effective theory (LaMET) matching relation in the hybrid renormalization scheme that converts finite-momentum quasi-distribution amplitudes into light-cone distribution amplitudes.

If this is right

  • The V, A, and T quasi-DAs can be defined consistently with their spin-flavor and coordinate-space symmetries, including vanishing local limits for antisymmetric amplitudes.
  • Systematic uncertainties associated with the infinite-momentum limit, continuum extrapolation, and physical pion mass can be quantified for any baryon LCDA.
  • The same pipeline supplies the renormalization and matching tools needed for first-principles x-dependent baryon LCDAs.
  • Application to the Lambda baryon supplies a concrete template that can be repeated for the nucleon and other baryons.

Where Pith is reading between the lines

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

  • The hybrid renormalization prescription developed for the (z1,z2) plane may simplify lattice calculations of other multi-parton correlators.
  • Once LCDAs for several baryons are available, comparisons with meson LCDAs could test flavor-symmetry relations at the amplitude level.
  • The large-distance extrapolation method could be tested on simpler objects such as meson LCDAs where independent results already exist.

Load-bearing premise

The newly developed large-λ extrapolation strategy based on the asymptotic large-distance behavior of Euclidean correlators accurately recovers the physical LCDAs.

What would settle it

A higher-momentum or finer-lattice computation of the same Lambda A-structure amplitude whose extrapolated and matched result differs by more than the quoted uncertainties from the result obtained with the seven ensembles used in the paper.

Figures

Figures reproduced from arXiv: 2606.30387 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. Schematic structure of the light-cone three-quark [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Structure of baryon leading-twist quasi-DAs. Three [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Distribution of the lattice ensembles in the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The region partition on the ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Projector dependence of the real part of the normal [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Combined fit of the lattice dispersion relation using [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The region partition for the hybrid renormalization [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Real part of the bare zero-momentum coordinate-space matrix elements [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Extraction of the linear divergence coefficient [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Second-step fitting to the [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Comparison of bare (left) and hybrid-renormalized (right) Λ-baryon [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Residual renormalization-scale dependence of the [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The region partition for large- [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Practical region partition for the numerical im [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Representative line-cut extrapolation results for the Λ [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Representative line-cut extrapolation results for the Λ [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Overview of the original and extrapolated coordinate-space Λ [PITH_FULL_IMAGE:figures/full_fig_p024_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Comparison of quasi-DAs and LCDAs on the [PITH_FULL_IMAGE:figures/full_fig_p026_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Central value of two-dimensional LCDA in physical [PITH_FULL_IMAGE:figures/full_fig_p026_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. LCDAs obtained from the seven ensembles used in this work. Each panel shows the [PITH_FULL_IMAGE:figures/full_fig_p027_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. Combined extrapolation for LCDAs on each each ensemble and momentum, with selected one-dimensional slices [PITH_FULL_IMAGE:figures/full_fig_p029_22.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. comparison between the results from combined and [PITH_FULL_IMAGE:figures/full_fig_p030_24.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. First step of the sequential extrapolation for the Λ [PITH_FULL_IMAGE:figures/full_fig_p030_23.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25. Scale dependence of the Λ [PITH_FULL_IMAGE:figures/full_fig_p031_25.png] view at source ↗
Figure 27
Figure 27. Figure 27: FIG. 27. Comparison of the final Λ [PITH_FULL_IMAGE:figures/full_fig_p032_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: FIG. 28. Absolute uncertainty budget for the final Λ [PITH_FULL_IMAGE:figures/full_fig_p032_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: FIG. 29. Final central value, statistical uncertainty and sys [PITH_FULL_IMAGE:figures/full_fig_p033_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: FIG. 30. Central value of the extrapolated two-dimensional [PITH_FULL_IMAGE:figures/full_fig_p034_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: FIG. 31. Schematic representation of the first dispersive channel in the large-distance expansion of the baryon quasi-DA matrix [PITH_FULL_IMAGE:figures/full_fig_p040_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: FIG. 32. Schematic representation of the second connected channel used in the dispersive analysis of the baryon quasi-DA [PITH_FULL_IMAGE:figures/full_fig_p041_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: FIG. 33. Schematic representation of the third connected channel used in the dispersive analysis of the baryon quasi-DA matrix [PITH_FULL_IMAGE:figures/full_fig_p042_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: FIG. 34. Matched LCDAs for Λ [PITH_FULL_IMAGE:figures/full_fig_p053_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: FIG. 35. Matched LCDAs for Λ [PITH_FULL_IMAGE:figures/full_fig_p054_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: FIG. 36. Matched LCDAs for Λ [PITH_FULL_IMAGE:figures/full_fig_p054_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: FIG. 37. Matched LCDAs for Λ [PITH_FULL_IMAGE:figures/full_fig_p054_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: FIG. 38. Matched LCDAs for Λ [PITH_FULL_IMAGE:figures/full_fig_p054_38.png] view at source ↗
Figure 39
Figure 39. Figure 39: FIG. 39. Matched LCDAs for Λ [PITH_FULL_IMAGE:figures/full_fig_p055_39.png] view at source ↗
Figure 40
Figure 40. Figure 40: FIG. 40. Matched LCDAs for Λ [PITH_FULL_IMAGE:figures/full_fig_p055_40.png] view at source ↗
read the original abstract

