arxiv: 2604.18796 · v1 · submitted 2026-04-20 · ✦ hep-ph · hep-ex· hep-lat

Recognition: unknown

Mass spectrum, magnetic moments and Regge trajectories of Ω_{ccb} and Ω_{cbb} baryons in the nonrelativistic quark--diquark model

Halil Mutuk, \"Oznur \c{C}ak{\i}r

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:33 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-lat

keywords triply heavy baryonsquark-diquark modelmass spectrummagnetic momentsRegge trajectoriesOmega_ccbOmega_cbb

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The pith

Nonrelativistic quark-diquark model predicts masses of 8 GeV for Ω_ccb and 11 GeV for Ω_cbb baryons

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

The paper applies a nonrelativistic constituent quark model in the quark-diquark approximation to the triply heavy baryons Ω_ccb and Ω_cbb. Parameters are fixed by fitting to the measured B_c meson spectrum to connect the heavy meson and baryon sectors. It computes ground-state and excited masses, magnetic moments for both spin-1/2 and spin-3/2 states, and Regge trajectories in the radial plane. The results give masses near 8.0 GeV and 11.0 GeV with trajectories that scale with heavy-quark content. Readers would care because these baryons remain unobserved and the predictions supply concrete targets for experiments at facilities such as LHCb.

Core claim

The nonrelativistic quark-diquark model with parameters fixed from the B_c meson spectrum yields ground-state masses of approximately 8.0 GeV for Ω_ccb and 11.0 GeV for Ω_cbb. All three possible diquark clusterings are examined for each baryon to indicate sensitivity to the decomposition. The computed magnetic moments of the spin-1/2 and spin-3/2 states are consistent with results from various other approaches. A radial Regge analysis in the (n_r, M^2) plane reveals approximately linear P-wave trajectories and mildly curved S-wave trajectories, with slope and intercept parameters that scale systematically with the heavy-quark content.

What carries the argument

The quark-diquark approximation that reduces the three-body baryon problem to an effective two-body system, using model parameters fitted to the B_c meson spectrum and considering all three possible diquark clusterings

If this is right

Ground-state masses near 8.0 GeV for Ω_ccb and 11.0 GeV for Ω_cbb provide benchmarks for experimental searches.
Magnetic moments for spin-1/2 and spin-3/2 states remain consistent across different theoretical methods.
Regge trajectories in the (n_r, M^2) plane are linear for P-waves and mildly curved for S-waves.
Slope and intercept parameters scale systematically with the heavy-quark content of the baryon.
The framework supplies a consistent link between the heavy meson and baryon sectors.

Where Pith is reading between the lines

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

High-precision mass measurements could test the sensitivity of results to different diquark clusterings.
The pattern of Regge-parameter scaling with quark content could support similar predictions for other triply heavy systems.
Confirmation of the masses at LHCb would support the transfer of meson-fitted parameters to baryons.
Deviations from the predicted masses would indicate where the nonrelativistic approximation begins to break down.

Load-bearing premise

The quark-diquark approximation is valid for triply heavy baryons and the parameters fitted to the B_c meson spectrum transfer reliably to these baryon systems.

What would settle it

An experimental measurement of the Ω_ccb ground-state mass that differs substantially from 8.0 GeV would challenge the model's applicability to these systems.

Figures

Figures reproduced from arXiv: 2604.18796 by Halil Mutuk, \"Oznur \c{C}ak{\i}r.

**Figure 3.** Figure 3: FIG. 3: Radial Regge trajectory of the Ω [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: Radial Regge trajectory of the Ω [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

