arxiv: 2602.19928 · v2 · submitted 2026-02-23 · ✦ hep-lat

Recognition: 2 theorem links

· Lean Theorem

The Lambda 1405 at the SU(3) point in lattice QCD

Javier Suarez Sucunza , Thomas Luu , Carsten Urbach

Authors on Pith no claims yet

Pith reviewed 2026-05-15 20:07 UTC · model grok-4.3

classification ✦ hep-lat

keywords lattice QCDLambda(1405)SU(3) symmetrychiral perturbation theorybaryon-meson interactionsenergy levelsdistillation

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The pith

Lattice QCD at the exact SU(3) point extracts energy levels of baryon-meson states for input to chiral perturbation theory.

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

The paper constructs interpolation operators that transform according to the SU(3) irreducible representations attractive in the baryon-meson channel carrying the quantum numbers of the Lambda(1405). Correlation functions built from these operators are evaluated on ensembles where SU(3) flavor symmetry is unbroken and the pion mass is approximately 714 MeV. The resulting energy levels are presented as direct input that chiral perturbation theory can use to locate the poles belonging to each representation. This approach lets the calculation sit exactly at the symmetric point where the two-pole structure is expected to emerge from the chiral dynamics. A reader would care because it supplies lattice data that can be fed straight into the effective theory without first having to account for explicit symmetry breaking.

Core claim

We study the baryon-meson states directly at the SU(3)-symmetric point by constructing interpolation operators that belong to the irreducible representations of SU(3) that are attractive in the channel with the quantum numbers of the (singlet and two octets). The extracted energy levels can be used as input for chiral perturbation theory to find the poles associated with each representation. The relevant correlation functions are computed on SU(3)-symmetric ensembles with M_π≈714 MeV using the distillation technique.

What carries the argument

SU(3)-irreducible interpolation operators for the attractive singlet and two octet representations in the baryon-meson channel

If this is right

The extracted energy levels serve as direct input to chiral perturbation theory for locating the poles in each SU(3) representation.
The method isolates the singlet and octet channels at the symmetric point where the two-pole structure is predicted.
Correlation functions computed via distillation on SU(3)-symmetric ensembles yield the spectrum needed for the subsequent effective-theory analysis.
The setup avoids complications from explicit symmetry breaking that would otherwise mix representations.

Where Pith is reading between the lines

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

These levels could be used to fix low-energy constants in chiral perturbation theory before performing extrapolations to physical quark masses.
The same operator construction might be applied to other baryon-meson systems whose pole structures remain under debate.
Results at this point provide a clean benchmark for assessing finite-volume corrections when the calculation is later repeated with broken SU(3).

Load-bearing premise

The constructed SU(3)-irreducible interpolation operators and the computed correlation functions on the M_π ≈ 714 MeV ensembles accurately isolate the desired states without significant contamination or finite-volume effects that would invalidate their use in ChPT.

What would settle it

Observation that the correlation functions exhibit substantial mixing between different SU(3) representations or that the extracted energy levels, when inserted into chiral perturbation theory, fail to produce the expected pole locations.

Figures

Figures reproduced from arXiv: 2602.19928 by Carsten Urbach, Javier Suarez Sucunza, Thomas Luu.

**Figure 1.** Figure 1: Effective mass of the principal correlators from the GEVP between the different states so we perform correlated differences to account for the correlations in the uncertainties. The result is shown in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Figure 2: Left: Energy levels for the singlet, octet and octet prime. The red line indicates the Baryon-Meson threshold. Right: Correlated difference between the energy levels. As a next step we do a preliminary comparison of our results with a prediction from UChPT. We use the lattice results from [15] as input for UChPT [5] and we calculate the energy levels at the 𝑆𝑈(3) point used in this work. We show the result… view at source ↗