Baryon light-cone distribution amplitudes (LCDAs) are inherently multidimensional objects parametrized by two independent longitudinal momentum fractions, making their first-principles determination substantially more challenging than that of meson LCDAs. We present a systematic large-momentum effective theory (LaMET) framework for determining baryon leading-twist LCDAs from lattice QCD. The framework covers the complete path from equal-time three-quark quasi-distribution amplitudes to physical baryon LCDAs. We formulate the leading-twist $V$, $A$, and $T$ quasi-DAs and analyze their spin-flavor and coordinate-space symmetries, including antisymmetric amplitudes with vanishing local limits. We develop a hybrid renormalization prescription on the $(z_1,z_2)$ plane, introduce a newly developed large-$\lambda$ extrapolation strategy based on the asymptotic large-distance behavior of Euclidean correlators, and derive the corresponding one-loop LaMET matching relation in the hybrid renormalization scheme. As a demonstration, we apply the complete analysis pipeline to the $\Lambda$-baryon $A$-structure quasi-DAs using seven $2+1$--flavor lattice ensembles, and use this amplitude to examine the impact of large-distance extrapolation, perturbative matching, and extrapolation to the continuum, physical-pion-mass, and infinite-momentum limits, together with the associated systematic uncertainties. This work provides the formalism, renormalization, extrapolation, and matching infrastructure for first-principles determinations of $x$-dependent 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.

Referee Report

0 major / 3 minor

Summary. The manuscript develops a systematic LaMET framework for baryon leading-twist LCDAs, formulating V/A/T quasi-DAs with their symmetries (including antisymmetric cases with vanishing local limits), introducing hybrid renormalization on the (z1,z2) plane, a new large-λ extrapolation from Euclidean correlator asymptotics, and the corresponding one-loop matching in that scheme. It demonstrates the full pipeline on the Λ-baryon A-structure quasi-DAs using seven 2+1-flavor ensembles and quantifies impacts from large-distance extrapolation, perturbative matching, and extrapolations to continuum, physical pion mass, and infinite momentum, along with associated systematics.

Significance. If the central derivations and extrapolation hold, the work supplies the complete infrastructure needed for first-principles x-dependent baryon LCDAs, a longstanding challenge due to their two-dimensional momentum-fraction dependence. Credit is due for the end-to-end pipeline (quasi-DAs through hybrid renormalization and matching), the novel large-λ strategy grounded in Euclidean asymptotics, and the multi-ensemble demonstration that permits explicit assessment of multiple systematic uncertainties.

