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arxiv: 2602.19504 · v3 · pith:3RIPBK53new · submitted 2026-02-23 · ✦ hep-ph · hep-ex· nucl-th

Three-body molecular states composed of D^((*)) and two nucleons

Si-Yi Chen , Fei-Yu Chen , Xu-Liang Chen , Lu Meng , Ning Li , Wei Chen This is my paper

Pith reviewed 2026-05-25 07:02 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-th
keywords charmed mesonnucleonthree-body bound stateheavy quark symmetrymolecular stateGaussian expansion methodDNN system
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0 comments X

The pith

The DNN system forms a robust compact bound state in the 1/2(1-) channel over a broad range of cutoffs even when the DN subsystem is weakly bound or unbound.

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

This paper investigates three-body molecular states of a D or D* meson with two nucleons by combining a realistic nucleon-nucleon interaction with a D(*)N potential fixed by heavy-quark symmetry. The three-body Schrödinger equation is solved using the Gaussian Expansion Method, and the spectrum is analyzed with the Complex Scaling Method to identify bound states and check for resonances. The central result is that DNN supports a stable, spatially compact bound state in the I(J^P)=1/2(1^-) channel across wide cutoff variations. For D*NN the spin-1 nature of the heavy meson produces a clear hierarchy of binding energies and sizes across 0^-, 1^-, and 2^- channels, all more compressed than the deuteron. These calculations supply quantitative predictions for possible charmed-meson-nuclear bound states.

Core claim

The DNN system supports a robust and compact bound state in the I(J^P)=1/2(1^-) channel over a broad range of cutoff values, even when the corresponding DN subsystem is weakly bound or unbound. For D*NN the spin-1 nature of the heavy meson generates a clear spin hierarchy: deeply bound states appear in both 0^- and 2^- channels, while the 1^- channel exhibits a two-branch pattern with one strongly bound compact branch and one more weakly bound spatially extended branch. Root-mean-square radii show pronounced spatial compression relative to the deuteron, and no three-body resonances appear under complex scaling in the explored parameter space.

What carries the argument

The three-body Schrödinger equation solved by the Gaussian Expansion Method after combining a realistic NN potential with a D(*)N potential constrained by heavy-quark symmetry, together with the Complex Scaling Method for locating resonances.

If this is right

  • DNN remains bound even when the two-body DN subsystem is unbound or only weakly bound.
  • D*NN exhibits a spin-dependent hierarchy with compact states in 0^- and 2^- channels and a two-branch structure in the 1^- channel.
  • All predicted states have root-mean-square radii smaller than the deuteron, indicating cooperative compression from NN correlations and D(*)N forces.
  • No three-body resonances are found across the scanned cutoff range.

Where Pith is reading between the lines

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

  • Similar compact states may exist when the D meson is replaced by a B meson, extending the same heavy-quark symmetry framework to bottom flavor.
  • The predicted mass and size ranges could guide dedicated searches in heavy-ion or electron-beam experiments that produce charmed mesons near threshold.
  • If the states are observed, their radii would test whether heavy-quark symmetry remains accurate inside a three-body nuclear environment.

Load-bearing premise

The D(*)N interaction is correctly captured by heavy-quark symmetry when added to a realistic NN force.

What would settle it

An experimental search that either detects or rules out a bound state with the predicted binding energy, isospin, and spin-parity in the DNN system at the expected mass would confirm or refute the result.

Figures

Figures reproduced from arXiv: 2602.19504 by Fei-Yu Chen, Lu Meng, Ning Li, Si-Yi Chen, Wei Chen, Xu-Liang Chen.

Figure 1
Figure 1. Figure 1: FIG. 1. Feynman diagrams used to derive OBE potentials for the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Two sets of Jacobi coordinates corresponding to different [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Binding energies of the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Root-mean-square (RMS) radii of the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Binding energies of the three-body [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. RMS radii of the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Pole trajectories of the [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

