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Exploring the two-body strong decay properties of the possible $\Lambda_cK^{*}$ and $\Sigma_cK^{(*)}$ molecules

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Predicted charm-strange molecular pentaquarks decay with widths from a few MeV to about 200 MeV, and their branching ratios are nearly binding-energy-independent.

desk verdict First decay-width predictions for the YcK* molecular candidates, with a clear pattern of dominant channels, but the broad states with Gamma >> binding energy are not self-consistently treated as bound states. read the letter →

arxiv 2501.10968 v2 pith:XYSCPLBB submitted 2025-01-19 hep-ph

Jin-yu Huo , Rui Chen This is my paper · ORCID
classification hep-ph PACS 14.20.Pt13.30.Eg
keywords hadronicmoleculescharm-strangepentaquarkseffectiveLagrangianapproachtwo-bodystrongdecaysLambda_cK*moleculeSigma_cdecaywidthsSU(4)flavorsymmetry
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish concrete two-body strong decay signatures for six predicted charm-strange molecular pentaquarks, each made of a charmed baryon ($\Lambda_c$ or $\Sigma_c$) bound to a kaon or vector kaon $K^*$. Using an effective Lagrangian approach with wave functions from an earlier one-boson-exchange study, it computes total and partial widths for the allowed $S$-wave decay channels. The central finding is a strong quantum-number dependence: widths run from a few MeV for the coupled $\Sigma_c K/\Lambda_c K^*/\Sigma_c K^*$ state with $1/2(1/2^-)$, where $D_s N$ dominates, up to about 200 MeV for the single $\Sigma_c K^*$ $1/2(1/2^-)$ state. In every channel the branching ratios are nearly independent of binding energy, which makes the predicted channel ratios a stable fingerprint for experimental searches. These numbers give experiments a quantitative way to tell a loosely bound molecule from a compact pentaquark.

What carries the argument

The central machinery is the effective Lagrangian description of the $S$-wave two-body decay of a hadronic molecule, where the total amplitude is a coherent sum over the molecular channels of the transition amplitude for each constituent pair, weighted by the channel wave function. The paper uses meson-exchange and baryon-exchange amplitudes built from the effective Lagrangians $\mathcal{L}_{PPV}$, $\mathcal{L}_{VVP}$, $\mathcal{L}_{VVV}$, $\mathcal{L}_{BBP}$, $\mathcal{L}_{BBV}$, $\mathcal{L}_{BDP}$, and $\mathcal{L}_{BDV}$, with all charmed coupling constants fixed by SU(4) flavor symmetry from tabulated nucleon couplings. The wave functions for the six predicted molecules come from a previous one-boson-exchange study, and coupled-channel effects enter by summing the individual channel contributions with their $S$-wave probabilities. This setup converts a molecular prediction into a definite list of partial widths whose pattern is robust to the binding energy.

What would settle it

Look for a $1/2(1/2^-)$ state near the $\Sigma_c K^*$ threshold in the $\Lambda_b \to \Lambda_c K \bar K \pi$ reaction: with a binding energy near $-5$ MeV the calculation predicts a total width of about 159 MeV and branching ratios of roughly 54\% $\Sigma_c K$ and 38\% $\Lambda_c K$; a measured width below about 50 MeV, or a dominant mode other than $\Sigma_c K$, would contradict the prediction.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is a decay-width hierarchy for the predicted $Y_c K^{(*)}$ molecules. The coupled $\Sigma_c K/\Lambda_c K^*/\Sigma_c K^*$ state with $I(J^P)=1/2(1/2^-)$ has a total width of about 4--13 MeV, dominated by $D_s N$ (about 91\%). The coupled $\Lambda_c K^*/\Sigma_c K^*$ states have widths of 14--33 MeV for $1/2(1/2^-)$, with $\Sigma_c K$ (about 54\%) and $\Lambda_c K$ (about 36\%) leading, and 25--70 MeV for $1/2(3/2^-)$, dominated by $\Sigma_c^* K$ (about 90\%). The single $\Sigma_c K^*$ molecule with $1/2(1/2^-)$ is the broadest, reaching 50--245 MeV with $\Sigma_c K$ (about 54\%) and $\Lambda_c K$ (about 38\%) as the main modes; its $1/2(3/2^-)$ and $3/2(1/2^-)$ partners are narrower, with widths of 5--30 MeV and 10--39 MeV, respectively. In all cases the branching ratios stay almost flat as the binding energy varies over the plotted ranges. The paper attributes the large widths to light pion and rho exchange between the constituents, and it shows that coupled-channel effects, especially the small $\Sigma_c K^*$ component in the $\Lambda_c K^*/\Sigma_c K^*$ states, can change the width through partial coherence.