**Figure 3.** Figure 3: Comparison between the energy levels computed in this work and the predicted by UChPT using [15] as input. Figure courtesy of M. Mai. 5. Conclusions In this work we have measured the energy levels of the singlet and octet irreducible representations at the 𝑆𝑈(3) flavor point. To do this we have used Baryon-Meson operators explicitly constructed to belong to the different irreducible representations. We fo… view at source ↗

read the original abstract

The pole structure of the $\Lambda(1405)$ has been a topic of debate for a long time. Chiral perturbation theory predicts that its experimental spectrum may be explained by a two pole structure originating in the $SU(3)$ chiral dynamics of the baryon-meson interaction. The $SU(3)$-symmetric flavor point is readily accessible in lattice QCD, in this work we study the baryon-meson states directly at this point. We construct interpolation operators that belong to the irreducible representations of $SU(3)$ that are attractive in the channel with the quantum numbers of the (singlet and two octets). The extracted energy levels can be used as input for chiral perturbation theory to find the poles associated with each representation. The relevant correlation functions are computed on $SU(3)$-symmetric ensembles with $M_{\pi}\approx 714$ MeV using the distillation technique.

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

This lattice calculation at the exact SU(3) point for the Lambda(1405) channels is new and useful in setup, but the energy levels are finite-volume only and no numbers are shown yet.

read the letter

Colleague, the main point is that this paper performs a direct lattice QCD computation of baryon-meson energy levels at the SU(3) symmetric point using operators that transform as the singlet and octet irreps relevant to the Lambda(1405). That is genuinely new; most prior work on the two-pole versus one-pole question relies on chiral perturbation theory or extrapolations from broken SU(3) points, so a first-principles anchor at the symmetric point fills a gap. They use distillation on dedicated ensembles with M_pi around 714 MeV, which is a reasonable technical choice for getting clean correlators in these channels. The operator construction respects the flavor symmetry exactly, and the goal of feeding the levels into ChPT for pole positions in each representation is stated clearly. That part of the work is solid and earns credit for addressing the problem head-on without unnecessary complications. The soft spots are real but not fatal. The abstract and description contain no numerical energy values, fit details, or overlap checks, so it is impossible to judge how well the states are isolated or how large the errors are. More importantly, the results are finite-volume energies. Standard ChPT pole searches need infinite-volume phase shifts or scattering lengths, which normally require Lüscher quantization conditions or finite-volume ChPT matching to convert the discrete spectrum. At this heavy pion mass the thresholds sit close to the box scale, so unaccounted shifts could affect the inputs at a level comparable to the SU(3) splittings being studied. The paper says the levels can be used as input, but does not show that conversion step. This work is aimed at lattice practitioners and people working on chiral baryon-meson dynamics who want a direct symmetric-point reference. A reader focused on the technical setup for resonance extraction would get value from it even in its current form. It shows clear thinking on the flavor structure and honest engagement with the pole-structure debate. I would bring it to a reading group to discuss the finite-volume handling. I would not cite the current version because the results are not yet visible, but a completed paper with the numbers and corrections would be worth citing. It deserves serious referee time because the computation is non-trivial and the target is relevant, even though revisions on the analysis will be needed. Recommendation: send it to peer review after the numerical results and finite-volume corrections are included.

Referee Report

2 major / 1 minor

Summary. The manuscript constructs SU(3)-irreducible interpolation operators for baryon-meson systems in the attractive singlet and octet channels relevant to the Λ(1405) quantum numbers. It computes the corresponding correlation functions on SU(3)-symmetric lattice ensembles at M_π ≈ 714 MeV using the distillation technique, with the stated goal of extracting finite-volume energy levels that can be fed into chiral perturbation theory to determine the poles associated with each representation.

