arxiv: 2603.01037 · v2 · submitted 2026-03-01 · ✦ hep-ph · hep-ex

Recognition: 2 theorem links

· Lean Theorem

Quark-diquark effective mass formalism for heavy baryon spectroscopy

Binesh Mohan , Rohit Dhir

Authors on Pith no claims yet

Pith reviewed 2026-05-15 18:32 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords heavy baryonsquark-diquark modelbaryon spectroscopycharm baryonsbottom baryonseffective mass formalismheavy quark symmetrydiquark parameters

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The pith

A quark-diquark effective mass model reproduces heavy baryon spectra with parameters fixed only by quark content across all heavy sectors.

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

The paper builds a description of heavy baryons as a single quark bound to a diquark, where the diquark's effective mass and spin-dependent couplings are set once by the flavors of the quarks inside it. A binding energy term that grows with the overall mass is added to handle the change from spin-dependent color forces at lighter masses to color-Coulomb dominance at heavier masses. The same fixed parameters are applied to the 1/2+ and 3/2+ states in singly, doubly, and triply heavy systems, and the calculated masses line up with measured values and lattice results. This stability across charm and bottom sectors is presented as evidence that the approach respects heavy-quark spin symmetry in the appropriate limit and can serve as a baseline for further calculations.

Core claim

The central claim is that constituent quark masses, effective diquark masses, and chromomagnetic couplings can be determined solely from the quark content of each state, combined with one mass-dependent binding term that accounts for spin-independent chromoelectric effects, and that this construction yields predictions in agreement with experiment and lattice QCD for the 1/2+ and 3/2+ heavy baryon spectra while preserving heavy-quark spin symmetry in the heavy limit.

What carries the argument

Quark-diquark effective mass formalism with a mass-dependent binding term that captures the transition from chromomagnetic to color-Coulomb dominance.

If this is right

Masses of still-unobserved heavy baryons can be predicted without introducing new parameters for each flavor sector.
The extracted diquark parameters remain the same from charm to bottom, supporting a unified description across heavy-flavor regimes.
The two scenarios (full dynamical diquark channels versus scalar and axial-vector only) provide complementary levels of detail for the same states.
The framework maintains consistency with heavy-quark spin symmetry when the binding term is applied in the heavy limit.

Where Pith is reading between the lines

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

The same binding term might be tested on states that mix light and heavy quarks to see where the transition between force regimes occurs.
If the parameters stay stable, the model could be used to estimate widths or decay rates of the predicted states without additional tuning.
The restriction to scalar and axial-vector diquarks in one scenario may simplify calculations for triply heavy baryons while still matching data.

Load-bearing premise

Effective diquark masses and couplings can be fixed by quark content alone without any sector-dependent retuning, and a single binding term is enough to describe the change in dominant forces while keeping heavy-quark spin symmetry intact.

What would settle it

A clear mismatch between the model's mass predictions and new experimental or lattice results for one or more unobserved heavy baryons in the charm or bottom sector.

Figures

Figures reproduced from arXiv: 2603.01037 by Binesh Mohan, Rohit Dhir.

**Figure 2.** Figure 2: Unlike Scenario I, which includes all diquark configurations, Scenario II restricts heavy flavor diquarks to the three dominant cases, Dcc , Dcb, and Dbb, while omitting heavy-light diquarks. This selective treatment provides a consistent and tractable framework for conventional baryons and can be extended to exotic states. Using these inputs within the QDEMF, we compute the masses of heavy flavor baryons … view at source ↗

**Figure 2.** Figure 2: Variation of hyperfine splitting, ∆M = MA − MS in scenarios I and II with corresponding diquark masses. Table V: Binding energy (in MeV). Experimental BE(QQ ′ ) BE(QQ′ ) inputs [1] D∗+ s , D+ s cs −78.55 cs −39.28 J/Ψ, ηc cc −262.36 cc −131.18 B∗0 s , B0 s bs −93.57 bs −46.79 B∗+ c a , B+ c bc −356.26 bc −178.13 Υ, ηb bb −570.29 bb −285.14 a The B∗+ c mass of 6331 MeV from LQCD [57] is used to compute the … view at source ↗