minor comments (3)
  1. [Abstract] Abstract: the statement that the framework covers the 'complete path' from quasi-DAs to physical LCDAs would be strengthened by an explicit cross-reference to the section deriving the one-loop matching kernel in the hybrid scheme.
  2. [Formalism (spin-flavor and coordinate-space symmetries)] The discussion of coordinate-space symmetries for antisymmetric amplitudes notes vanishing local limits; an explicit numerical check or table entry confirming this property on the lattice ensembles would improve clarity.
  3. [Large-λ extrapolation strategy] The large-λ extrapolation is applied to the Λ A-structure; the manuscript should state the functional form assumed for the asymptotic large-distance behavior and the fitting range in λ explicitly.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our work and for recommending minor revision. No major comments were provided in the report, so we interpret the recommendation as pertaining to minor editorial or presentational adjustments that we will address in the revised version.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper derives the full LaMET pipeline for baryon LCDAs with explicit new elements: definitions of V/A/T quasi-DAs and their symmetries, hybrid renormalization on the (z1,z2) plane, a large-λ extrapolation from Euclidean correlator asymptotics, and the one-loop matching kernel in that scheme. These steps are formulated equation-by-equation without reducing the output LCDAs to input parameters by construction or to self-citations whose validity is presupposed. The Λ-baryon demonstration quantifies extrapolation, matching, and continuum/physical-mass/infinite-momentum systematics on seven ensembles, providing independent content. Self-citations to prior LaMET work are foundational but not load-bearing for the baryon-specific results.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard LaMET validity for three-quark operators and lattice QCD assumptions; no new free parameters or invented entities are introduced in the abstract description.

axioms (2)
  • domain assumption LaMET applies to baryon leading-twist quasi-distribution amplitudes with the stated spin-flavor symmetries
    Invoked when formulating V, A, T quasi-DAs and when claiming the complete path to physical LCDAs.
  • domain assumption Hybrid renormalization on the (z1,z2) plane removes lattice artifacts without residual scheme dependence after matching
    Central to the renormalization step described in the abstract.

pith-pipeline@v0.9.1-grok · 5859 in / 1403 out tokens · 58705 ms · 2026-06-30T03:10:24.907985+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

142 extracted references

  1. [1]

    Sym” represents the symmetric behavior under thez 1 ↔z 2 exchange, while “A-Sym

    Spinor Contraction of Two-point correlations The source-side interpolators we used in calculation are defined as Eq. (27): Osrc,KE Λ =ϵ ijk 1√ 6 2(ui,T Cγ 5γt dj)s k + (ui,T Cγ 5γt sj)d k + (si,T Cγ 5γt dj)u k , Osrc,KE p =ϵ ijk (ui,T Cγ 5γt dj)u k . (A1) Using ψ=ψ †γt andγ t(Cγ 5γt)†γt =−Cγ 5γt, we have: O src,KE Λ =−ϵ ijk 1√ 6 2 sk (ui Cγ 5γt d j,T ) + ...

  2. [2]

    II C, we stated that the Λ and proton quasi-DAs possess definite symmetry or antisymmetry under the exchangez 1 ↔z 2

    Derivation of Symmetry Properties of Baryon DAs In Sec. II C, we stated that the Λ and proton quasi-DAs possess definite symmetry or antisymmetry under the exchangez 1 ↔z 2. In this subsection, we show that these properties follow directly from the propagator-level structure of the nonlocal two-point correlation functions defined above, together with the ...

  3. [3]

    Heavy-quark Representation of Wilson Lines Following Ref. [114], the first step in deriving the large-distance behavior of Euclidean correlators is to replace the Wilson lines in the nonlocal baryon operators by the propagators of auxiliary heavy quarks. This trick makes it possible to use a standard spectral decomposition in terms of physical color-singl...

  4. [4]

    The asymptotic behavior forz→ ∞is obtained by the saddle-point approximation of the phase-space integral

    Dispersive Relation To analyze the asymptotic behavior of the nonlocal matrix elements, one inserts two complete sets of intermediate states into the matrix elements: ϵijk ⟨0| ¯Qα′,i′(z1)qi′ α(z1)Q i α′′(0)hk γ(0)Gj β′′(0) ¯Gβ′,j′(z2)gj′ β (z2)|B(P)⟩ = X X1,X2 Z dΓX1(k1) dΓX2(k2)⟨0| ¯Qα′qα(z1)|X1(k1)⟩ ⟨X 1(k1)|Qα′′hγGβ′′(0)|X2(k2)⟩ ⟨X 2(k2)| ¯Gβ′gβ(z2)|B(...

  5. [5]

    Classification of Connected Channels and Asymptotic Behavior The asymptotic behavior of the baryon quasi-DA matrix elements can be analyzed by inserting complete sets of intermediate states between the heavy-quark operators in Eq. (B4). Depending on how the external baryon state|B(P)⟩is connected to the quark operators, the contributions are classified in...