Load-bearing premise

The calculation assumes that SU(4) flavor symmetry sets every charmed-baryon coupling from well-known nucleon couplings, with deviations under about 20%; if charm couplings break the symmetry more strongly, the computed widths and the ordering of dominant channels could change.

Editorial extensions

If this is right

  • Searches in $B \to \Lambda_c (\Sigma_c) \bar\Lambda_c K$ and $\Lambda_b \to \Lambda_c K \bar K \pi$ should look for the predicted width ranges; a $1/2(1/2^-)$ $\Sigma_c K^*$ molecule should appear as a broad structure near threshold with $\Sigma_c K$ and $\Lambda_c K$ as the leading final states.
  • The near-constancy of branching ratios means experimental identification can rely on relative rates rather than on a precise knowledge of the binding energy.
  • The width hierarchy is a discriminating test: states with different spin-parity have different dominant decay modes ($\Sigma_c K$ versus $\Sigma_c^* K$), so the measured final state identifies the quantum numbers.
  • Coupled-channel effects matter for the $\Lambda_c K^*/\Sigma_c K^*$ predictions: ignoring the small $\Sigma_c K^*$ component would remove the partial coherence that shifts the total width.
  • Three-body modes through $K^* \to K\pi$ may be significant for the $K^*$-containing molecules and are flagged by the paper as the next step.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If a future measurement resolves a candidate near a $Y_c K^{(*)}$ threshold with a width outside the predicted window, the molecular interpretation of that state would be in tension; a width inside the window would support it over a compact-pentaquark picture.
  • The SU(4) coupling relations are the main systematic uncertainty; a direct lattice computation of a charmed-baryon coupling such as $\Lambda_c \to \Sigma_c \pi$ would test the paper's 20% symmetry-breaking estimate.
  • The same effective-Lagrangian machinery could be applied to bottom partners built from $Y_b$ and $K^{(*)}$ mesons, where the heavier quark mass should make the molecular picture more reliable.
  • The binding-energy insensitivity of the branching ratios suggests a future analysis could invert the calculation and use measured channel ratios to constrain which coupled-channel component dominates the wave function.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This manuscript computes two-body strong decay widths for seven predicted YcK(*) molecular pentaquark candidates using the effective Lagrangian approach. The initial wave functions are taken from the authors' previous coupled-channel bound-state calculation [16], the transition amplitudes for S-wave decays are tabulated in Table 1, and the coupling constants are fixed by SU(4) flavor symmetry from nucleon couplings (Table 2). The authors report total and partial widths as functions of binding energy for each state, including a rescaling of the heavy-quark couplings by 0.8, 1.0, and 1.2 (Table 4). The main results are: the coupled Sigma_c K / Lambda_c K* / Sigma_c K* 1/2(1/2^-) state is narrow, with D_s N dominant; the coupled Lambda_c K* / Sigma_c K* states have widths of tens of MeV with Sigma_c K and Sigma_c^* K dominant; the single Sigma_c K* 1/2(1/2^-) state can be as broad as about 200 MeV; and the branching ratios are nearly independent of the binding energy.

Significance. If the predictions were reliable, the paper would provide concrete decay signatures for as-yet-unobserved charm-strange molecular pentaquarks and a way to distinguish molecular from compact interpretations. The authors provide explicit amplitude tables, check that D-wave admixtures affect the widths by less than 2%, and demonstrate that the branching ratios are stable under binding-energy variation and under a modest rescaling of the couplings. These are genuine strengths. The main significance is limited by the fact that no external data exist for the predicted states and, more importantly, by the internal inconsistency of the bound-state treatment for the broadest states, which is the subject of the major comments below.