**Figure 3.** Figure 3: Lower half illustrates the diquark binding energies, while the upper half shows [PITH_FULL_IMAGE:figures/full_fig_p033_3.png] view at source ↗

read the original abstract

We develop a quark-diquark effective mass formalism for heavy-flavor baryon spectroscopy and apply it to the $J^P = \tfrac{1}{2}^+$ and $J^P = \tfrac{3}{2}^+$ spectra across the singly, doubly, and triply heavy sectors. The analysis is carried out in two complementary scenarios: Scenario I treats all quark-quark diquark channels dynamically, while Scenario II restricts the dynamics to scalar and axial-vector diquarks, providing a more selective and physically transparent description. Constituent quark masses, effective diquark masses, and chromomagnetic couplings are extracted from known heavy-baryon masses, with the couplings determined solely by the quark content of each state and no sector-dependent adjustment introduced. A mass-dependent binding term is implemented to account for spin-independent chromoelectric effects and to describe the transition from chromomagnetic to color-Coulomb dominance across the light-to-heavy quark regime, ensuring consistency with heavy-quark spin symmetry in the heavy-quark limit. The resulting predictions are in good agreement with available experimental measurements and lattice QCD results across both charm and bottom sectors. The extracted diquark parameters remain stable across all heavy-flavor sectors, establishing the present framework as a symmetry-constrained spectroscopic baseline for heavy-baryon structure.

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 gives a unified quark-diquark parametrization for heavy baryons with stable parameters across sectors, but the lack of visible fit details leaves the independence of predictions unclear.

read the letter

The paper offers a quark-diquark effective mass approach that covers the 1/2+ and 3/2+ spectra for singly, doubly, and triply heavy baryons in one framework. It runs two scenarios and adds a mass-dependent binding term meant to interpolate between chromomagnetic and color-Coulomb regimes while preserving heavy-quark spin symmetry in the limit. Parameters are fixed by quark content alone, with no sector-by-sector retuning, and the extracted diquark masses and couplings are reported to stay stable from charm to bottom. The predictions line up with existing data and lattice results, which is the main practical claim. That combination of two scenarios plus the uniform binding term is a modest but concrete step beyond earlier quark-diquark models. The construction looks internally consistent on paper and the symmetry constraint is handled explicitly rather than imposed by hand. The soft spot is the circularity risk. All masses, couplings, and the binding term itself are extracted from known heavy-baryon masses, so any new states risk being interpolations inside the fitted space rather than independent tests. The abstract states agreement with experiment and lattice but does not list which states entered the fit, which were held out, or the size of the uncertainties. Without those numbers it is difficult to judge how much the stability claim actually constrains the model. This is the sort of work that experimental groups at LHCb or theorists building quick spectroscopic tools might find useful as a baseline. A reader who already works with constituent quark models for heavy flavors would get the most out of the parameter stability and the two-scenario comparison. It deserves peer review so referees can examine the global fit results and check whether the out-of-sample predictions hold once the full tables are in front of them.

Referee Report

1 major / 1 minor

Summary. The manuscript develops a quark-diquark effective mass formalism for the J^P=1/2^+ and 3/2^+ spectra of singly, doubly, and triply heavy baryons. Constituent quark masses, effective diquark masses, and chromomagnetic couplings are extracted from known heavy-baryon masses with couplings fixed solely by quark content and no sector-dependent adjustments; a mass-dependent binding term accounts for spin-independent chromoelectric effects and enforces consistency with heavy-quark spin symmetry in the heavy limit. Two scenarios are considered (full dynamical diquark channels versus restriction to scalar and axial-vector diquarks), and the resulting predictions are stated to agree with experimental data and lattice QCD results while the extracted parameters remain stable across charm and bottom sectors.