  6. [6]

    Here we analyze the general spin structures and binding energies enter the asymptotic forms

    General Structure of the Extrapolation In this work, the exponentials in the asymptotic forms of quasi-DAs contain the binding energies selected by the channel quantum numbers. Here we analyze the general spin structures and binding energies enter the asymptotic forms. a. Spin Structures of different amplitudes The spin structure connecting theqandgquarks...

  7. [7]

    In addition, the intermediate states can also include heavy–light baryons withJ P = 1/2 − andJ P = 1/2+, whose binding energies we denote by Λ 1/2− and Λ1/2+ , respectively

    and axial-vector (1 +, e.g.D 1,B 1) mesons, which share the same binding energy Λ 0+ = Λ1+ up toO(Λ QCD/mQ) corrections. In addition, the intermediate states can also include heavy–light baryons withJ P = 1/2 − andJ P = 1/2+, whose binding energies we denote by Λ 1/2− and Λ1/2+ , respectively. For each channel, the specific set of binding energies that ap...

  8. [8]

    GA,1 + G(1) A,1 |z1| + G(2) A,1 |z2| +· · · # + eiz2P z e−Λ0− |z1|e−Λ1/2− |z2|

    Full Asymptotic Expressions The (z1, z2) plane is divided into several regions according to which coordinate separations become large, as discussed in Sec. V A, following the same convention and region partition shown in Fig. 13. In the derivation above, we used the casez 1z2 <0 as an illustrative example. In the full baryon quasi-DA matrix element, howev...

  9. [9]

    Expressions of theC n Functions The functionsC n appearing in one-loop matching kernel in the MS scheme Eqs. (67)–(68) are explicitly defined as 48 C2(x1, x2;y 1, y2;P z, µ) =    (x1 +y 1)(x3 +y 3) y1y3(y1 −x 1) ln y1 −x 1 −x1 − x3(x1 +y 1 + 2y3) y3(y1 −x 1)(y1 +y 3) ln x3 −x1 x1 <0 (x1 −3y 1 −2y 3)x1 y1(x3 −y 3)(y1 +y 3) − ...

  10. [10]

    Explicit Forms of the Hybrid Counterterms In hybrid renormalization scheme, to computing the hard kernels and express the complicated hybrid counterterms, it is convenient to define a set of master integrals as follows: I1 {L2, L1}, p ≡ Z L2 L1 dz 2π e−ipz ln(z2) = + i γE + log(−ipL1) + −1 + e ipL1 log(L1) + Γ(0,−ipL1) 2πp − i γE + log(−ipL2) + −1 + e ipL...

  11. [11]

    + 3 4 ln((z1 −z 2)2) # × θ(2zs − |z1|)θ(zs − |z2|) +θ(z s − |z1|)θ(|z2| −z s)θ(2zs − |z2|) =7 8   +I0({2zs,−2z s}, p2)I1({zs,−z s}, p1) + I1({zs,−z s}, p2) I0({2zs,−2z s}, p1)−I0({z s,−z s}, p1) +I0({zs,−z s}, p1)I1({2zs,−2z s}, p2) + I0({zs,−z s}, p2) I1({2zs,−2z s}, p1)−I1({z s,−z s}, p1)   + 3 8π(p1 +p 2)   + sin((p1 +p 2)...

  12. [12]

    + 7 8 ln((2zs)2) + 3 4 ln((z1 −2z ssign[z2])2) # = 1 8   +6e2ip1zsI1({−zs,−3z s}, p1)I0({∞,2z s}, p2) + 6e−2ip1zsI1({3zs, zs}, p1)I0({−2zs,−∞}, p 2) +7 I0({∞,−∞}, p 2)−I0({2z s,−2z s}, p2) log(4z2 s)I0({zs,−z s}, p1) + I1({zs,−z s}, p1)   , (C9) I V /A HSII(p1, p2) ≡ Z dz1 2π dz2 2π e−ip1z1−ip2z2 θ(|z1| −2z s)θ(zs − |z2|)× " 7 8 ln((2zs)2) + 7 8 ln(z2

  13. [13]

    (C13) b.Tcounterterms TheTamplitude has different spin structure fromVandAamplitudes, certain perturbative loop corrections vanish

    + 3 4 ln((sign[z1]2zs −z 2)2) # = 1 8   +6e2ip2zsI1({−zs,−3z s}, p2)I0({∞,2z s}, p1) + 6e−2ip2zsI1({3zs, zs}, p2)I0({−2zs,−∞}, p 1) +7 I0({∞,−∞}, p 1)−I0({2z s,−2z s}, p1) log(4z2 s)I0({zs,−z s}, p2) + I1({zs,−z s}, p2)   , (C10) I V /A HSIII(p1, p2) ≡ Z dz1 2π dz2 2π e−ip1z1−ip2z2 θ(|z1| −z s)θ(|z2| −z s)θ(zs − |z1 −z 2|) × " 7 8 ln((zs + (z1 −z 2)θ(...