major comments (3)
  1. [§3, Table 4 and Fig. 5] The bound-state assumption is internally inconsistent for the broad states. For the single Sigma_c K* 1/2(1/2^-) molecule, Table 4 gives Gamma=159 MeV at E=-4.75 MeV, and Table 3/Fig. 5 give Gamma up to 245 MeV over E in (0,-12) MeV; the imaginary part of the would-be pole, Gamma/2, is thus 30-80 times larger than the binding energy. A normalizable bound-state wave function combined with a first-order width formula [Eqs. (1)-(4)] is not justified in this regime. The same problem affects the coupled Lambda_c K* / Sigma_c K* 1/2(3/2^-) state (Gamma=54.6 MeV at E=-1.14 MeV) and the coupled 1/2(1/2^-) state (Gamma=30.5 MeV at E=-4.88 MeV). The headline 'one hundred MeV' width therefore needs a complex-pole or full scattering treatment before it can be considered a prediction.
  2. [§3 and Ref. [16]] The large computed widths also show that the lower channels omitted when obtaining the wave functions are not weakly coupled. Reference [16] solved the coupled-channel Schrodinger equation without D_s N, Lambda_c K, and Sigma_c K, yet for the single Sigma_c K* 1/2(1/2^-) state Table 3 assigns 54% of the width to Sigma_c K and 38% to Lambda_c K. When the decay channels carry a width comparable to or larger than the binding energy, their feedback on the pole position and on the wave-function composition cannot be neglected; the predicted existence and mass of the broad states are therefore not robust. The authors should either include these channels in a coupled-channel scattering calculation or restrict the claims to parameter ranges where Gamma/2 is much smaller than |E|.
  3. [§3, Table 4 and Sec. 4] The claimed 'less than 20%' uncertainty from SU(4) breaking is not reflected in the numerical spread. Rescaling g_H from 0.8 g_H to 1.2 g_H changes the total width of the Sigma_c K* 1/2(1/2^-) state from 102.7 to 227.0 MeV (Table 4), a factor of 2.2, and the other rows show factors close to 2 as well. This likely results from coherence and cancellations among amplitudes, but the manuscript does not explain why a 20% coupling uncertainty produces such a large width uncertainty. The paper should quote the resulting uncertainty bands or justify why the estimate does not propagate.
minor comments (4)
  1. [Eq. (19)] In Eq. (19) the tensor term contains gamma_alpha gamma_beta - gamma_alpha gamma_beta, which appears to be a typo for gamma_alpha gamma_beta - gamma_beta gamma_alpha.
  2. [Throughout] There are numerous typographical errors, including 'V ol.', 'effective Largrangians', 'can be play an important role', 'the the binding energy', and 'Branch ratios' in the Fig. 5 caption; these should be corrected.
  3. [References] References 53 and 56 are the same paper (Z. L. Wang, C. W. Shen, D. Ronchen et al., Eur. Phys. J. C 82, 497 (2022)) and should be merged or cross-referenced.
  4. [Introduction] The phrase 'observed in the zai decay channel' in the Introduction appears to be a corrupted or incomplete sentence and should be rephrased.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the widths are new observables; the only self-citation is the input wave-function source, not a reduction to the target.

full rationale

The derivation chain is Eqs. (1)-(4): the decay amplitude for each predicted YcK(*) state is formed by folding the two-body scattering amplitudes (Table 1, built from the effective Lagrangians (5)-(11) with SU(4)-derived couplings in Table 2) with the wave functions 'adopt[ed] ... obtained in Ref. [16]'. No parameter in this paper is fitted to the computed widths or branching ratios, and the widths are not used as input to any equation that defines the states; the only self-citation is Ref. [16] as the source of the input wave functions. That is model dependence, not logical circularity, because the decay observables are new quantities computed from independent literature couplings (gNNrho, fNNrho, gNNpi, gDeltaNpi, gVVP, gPPV, gVVV, alphaBBV) and existing wave functions. The paper's own stated limitations - that the coupled-channel Schrodinger calculation in Ref. [16] 'did not include' the lower channels DsN, Lambda_c K, Sigma_c K (Sec. 1), that the three-body K*->K pi modes 'may be important' (Sec. 4), and that SU(4) breaking is estimated at <20% from one comparison (Sec. 4) - affect the robustness and physical consistency of the predictions (e.g., Gamma~159 MeV at E=-4.75 MeV for the Sigma_c K* 1/2(1/2-) state exceeds the binding energy by an order of magnitude), but they do not make any 'prediction' reduce by construction to an input. Therefore no circular step is identified.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The calculation imports the molecular bound-state wave functions from Ref [16] and the SU(4) coupling scheme, then computes new decay observables. No data are fitted; the only hand-chosen knobs are the binding-energy scan and the g_H rescaling. No new particles or forces are introduced.