Significance. If the global fit is robust and the predictions are demonstrably independent of the fitted states, the work would supply a symmetry-constrained spectroscopic baseline that interpolates between light and heavy regimes while respecting heavy-quark spin symmetry. Parameter stability across sectors would support its utility for guiding future experimental searches and lattice calculations in the heavy-baryon sector.

major comments (1)

[Abstract and parameter-extraction section] The central claim that parameters are extracted from known masses and that predictions agree with data cannot be verified because the manuscript provides neither the explicit mass formula, the list of states used for the fit versus those predicted, the numerical values of the fitted parameters with uncertainties, nor any goodness-of-fit metric (e.g., chi^2). This information is required to assess whether the mass-dependent binding term produces genuine out-of-sample predictions or merely interpolates within the fitted space.

minor comments (1)

[Abstract] The distinction between Scenario I (all diquark channels dynamical) and Scenario II (restricted to scalar and axial-vector diquarks) is stated but not illustrated with a brief comparison of the resulting spectra or parameter counts, which would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address the major point on transparency of the fitting procedure below and will revise the manuscript accordingly to make all details verifiable.

read point-by-point responses

Referee: [Abstract and parameter-extraction section] The central claim that parameters are extracted from known masses and that predictions agree with data cannot be verified because the manuscript provides neither the explicit mass formula, the list of states used for the fit versus those predicted, the numerical values of the fitted parameters with uncertainties, nor any goodness-of-fit metric (e.g., chi^2). This information is required to assess whether the mass-dependent binding term produces genuine out-of-sample predictions or merely interpolates within the fitted space.

Authors: We agree that these elements are essential for independent verification. The revised manuscript will include: (i) the explicit mass formula with the mass-dependent binding term, (ii) a clear table or list separating the experimental states used in the global fit from the out-of-sample predictions, (iii) the full set of fitted parameters (constituent quark masses, effective diquark masses, and chromomagnetic couplings) together with their uncertainties, and (iv) the chi-squared per degree of freedom for the fit. These additions will allow direct assessment of parameter stability across sectors and confirm that the binding term supports genuine predictions consistent with heavy-quark spin symmetry. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper extracts constituent quark masses, effective diquark masses, and chromomagnetic couplings from known heavy-baryon masses and introduces a mass-dependent binding term to model the transition between regimes while preserving heavy-quark spin symmetry. Predictions for additional states in the charm and bottom sectors are then compared against independent experimental data and lattice QCD results. Because validation draws on external benchmarks (lattice QCD) that are not constructed from the fitted values, and no self-citations, uniqueness theorems, or definitional loops appear in the derivation, the chain does not reduce to its inputs by construction. The framework remains a symmetry-constrained baseline whose parameters are reported as stable across sectors.

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 1 invented entities

The framework rests on several fitted quantities and modeling assumptions whose independent support is not shown in the abstract.

free parameters (4)

constituent quark masses
Extracted from known heavy-baryon masses
effective diquark masses
Extracted from known heavy-baryon masses
chromomagnetic couplings
Determined solely by quark content of each state
mass-dependent binding term parameters
Introduced to account for spin-independent chromoelectric effects

axioms (3)

domain assumption Baryons can be modeled as a quark bound to a diquark
Core modeling choice stated in the title and abstract
domain assumption Heavy-quark spin symmetry holds in the heavy limit
Invoked to ensure consistency of the binding term
ad hoc to paper No sector-dependent adjustment of couplings is needed
Explicitly stated as a constraint on the fit

invented entities (1)

effective diquark mass no independent evidence
purpose: To represent the composite diquark as a single degree of freedom with its own mass
Postulated quantity fitted to data; no independent evidence given

pith-pipeline@v0.9.0 · 5529 in / 1733 out tokens · 60670 ms · 2026-05-15T18:32:16.834496+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/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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

We develop a quark-diquark effective mass formalism … Constituent quark masses, effective diquark masses, and chromomagnetic couplings are extracted from known heavy-baryon masses … A mass-dependent binding term is implemented …
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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

The resulting predictions are in good agreement with … lattice QCD results … diquark parameters remain stable across all heavy-flavor sectors.

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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