read the original abstract

In this work, we investigate the mass spectra, magnetic moments, and Regge trajectories of the triply heavy baryons $\Omega_{ccb}$ and $\Omega_{cbb}$ within a nonrelativistic constituent quark model based on the quark--diquark approximation, which reduces the three-body problem to an effective two-body system. For each baryon, all three possible diquark clusterings are considered, providing a qualitative indication of the sensitivity of the results to the quark--diquark decomposition. The model parameters are fixed by a fit to the measured $B_c$ meson spectrum, thereby anchoring the baryon predictions to experimentally constrained inputs and establishing a consistent link between the heavy meson and baryon sectors. We obtain ground-state masses of approximately $8.0$~GeV for $\Omega_{ccb}$ and $11.0$~GeV for $\Omega_{cbb}$, with radial and orbital excitation patterns in good agreement with the results reported in the literature. The computed magnetic moments of the spin-$\tfrac{1}{2}$ and spin-$\tfrac{3}{2}$ states are consistent with the results of various approaches. A radial Regge analysis in the $(n_r, M^2)$ plane reveals approximately linear $P$-wave trajectories and mildly curved $S$-wave trajectories, with slope and intercept parameters that scale systematically with the heavy-quark content of the baryon. These results suggest that the nonrelativistic quark--diquark framework provides a reliable description of triply heavy baryons and serves as a useful reference for future experimental searches, particularly at LHCb.

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 supplies concrete numerical targets for Ω_ccb and Ω_cbb masses, moments, and trajectories by fitting a quark-diquark model to B_c data, but the transfer of those parameters to the baryon sector is the step that needs the most scrutiny.

read the letter

The paper reports ground-state masses near 8 GeV for Ω_ccb and 11 GeV for Ω_cbb, plus magnetic moments for the spin-1/2 and 3/2 states and linear-ish Regge trajectories in the (n_r, M²) plane. It does this by reducing each baryon to an effective two-body quark-diquark system, trying all three possible clusterings, and fixing the potential parameters on the measured B_c spectrum. That produces a consistent set of numbers that can be compared directly with other model calculations and with future LHCb data. The systematic variation over clusterings is useful; it shows how the results shift when the diquark composition changes, and the Regge slopes scale in a way that tracks the heavy-quark content. Those are the parts that give the work its practical value as a reference table rather than just another model run. The approach follows standard nonrelativistic quark-model practice and the outputs line up with existing literature, which is what one expects from this framework. The central limitation is the parameter transfer itself. The fit is done on mesons, then applied to baryons where the color factor for the antitriplet diquark and the reduced-mass treatment are different. The paper does not show an independent check, such as a lattice comparison or a variation of the color factor, that would quantify how much those choices move the quoted masses. Without that, the numerical results inherit the uncertainty of the meson-to-baryon extrapolation even though the internal calculations for moments and trajectories are internally consistent. The work is aimed at people who model heavy hadrons or plan searches for them. A reader who already uses quark-diquark or potential models will find the numbers and the clustering scan worth having on hand. It is not a breakthrough in method, but it is a careful application that adds specific, citable targets. I would send it to peer review; the calculations are transparent enough that referees can check the numerics and the model assumptions directly.

Referee Report

2 major / 2 minor

Summary. The paper investigates the mass spectra, magnetic moments, and Regge trajectories of the triply heavy baryons Ω_ccb and Ω_cbb in a nonrelativistic constituent quark model employing the quark-diquark approximation to reduce the three-body problem to an effective two-body system. Parameters are fixed via a fit to the B_c meson spectrum, all three possible diquark clusterings are examined for sensitivity, and predictions are made for ground-state masses (~8.0 GeV for Ω_ccb, ~11.0 GeV for Ω_cbb), excitations, magnetic moments, and approximately linear P-wave Regge trajectories whose slopes scale with heavy-quark content.

Significance. If the parameter transfer from the B_c fit holds, the work supplies concrete phenomenological benchmarks for undiscovered triply heavy baryons that could inform LHCb searches. The explicit consideration of multiple diquark clusterings and the systematic scaling of Regge slopes with quark content are positive features that link the heavy-meson and baryon sectors in a consistent framework.

major comments (2)

[Abstract] Abstract: the assertion of a 'reliable description' of triply heavy baryons rests on transferring parameters fitted exclusively to the B_c meson spectrum; the manuscript provides no quantitative fit-quality metrics (χ², degrees of freedom) or uncertainty propagation to the baryon masses, leaving the numerical predictions (~8.0 GeV, ~11.0 GeV) without error estimates.
[Section 3] Section 3 (numerical results): while the three diquark clusterings are varied, the color factor 1/2 for the antitriplet diquark is held fixed and no lattice-QCD anchor or variation of the reduced-mass treatment is shown; this makes the central mass values and the claim of consistency with literature sensitive to the untested transfer assumption.

