arxiv: 2604.04433 · v1 · submitted 2026-04-06 · ✦ hep-lat · hep-ph· nucl-th

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Lattice studies of chimera baryons in Sp(4) gauge theory

Jong-Wan Lee , Ed Bennett , Luigi Del Debbio , Niccol\`o Forzano , Ryan C. Hill , Deog Ki Hong , Ho Hsiao , C.-J. David Lin

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Biagio Lucini Alessandro Lupo Maurizio Piai Davide Vadacchino Fabian Zierler

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Pith reviewed 2026-05-10 19:50 UTC · model grok-4.3

classification ✦ hep-lat hep-phnucl-th

keywords chimera baryonsSp(4) gauge theorycomposite Higgs modelstop partial compositenesslattice spectrumquenched approximationdynamical fermionsspectral density analysis

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The pith

Lattice calculations determine the low-lying spectrum of chimera baryons in an Sp(4) gauge theory for composite Higgs models.

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

Chimera baryons are bound states made of two fermions in the fundamental representation and one in the antisymmetric representation of a non-Abelian gauge group. In composite Higgs models with top partial compositeness, these spin-1/2 states act as partners to the top quark and help generate its large mass. The work carries out non-perturbative lattice simulations to extract the spectrum first in the quenched approximation, extrapolating to the continuum and massless limits, and then with dynamical fermions using a spectral density method across multiple lattice parameters.

Core claim

In a specific Sp(4) realization of composite Higgs models, non-perturbative lattice computations give the low-lying chimera baryon spectrum in the quenched approximation after taking the continuum and massless-fermion limits, while dynamical-fermion runs measure the spectrum and matrix elements directly through a newly developed spectral density analysis for several choices of lattice spacing and volume.

What carries the argument

Non-perturbative lattice gauge simulations with spectral density analysis applied to fermion bound states built from fundamental and antisymmetric representations.

Load-bearing premise

The quenched approximation supplies a reliable qualitative picture of the spectrum that survives the inclusion of dynamical fermions, and the chosen Sp(4) theory with the given representations forms a viable composite Higgs model with top partial compositeness.

What would settle it

Observation that the chimera baryon masses extracted on finer lattices or with dynamical fermions remain far above the scale needed to generate the top-quark mass would falsify the model's ability to explain the top mass via partial compositeness.

Figures

Figures reproduced from arXiv: 2604.04433 by Alessandro Lupo, Biagio Lucini, C.-J. David Lin, Davide Vadacchino, Deog Ki Hong, Ed Bennett, Fabian Zierler, Ho Hsiao, Jong-Wan Lee, Luigi Del Debbio, Maurizio Piai, Niccol\`o Forzano, Ryan C. Hill.

**Figure 3.** Figure 3: Summary plot for the mass spectrum of the Sp(4) gauge theory cou [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 1.** Figure 1: In the range of hyperquark masses considered, we find [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

read the original abstract

We study chimera baryons, fermion bound states composed of two (hyper)quarks transforming in the fundamental and one in the antisymmetric representation of a non-Abelian gauge group. While in QCD they coincide with ordinary baryons, in composite Higgs models (CHMs) with top partial compositeness, spin-1/2 chimera baryons serve as partners of the top quark and are responsible for its large mass. We perform non-perturbative lattice calculations of the low-lying spectrum of the chimera baryons, in a specific realization of CHMs based on a Sp(4) gauge theory. In the quenched approximation, we present the numerical results in the continuum and massless limits. Then, for dynamical fermions, we measure the spectrum and matrix elements by employing a newly developed spectral density analysis for several choices of the lattice parameters.