free parameters (2)
  • Binding energy E = 0 to -12 MeV (state-dependent ranges)
    Scanned as the assumed binding of each molecular candidate; widths depend strongly on it, so results are given as ranges.
  • Heavy-quark coupling rescaling g_H = 0.8, 1.0, 1.2 times SU(4) values
    Hand-chosen to bracket SU(4) symmetry breaking; produces factor-of-2 changes in widths.
assumptions (4)
  • domain assumption SU(4) flavor symmetry maps nucleon couplings to all charmed-baryon couplings used in Table 2.
    All g and f constants in Table 2 are obtained this way; the authors test only one vertex against data (Sec. 4).
  • domain assumption The Y_cK(*) molecular states exist with the wave functions of Ref [16].
    Sec. 3: 'we adopt the wave functions obtained in Ref [16]'; the states themselves are not experimentally established.
  • domain assumption S-wave two-body final states dominate the strong decays.
    Sec. 3 states D-wave probabilities <1% and that including D-waves changes total widths by <2%.
  • domain assumption Meson and baryon exchange amplitudes in Table 1 close over the intermediate states without significant other contributions.
    The effective Lagrangians of Eqs. (5)-(11) are the complete input; no contact terms or higher-order loops are included.

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Pith. "Pith review of Exploring the two-body strong decay properties of the possible $\Lambda_cK^{*}$ and $\Sigma_cK^{(*)}$ molecules." pith.science (2026). https://pith.science/paper/XYSCPLBB

@misc{pith2026250110968,
  author       = {Pith},
  title        = {Pith review of: Exploring the two-body strong decay properties of the possible $\Lambda_cK^*$ and $\Sigma_cK^(*)$ molecules},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XYSCPLBB}},
  note         = {Machine review of arXiv:2501.10968}
}
abstract

In this work, we apply the effective Lagrangian approach to investigate the two-body strong decay behaviors of the possible $\Lambda_c K^*$ and $\Sigma_c K^{(*)}$ molecules, as predicted in our previous study [\href{https://doi.org/10.1103/PhysRevD.108.054011}{Phys. Rev. D \textbf{108}, 054011 (2023)}]. Our results indicate that the decay width for the coupled $\Sigma_c K / \Lambda_c K^* / \Sigma_c K^*$ molecule with $I(J^P) = 1/2(1/2^-)$ is on the order of several MeV, with the $D_s N$ channel being dominant. For the coupled $\Lambda_c K^* / \Sigma_c K^*$ molecule with $1/2(1/2^-, 3/2^-)$, the decay widths are on the order of tens of MeV, with the dominant channels being $\Sigma_c K$ and $\Sigma_c^* K$, respectively. For the $\Sigma_c K^*$ molecules with $1/2(1/2^-)$, the decay width can reach one hundred MeV, with $\Sigma_c K$ and $\Lambda_c K$ being the dominant decay channels. The decay widths for the $\Sigma_c K^*$ molecules with $1/2(3/2^-)$ and $3/2(1/2^-)$ are on the order of tens of MeV, with the dominant decay modes being $\Sigma_c^* K$ and $\Sigma_c K$, respectively. The branching ratios for all the discussed channels show little dependence on the binding energies.

Figures

Figures reproduced from arXiv: 2501.10968 by the authors.

Figure 1
Figure 1. The diagram for the Pcs¯ molecules decaying into f1 and f2 final states. In this work, we focus on the two-body strong decay proper￾ties for the predicted Pcs¯ molecules via S−wave interactions. In [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The two-body strong decay width for the coupled [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The two-body strong decay width for the coupled [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 6
Figure 6. Figure 6: The two-body strong decay width for the single [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: The two-body strong decay width for the single [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.