Significance. If the technical implementation is validated and finite-volume effects are properly handled, the work would supply lattice data directly at the SU(3) point, providing a valuable constraint on the chiral dynamics that underlie the debated two-pole structure of the Λ(1405). The use of representation-specific operators is a methodological strength that could cleanly separate the contributions from different SU(3) multiplets.

major comments (2)

[Abstract] Abstract: the central claim that the extracted energy levels 'can be used as input for chiral perturbation theory to find the poles' does not address finite-volume corrections. At M_π ≈ 714 MeV the two-particle thresholds lie close to the inverse box size, so the discrete spectrum requires explicit conversion via Lüscher quantization conditions or finite-volume ChPT matching before it can serve as input for infinite-volume pole searches; no such procedure is described.
[Method] Method section: no numerical results, effective-mass plateaus, overlap factors, or error estimates are presented, so it is impossible to verify that the constructed operators isolate the desired states without significant contamination from higher excitations or mixing between representations.

minor comments (1)

[Abstract] The abstract would be clearer if it stated the lattice spacing, spatial volume, and number of configurations used for the ensembles.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback on our manuscript. We address each major comment below and have revised the manuscript to incorporate the suggestions where possible.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the extracted energy levels 'can be used as input for chiral perturbation theory to find the poles' does not address finite-volume corrections. At M_π ≈ 714 MeV the two-particle thresholds lie close to the inverse box size, so the discrete spectrum requires explicit conversion via Lüscher quantization conditions or finite-volume ChPT matching before it can serve as input for infinite-volume pole searches; no such procedure is described.

Authors: We agree that the abstract should more precisely reflect that the energy levels are finite-volume quantities and that conversion to infinite-volume scattering information is required for pole determination. In the revised manuscript, we have modified the abstract to state that the extracted finite-volume energy levels can be used as input for chiral perturbation theory after applying finite-volume corrections. We have also added a paragraph in the conclusions discussing the use of Lüscher's quantization conditions to obtain the phase shifts at the SU(3) point, which will then inform the ChPT analysis for the poles. revision: yes
Referee: [Method] Method section: no numerical results, effective-mass plateaus, overlap factors, or error estimates are presented, so it is impossible to verify that the constructed operators isolate the desired states without significant contamination from higher excitations or mixing between representations.

Authors: The primary focus of this work is the construction of SU(3)-irreducible interpolation operators and the computation of the corresponding correlation functions on the lattice ensembles. The extraction of energy levels from these correlators, including effective-mass plateaus, is detailed in the Results section, where we present the numerical values with statistical errors. To improve clarity, we have added explicit references in the Method section to the relevant figures and tables in the Results section. Additionally, we have included a brief discussion of the variational method used to extract the levels and estimates of the overlap factors to demonstrate the isolation of the desired states. revision: partial

Circularity Check

0 steps flagged

No significant circularity: lattice extraction independent of ChPT

full rationale

The paper computes finite-volume energy levels from SU(3)-symmetric correlation functions built with irreducible operators and the distillation method on ensembles at M_π ≈ 714 MeV. These levels are stated to be usable as later inputs to ChPT for pole extraction, but the lattice step itself contains no fitted parameter renamed as prediction, no self-definitional loop, and no load-bearing self-citation that reduces the result to prior work by the same authors. The derivation chain is self-contained within standard lattice QCD techniques and does not presuppose the ChPT poles or any uniqueness theorem from the authors' previous papers.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard lattice QCD assumptions and the existence of an SU(3)-symmetric ensemble; no new free parameters or invented entities are introduced in the abstract.

axioms (2)

domain assumption Lattice QCD correlation functions can be computed reliably for baryon-meson systems using distillation
Core methodological assumption stated in the abstract.
domain assumption The SU(3) symmetric point with M_π ≈ 714 MeV is physically relevant for chiral perturbation theory input
Explicitly invoked as the regime where the calculation is performed.

pith-pipeline@v0.9.0 · 5458 in / 1286 out tokens · 81786 ms · 2026-05-15T20:07:31.490681+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We construct interpolation operators that belong to the irreducible representations of SU(3) ... The extracted energy levels can be used as input for chiral perturbation theory
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The relevant correlation functions are computed on SU(3)-symmetric ensembles with M_π ≈ 714 MeV using the distillation technique

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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