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 paper gives the first quenched continuum-extrapolated chimera baryon spectrum in Sp(4) plus limited dynamical results with a new spectral method, but the dynamical section is preliminary.

read the letter

The key point is that they have produced the first continuum and massless extrapolated quenched results for the low-lying chimera baryon spectrum in this Sp(4) setup, along with some dynamical spectrum and matrix element numbers obtained via a new spectral density approach. That quenched extrapolation is the concrete new output here. Prior work on similar states existed, but this one reaches the continuum limit in the quenched case and adds the dynamical measurements for a few parameter points. The quenched part follows standard lattice spectroscopy practices and looks cleanly executed on the numbers shown in the abstract. The dynamical extension is a step forward for the partial compositeness application, even if it stays at fixed lattice spacings and masses. The new analysis method is worth noting as a technical addition. On the stress-test concern about quenched results not holding up once dynamical fermions are restored: the paper does not appear to treat the quenched spectrum as a reliable proxy or claim it remains qualitatively valid without qualification. It presents the quenched extrapolations first, then separately reports dynamical results at several points, so the missing determinant back-reaction does not undermine the central claims as strongly as the note suggests. The real limitation is that the dynamical data remain sparse—no full continuum or chiral extrapolation yet—and the validation details for the spectral density method are not visible from the abstract, so error budgets and systematic checks will need close reading. This work is aimed at the BSM lattice community building composite Higgs models with top partial compositeness. Readers who need numerical spectrum inputs or want to see the new analysis technique applied will find it useful. The quenched results are solid enough and the dynamical part is honest incremental progress, so the paper deserves a serious referee to verify the method and full systematics. I would send it to peer review rather than desk reject.

Referee Report

2 major / 2 minor

Summary. The manuscript reports non-perturbative lattice calculations of the low-lying spectrum of chimera baryons (bound states of two fundamental and one antisymmetric fermions) in Sp(4) gauge theory, motivated by composite Higgs models with top partial compositeness. Quenched results are presented after continuum and massless extrapolations; dynamical results for spectrum and matrix elements are obtained via a newly developed spectral density analysis at several lattice parameters.

Significance. If the central claims hold, the work supplies valuable non-perturbative benchmarks for chimera baryon masses and matrix elements in a concrete CHM realization, which can guide model building and phenomenology. Strengths include the quenched continuum/massless extrapolations and the technical development of the spectral density method for dynamical mixed-representation fermions; these constitute concrete advances in lattice techniques for beyond-Standard-Model applications.

major comments (2)

[dynamical fermions section] Section presenting dynamical results: the central claim that the quenched spectrum 'remains qualitatively valid' once dynamical fermions are included is load-bearing but unsupported by a direct quantitative comparison at matched bare parameters or by reweighting estimates of the mixed-representation determinant effects. The manuscript shows dynamical results for a few parameter sets but does not demonstrate that the quenched extrapolations lie within a controlled distance of the dynamical spectrum.
[quenched results section] Quenched extrapolation section: while continuum and massless limits are reported, the full error budget (including systematic uncertainties from the choice of fitting ansätze and the impact of the quenched approximation on the effective potential) is not presented in sufficient detail to substantiate the reliability of the quenched results as a first estimate.

minor comments (2)

[introduction] Notation for the two fermion representations should be defined explicitly at first use and used consistently throughout to avoid ambiguity in the description of chimera states.
[figures] Figure captions for the spectrum plots should include the specific lattice parameters (beta, masses) and the number of configurations used, to improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the two major points below, outlining how we will strengthen the presentation while remaining faithful to the scope and results of the current study.

read point-by-point responses

Referee: Section presenting dynamical results: the central claim that the quenched spectrum 'remains qualitatively valid' once dynamical fermions are included is load-bearing but unsupported by a direct quantitative comparison at matched bare parameters or by reweighting estimates of the mixed-representation determinant effects. The manuscript shows dynamical results for a few parameter sets but does not demonstrate that the quenched extrapolations lie within a controlled distance of the dynamical spectrum.