We study the three-body systems $DNN$ and $D^{*}NN$ within a hadronic molecular framework by combining a realistic nucleon-nucleon interaction with a $D^{(*)}N$ potential constrained by heavy-quark symmetry. The three-body Schr\"odinger equation is solved with the Gaussian Expansion Method, and the analytic structure of the spectrum is investigated using the Complex Scaling Method. We find that the $DNN$ system supports a robust and compact bound state in the $I(J^{P})=\tfrac{1}{2}(1^-)$ channel over a broad range of cutoff values, even when the corresponding $DN$ subsystem is weakly bound or unbound. For $D^{*}NN$, the spin-$1$ nature of the heavy meson and the associated spin-dependent forces generate a clear spin hierarchy: deeply bound states appear in both $0^-$ and $2^-$ channels, while the $1^-$ channel exhibits a characteristic two-branch pattern with a strongly bound compact branch and a more weakly bound, spatially extended branch. The root-mean-square radii indicate pronounced spatial compression compared with the deuteron scale, highlighting the cooperative roles of realistic $NN$ correlations, the $D^{(*)}N$ interactions, and heavy-quark symmetry in forming compact heavy-flavor few-body bound states. No three-body resonances under complex scaling are found in the explored parameter space. Our results provide quantitative benchmarks for future experimental searches for such charmed-meson-nuclear bound states.

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 investigates DNN and D*NN three-body systems in a hadronic molecular framework by combining a realistic NN interaction with D(*)N potentials constrained by heavy-quark symmetry. The three-body Schrödinger equation is solved using the Gaussian Expansion Method, and the analytic structure is analyzed via the Complex Scaling Method. The central claims are a robust, compact bound state in the DNN I(J^P)=1/2(1^-) channel persisting over a broad cutoff range even when the DN subsystem is weakly bound or unbound, a clear spin hierarchy for D*NN with deeply bound states in 0^- and 2^- channels plus a two-branch pattern in 1^-, pronounced spatial compression relative to the deuteron, and the absence of three-body resonances.

Significance. If the numerical results hold, this work supplies quantitative benchmarks for experimental searches of charmed-meson-nuclear bound states. It explicitly demonstrates the cooperative roles of realistic NN correlations, D(*)N interactions, and heavy-quark symmetry in forming compact heavy-flavor few-body states. The systematic survey over the single free parameter (cutoff) together with the use of the Complex Scaling Method to confirm the lack of resonances are positive methodological strengths that enhance the reliability of the bound-state claims.

minor comments (3)
  1. The abstract states that the DNN bound state persists 'over a broad range of cutoff values' but does not quote the explicit range or tabulate the binding energies versus cutoff; adding a compact table or figure panel would make the robustness claim immediately verifiable.
  2. Section describing the Gaussian Expansion Method implementation should include the basis size, number of channels retained, and explicit convergence tests with respect to the expansion parameters to allow independent reproduction of the three-body energies.
  3. The root-mean-square radii are compared to the deuteron scale, but the precise definition (e.g., matter radius versus charge radius) and the numerical extraction procedure from the GEM wave functions are not stated; a short clarifying sentence would remove ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript, the recognition of its methodological strengths (including the cutoff survey and Complex Scaling Method analysis), and the recommendation for minor revision. No specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity; results are numerical outputs from standard QM solver

full rationale

The derivation consists of combining a realistic NN potential with a D(*)N potential (constrained by heavy-quark symmetry and regularized by cutoff) and solving the three-body Schrödinger equation via the Gaussian Expansion Method, followed by Complex Scaling Method analysis. The reported bound states and radii are direct numerical results of this procedure across a range of cutoffs; they do not reduce to the inputs by construction, nor does the paper rename fitted quantities as predictions or rely on load-bearing self-citations for uniqueness. The methodology is self-contained and externally falsifiable via the Schrödinger equation itself.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the hadronic molecular framework, heavy-quark symmetry for the two-body potential, and the numerical accuracy of the Gaussian Expansion Method; the cutoff is the main adjustable parameter.

free parameters (1)
  • cutoff
    The D(*)N potential depends on a cutoff parameter, with results shown over a broad range of values.
axioms (2)
  • domain assumption Heavy-quark symmetry constrains the D(*)N potential
    Used to build the two-body potential from known symmetry principles.
  • domain assumption Realistic nucleon-nucleon interaction is used as input
    Combined with the meson-nucleon potential in the three-body calculation.

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discussion (0)

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Forward citations

Cited by 1 Pith paper

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    hep-ph 2026-04 unverdicted novelty 5.0

    The DDK system supports a deeply bound compact state across wide parameters and possibly a shallow three-body halo state near the D-DK threshold, with negligible D*D*K coupling and no resonances.

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