  14. [14]

    + 1 2 ln((z1 −z 2)2) # × θ(2zs − |z1|)θ(zs − |z2|) +θ(z s − |z1|)θ(|z2| −z s)θ(2zs − |z2|) =7 8   +I0({2zs,−2z s}, p2)I1({zs,−z s}, p1) + I1({zs,−z s}, p2) I0({2zs,−2z s}, p1)−I0({z s,−z s}, p1) +I0({zs,−z s}, p1)I1({2zs,−2z s}, p2) + I0({zs,−z s}, p2) I1({2zs,−2z s}, p1)−I1({z s,−z s}, p1)   + 1 4π(p1 +p 2)   + sin((p1 +p 2)...

  15. [15]

    + 7 8 ln((2zs)2) + 1 2 ln((z1 −2z ssign[z2])2) # = 1 8   +4e2ip1zsI1({−zs,−3z s}, p1)I0({∞,2z s}, p2) + 4e−2ip1zsI1({3zs, zs}, p1)I0({−2zs,−∞}, p 2) +7 I0({∞,−∞}, p 2)−I0({2z s,−2z s}, p2) log(4z2 s)I0({zs,−z s}, p1) + I1({zs,−z s}, p1)   , (C15) I T HSII(p1, p2) ≡ Z dz1 2π dz2 2π e−ip1z1−ip2z2 θ(|z1| −2z s)θ(zs − |z2|)× " 7 8 ln((2zs)2) + 7 8 ln(z2

  16. [16]

    (C19) Appendix D: More Results for LaMET Matching We present more details of the LCDAs obtained after LaMET matching in Figs

    + 1 2 ln((sign[z1]2zs −z 2)2) # = 1 8   +4e2ip2zsI1({−zs,−3z s}, p2)I0({∞,2z s}, p1) + 4e−2ip2zsI1({3zs, zs}, p2)I0({−2zs,−∞}, p 1) +7 I0({∞,−∞}, p 1)−I0({2z s,−2z s}, p1) log(4z2 s)I0({zs,−z s}, p2) + I1({zs,−z s}, p2)   , (C16) I T HSIII(p1, p2) ≡ Z dz1 2π dz2 2π e−ip1z1−ip2z2 θ(|z1| −z s)θ(|z2| −z s)θ(zs − |z1 −z 2|) × " 7 8 ln((zs + (z1 −z 2)θ(z1 ...

  17. [17]

    Orthogonal polynomials up to third moments We use the shorthandx ijk ≡(x i, xj, xk),x i +x j +x k = 1 in following discussions. For a generic leading-twist amplitude, the truncated conformal parameterization up to third moments takes the form: FΛ(x123) = 120x1x2x3 " ηΛ,0 + 3X n=1 nX m=0 ηΛ,nm Pnm(x123) +· · · # ,(E1) where the coefficientsη Λ,nm denote di...

  18. [18]

    These expressions are obtained by imposing the exchange symmetries of the Λ-baryon leading-twist amplitudes, VΛ(x123) =−V Λ(x213), A Λ(x123) = +AΛ(x213), T Λ(x123) =−T Λ(x213)

    Fully expanded LCDAs in the normalization convention of this work We now give the explicitV Λ(x123),A Λ(x123), andT Λ(x123) parameterizations used in our numerical fit. These expressions are obtained by imposing the exchange symmetries of the Λ-baryon leading-twist amplitudes, VΛ(x123) =−V Λ(x213), A Λ(x123) = +AΛ(x213), T Λ(x123) =−T Λ(x213). (E3) The re...

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    These Φ/Π amplitudes are linear combinations of the same leading-twist LCDAsV,A, andT, rather than independent non-perturbative functions

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