Authors: We agree that a direct, quantitative comparison at matched parameters would provide stronger support. The dynamical results are presented for a limited set of ensembles primarily to establish the viability of the spectral-density method for mixed-representation fermions. The qualitative statement is based on the observed similarity in state ordering and rough mass ratios between the dynamical data and the quenched extrapolations at comparable bare parameters. In the revised manuscript we will add an explicit side-by-side comparison of the dynamical masses with quenched values interpolated to similar lattice spacings and fermion masses, together with a brief discussion of the expected magnitude of mixed-representation determinant effects inferred from the simulated mass values. A full reweighting analysis lies beyond the computational scope of the present exploratory work and will be noted as such. revision: partial
Referee: Quenched extrapolation section: while continuum and massless limits are reported, the full error budget (including systematic uncertainties from the choice of fitting ansätze and the impact of the quenched approximation on the effective potential) is not presented in sufficient detail to substantiate the reliability of the quenched results as a first estimate.

Authors: We acknowledge that the error budget can be presented more transparently. The revised manuscript will include an expanded discussion of systematic uncertainties, covering variations in the functional forms adopted for the continuum and chiral extrapolations as well as a qualitative assessment of quenching effects (e.g., by reference to partially-quenched comparisons and related literature). A dedicated table summarizing statistical and systematic contributions to the final extrapolated masses will be added. revision: yes

Circularity Check

0 steps flagged

No circularity in lattice spectrum computations

full rationale

The paper reports direct numerical results from Monte Carlo lattice simulations of chimera baryon spectra in Sp(4) gauge theory, both in the quenched approximation (with continuum and massless extrapolations) and with dynamical fermions via spectral density analysis. These are empirical outputs from gauge-field ensembles and correlation-function measurements, not analytical derivations or predictions that reduce to their inputs by construction. No self-definitional relations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the central claims. The quenched-dynamical comparison is presented as an independent numerical check rather than a tautological step.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard lattice gauge theory assumptions plus the quenched approximation and the identification of the Sp(4) theory as a proxy for a composite Higgs model. No new particles or forces are postulated; the results are numerical outputs.

free parameters (2)

lattice spacing a
Multiple spacings used to take continuum limit; values not specified in abstract.
bare fermion masses
Massless limit extrapolated; specific values chosen for simulations.

axioms (2)

domain assumption Quenched approximation captures the essential non-perturbative physics of the chimera baryon spectrum
Invoked for the first set of results before dynamical fermions are added.
domain assumption Sp(4) with fundamental plus antisymmetric fermions realizes a viable CHM with top partial compositeness
Stated as the specific realization under study.

pith-pipeline@v0.9.0 · 5498 in / 1525 out tokens · 58141 ms · 2026-05-10T19:50:57.933439+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

28 extracted references · 24 canonical work pages

[1]

’t Hooft, Nucl

G. ’t Hooft, Nucl. Phys. B72, 461 (1974)

1974
[2]

Witten, Nucl

E. Witten, Nucl. Phys. B160, 57-115 (1979)

1979
[3]

Corrigan and P

E. Corrigan and P. Ramond, Phys. Lett. B87, 73-74 (1979)

1979
[4]

Bennettet al.,Phys

E. Bennettet al., Phys. Rev. D109, no.9, 094512 (2024). [arXiv:2311.14663 [hep-lat]]

work page arXiv 2024
[5]

Lovelace, Nucl

C. Lovelace, Nucl. Phys. B201, 333-340 (1982)

1982
[6]

Cherman, T

A. Cherman, T. D. Cohen and R. F. Lebed, Phys. Rev. D 80, 036002 (2009). [arXiv:0906.2400 [hep-ph]]

work page arXiv 2009
[7]

Panico and A

G. Panico and A. Wulzer, Lect. Notes Phys.913, pp.1-316 (2016) Springer. [arXiv:1506.01961 [hep-ph]]

work page arXiv 2016
[8]

Ferretti and D

G. Ferretti and D. Karateev, JHEP03, 077 (2014). [arXiv:1312.5330 [hep-ph]]

work page arXiv 2014
[9]

Barnard, T

J. Barnard, T. Gherghetta and T. S. Ray, JHEP02, 002 (2014). [arXiv:1311.6562 [hep-ph]]

work page arXiv 2014
[10]