minor comments (2)

[Abstract] The abstract states 'good agreement with the results reported in the literature' without naming the specific references or quantifying the mass differences, which would help readers assess the level of consistency.
[Section 4] Magnetic-moment tables would benefit from explicit comparison columns to other approaches (e.g., lattice or quark-model values) rather than only qualitative statements of consistency.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and indicate the revisions we will implement in the next version.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion of a 'reliable description' of triply heavy baryons rests on transferring parameters fitted exclusively to the B_c meson spectrum; the manuscript provides no quantitative fit-quality metrics (χ², degrees of freedom) or uncertainty propagation to the baryon masses, leaving the numerical predictions (~8.0 GeV, ~11.0 GeV) without error estimates.

Authors: We acknowledge that the original manuscript omitted explicit χ²/dof values for the B_c fit and did not propagate parameter uncertainties to the baryon predictions. In the revised version we will report the χ² per degree of freedom for the fit to the B_c spectrum and include a short discussion of the fit procedure. For the baryon masses we will add a conservative uncertainty estimate obtained by varying the fitted parameters within the ranges that still reproduce the B_c data to within a few MeV; this will be presented as an indicative error band rather than a full statistical propagation. revision: partial
Referee: [Section 3] Section 3 (numerical results): while the three diquark clusterings are varied, the color factor 1/2 for the antitriplet diquark is held fixed and no lattice-QCD anchor or variation of the reduced-mass treatment is shown; this makes the central mass values and the claim of consistency with literature sensitive to the untested transfer assumption.

Authors: The color factor 1/2 follows directly from the SU(3)_c representation of the antitriplet diquark and is a standard, non-adjustable input in the quark-diquark model; altering it would change the underlying theoretical framework. We have already explored sensitivity by considering all three possible diquark clusterings for each baryon. Direct lattice-QCD results for Ω_ccb and Ω_cbb masses are not yet available in the literature for anchoring, so our comparisons are made to other phenomenological calculations. We will add an explicit statement in Section 3 justifying the fixed color factor and noting the current lack of lattice anchors as a limitation of the approach. revision: partial

Circularity Check

0 steps flagged

No significant circularity; meson fit transferred to distinct baryon systems without reduction by construction.

full rationale

The paper fixes model parameters via a fit to the measured B_c meson spectrum and then applies the same nonrelativistic quark-diquark framework to compute masses, magnetic moments, and Regge trajectories for the triply heavy baryons Ω_ccb and Ω_cbb. This constitutes a standard parameter transfer between related heavy-quark systems rather than any self-definitional loop, fitted input renamed as prediction, or load-bearing self-citation. The central numerical results (~8.0 GeV and ~11.0 GeV ground states) are genuine outputs of the effective two-body Schrödinger equation solved for the baryon reduced masses and potentials; they are not algebraically equivalent to the B_c fit data. No uniqueness theorems, ansatzes smuggled via prior self-work, or renaming of known patterns are invoked in a way that collapses the derivation. The approach is self-contained against external benchmarks once the meson fit is accepted as input.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central results rest on fitting a small set of model parameters to B_c meson data and on the assumption that the nonrelativistic quark-diquark reduction accurately captures the dynamics of triply heavy systems.

free parameters (1)

model parameters
Fixed by a fit to the measured B_c meson spectrum to anchor the baryon predictions.

axioms (2)

domain assumption nonrelativistic constituent quark model is applicable to triply heavy baryons
The entire calculation is performed in the nonrelativistic limit.
domain assumption quark-diquark approximation reduces the three-body problem to an effective two-body system
Explicitly stated as the basis for treating all three possible diquark clusterings.

pith-pipeline@v0.9.0 · 5623 in / 1352 out tokens · 44848 ms · 2026-05-10T03:33:51.624790+00:00 · methodology

discussion (0)

Reference graph

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