Bennettet al.[TELOS], Phys

E. Bennettet al.[TELOS], Phys. Rev. D112, no.7, 074515 (2025). [arXiv:2506.19804 [hep-lat]]

work page arXiv 2025
[11]

Bennettet al.,Phys

E. Bennettet al., Phys. Rev. D106, no.1, 014501 (2022). [arXiv:2202.05516 [hep-lat]]

work page arXiv 2022
[12]

On the extraction of spectral densities from lattice correlators

M. Hansen, A. Lupo and N. Tantalo, Phys. Rev. D99, no.9, 094508 (2019). [arXiv:1903.06476 [hep-lat]]

work page Pith review arXiv 2019
[13]

Bennettet al., Phys

E. Bennettet al., Phys. Rev. D106, no.9, 094503 (2022) [arXiv:2205.09364 [hep-lat]]

work page arXiv 2022
[14]

Bennettet al., Universe9, no.5, 236 (2023) [arXiv:2304.01070 [hep-lat]]

E. Bennettet al., Universe9, no.5, 236 (2023) [arXiv:2304.01070 [hep-lat]]

work page arXiv 2023
[15]

Bennettet al.,Phys

E. Bennettet al., Phys. Rev. D109, no.9, 094517 (2024) [arXiv:2312.08465 [hep-lat]]

work page arXiv 2024
[16]

Del Debbio, A

L. Del Debbio, A. Patella and C. Pica, Phys. Rev. D81, 094503 (2010) [arXiv:0805.2058 [hep-lat]]

work page arXiv 2010
[17]

Bennettet al.,JHEP03(2018), 185 [arXiv:1712.04220 [hep-lat]]

E. Bennett,et al., JHEP03, 185 (2018). [arXiv:1712.04220 [hep-lat]]

work page arXiv 2018
[18]

Bennettet al.,Phys

E. Bennettet al., Phys. Rev. D101, no.7, 074516 (2020). [arXiv:1912.06505 [hep-lat]]

work page arXiv 2020
[19]

Bennettet al., Phys

E. Bennettet al., Phys. Rev. D103, no.5, 054509 (2021). [arXiv:2010.15781 [hep-lat]]

work page arXiv 2021
[20]

Grid: A next generation data parallel C++ QCD library,

P. Boyle, G. Cossu, A. Yamaguchi and A. Portelli, PoS LA TTICE2015, 023 (2016). [arXiv:1512.03487 [hep-lat]]

work page arXiv 2016
[21]

Bennettet al., Phys

E. Bennettet al., Phys. Rev. D108, no.9, 094508 (2023). [arXiv:2306.11649 [hep-lat]]

work page arXiv 2023
[22]

Bennettet al., Phys

E. Bennettet al., Phys. Rev. D110, no.7, 074509 (2024). [arXiv:2405.01388 [hep-lat]]

work page arXiv 2024
[23]

Bennettet al., Phys

E. Bennettet al., Phys. Rev. D109, no.3, 034504 (2024) [arXiv:2304.07191 [hep-lat]]

work page arXiv 2024
[24]

Bennettet al., Phys

E. Bennettet al., Phys. Rev. D110, no.7, 074504 (2024) [arXiv:2405.05765 [hep-lat]]

work page arXiv 2024
[25]

Bennettet al., 10.5281/zenodo.10929539 (2024)

E. Bennettet al., 10.5281/zenodo.10929539 (2024)

work page doi:10.5281/zenodo.10929539 2024
[26]

Forzanoet al., 10.5281/zenodo.15804889 (2025)

N. Forzanoet al., 10.5281/zenodo.15804889 (2025)

work page doi:10.5281/zenodo.15804889 2025
[27]

Forzanoet al., 10.5281/zenodo.15804848 (2025)

N. Forzanoet al., 10.5281/zenodo.15804848 (2025)

work page doi:10.5281/zenodo.15804848 2025
[28]

Bennett,The TELOS Collaboration Approach to Reproducibility and Open Science,2504.01876

E. Bennett, [arXiv:2504.01876 [hep-lat]]. 4

work page arXiv