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REVIEW 3 major objections 6 minor 69 references

Possible explanations of the observed $\Lambda_c$ resonances

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper proposes that the disputed Λc(2940)+ resonance is a 2P-wave lambda-mode charmed baryon with spin-parity 3/2−, matching its measured width and decay ratios.

desk verdict A solid, honest quark-model decay study with useful, falsifiable ratio predictions; the central Λc(2940) assignment is promising but the paper overlooks one of the Belle ratios it cites. read the letter →

arxiv 2501.00268 v2 pith:3DNZ5AHH submitted 2024-12-31 hep-ph

Yu-Bin Zhang , Li-Ye Xiao , Xian-Hui Zhong This is my paper · ORCID
classification hep-ph
keywords charmedbaryonsLambda_cresonancesstrongdecaysquarkpaircreationmodelj-jcouplingschemelambda-modeexcitationsrho-modeexcitedbaryonspectroscopy
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

This paper tries to pin down the quark-model quantum numbers of the low-lying excited $\Lambda_c^+$ baryons by computing their OZI-allowed two-body strong decay widths in the quark pair creation model with $j$-$j$ coupling. Its central result is that the disputed $\Lambda_c(2940)^+$ is best described as the $2P$-wave $\lambda$-mode state with $J^P = 3/2^-$: the predicted total width is $23.65$ MeV, against the measured $20^{+6}_{-5}$ MeV, and the predicted $pD^0/\Sigma_c\pi$ ratio is $4.48$, close to Belle's $3.59 \pm 0.21 \pm 0.56$. The same calculation assigns $\Lambda_c(2910)^+$ to one of two $1P$-wave $\rho$-mode states that differ sharply in their $\Sigma_c\pi/\Sigma_c^*\pi$ ratio, and it reproduces $\Lambda_c(2595)^+$, $\Lambda_c(2625)^+$, and $\Lambda_c(2860)^+$ under standard assignments. If right, the controversial spectrum becomes an ordinary quark-model spectrum, with specific decay ratios for experiments to measure.

What carries the argument

The machine is the quark pair creation model, in which a $0^{++}$ quark-antiquark pair is created from the vacuum and rearranges with the quarks of the initial baryon into two final hadrons. Every partial width is a spin-flavor weighted overlap integral of simple harmonic oscillator spatial wave functions, multiplied by a vertex form factor $e^{-p^2/2\Lambda^2}$ with cut-off $\Lambda = 780$ MeV. States are classified in $j$-$j$ coupling as $|J^P, j\rangle_{\lambda/\rho}$, where $j$ is the total angular momentum of the light diquark, $\lambda$ denotes orbital excitation between the diquark and the charm quark, and $\rho$ denotes orbital excitation between the two light quarks. The oscillator parameter $\alpha_\rho = 0.4$ GeV controls the rho-mode wave functions, and their orthogonality to the ground state is what suppresses channels such as $ND$ and $D^*N$ for rho-mode states, leaving $\Sigma_c\pi$ and $\Sigma_c^*\pi$ as the decisive decay modes.

What would settle it

A decisive test is to measure the ratio $\Gamma[\Lambda_c(2910)^+ \to \Sigma_c\pi]/\Gamma[\Lambda_c(2910)^+ \to \Sigma_c^*\pi]$: the paper predicts about $1.99$ for the $3/2^-$ rho-mode candidate and about $0.51$ for the $5/2^-$ candidate, so a measured value significantly different from both, or a remeasurement of the $\Lambda_c(2940)^+$ $pD^0/\Sigma_c\pi$ ratio far from $4.48$, would rule out the proposed assignments.

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Extended reading notes

Core claim

Using the quark pair creation model, the paper computes OZI-allowed two-body strong decay widths for the $1P$-, $1D$-, $2S$-, and $2P$-wave $\Lambda_c$ states, in both $\lambda$-mode and $\rho$-mode excitations and in the $j$-$j$ coupling scheme. The positive assignment at the center of the paper is $\Lambda_{c1}|J^P = 3/2^-, 1\rangle_\lambda$ for $\Lambda_c(2940)^+$: this state gives a total width of $23.65$ MeV, close to the measured $20^{+6}_{-5}$ MeV, and a $pD^0/\Sigma_c\pi$ partial-width ratio of $4.48$, close to the measured $3.59 \pm 0.21 \pm 0.56$ and far from the $8.41$ of the $J^P = 1/2^-$ alternative. For $\Lambda_c(2910)^+$, the paper narrows the options to $\Lambda_c|J^P = 3/2^-, 2\rangle_\rho$ and $\Lambda_c|J^P = 5/2^-, 2\rangle_\rho$, whose widths both match the observed value but whose $\Sigma_c\pi/\Sigma_c^*\pi$ ratios are about $1.99$ and $0.51$. It also assigns $\Lambda_c(2860)^+$ to the $1D$ $\lambda$-mode $3/2^+$ state, leaves $\Lambda_c(2765)^+$ as a plausible $2S$ $\lambda$-mode $1/2^+$ candidate, and reports that $\Lambda_c(2880)^+$ cannot be reproduced as the $1D$ $\lambda$-mode $5/2^+$ partner.

Load-bearing premise

The load-bearing premise is that rho-mode excited wave functions are orthogonal to the ground-state wave function, so their $ND$ and $D^*N$ decays vanish and their widths come only from $\Sigma_c\pi$ and $\Sigma_c^*\pi$; if that orthogonality fails under the real decay vertex or the form factor, the predicted rho-mode widths and the $\Lambda_c(2910)^+$ discrimination change.

Editorial extensions

If this is right

  • If $\Lambda_c(2940)^+$ is the $2P$ $\lambda$-mode $3/2^-$ state, the $D^*N$ molecular interpretation is disfavored and the resonance belongs to the ordinary charmed-baryon spectrum.
  • $\Lambda_c(2910)^+$ can be identified by measuring $\Sigma_c\pi$ versus $\Sigma_c^*\pi$: the $3/2^-$ rho candidate predicts a ratio near $1.99$, while the $5/2^-$ candidate predicts near $0.51$.
  • $\Lambda_c(2860)^+$ as the $1D$ $\lambda$-mode $3/2^+$ state should appear in $\Sigma_c\pi$ and $nD^+$ final states as well as the $pD^0$ channel where it was discovered.
  • If $\Lambda_c(2765)^+$ is the $2S$ $\lambda$-mode $1/2^+$ candidate, its width should be near $21$ MeV and its $\Sigma_c\pi$ and $\Sigma_c^*\pi$ partial widths nearly equal.
  • The paper's failure to reproduce $\Lambda_c(2880)^+$ as the $1D$ $5/2^+$ partner leaves that state's assignment open.

Reading between the lines

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

  • A high-statistics ratio measurement for $\Lambda_c(2910)^+$ is the paper's sharpest testable handle; a central value between the two predicted ratios would indicate that the simple quark-model assignment is incomplete.
  • The orthogonality suppression of rho-mode decays rests on one oscillator parameter, $\alpha_\rho = 0.4$ GeV; repeating the overlaps with wave functions constrained by lattice QCD would show whether the predicted rho-mode widths are robust or an artifact of the oscillator basis.
  • If $\Lambda_c(2940)^+$ is confirmed as the $2P$ $\lambda$-mode $3/2^-$ state, the $nD^+$ channel should be almost as strong as $pD^0$; a dedicated search for $\Lambda_c(2940)^+ \to nD^+$ would provide an independent check.
  • Because $\Lambda_c(2880)^+$ resists the $1D$ $5/2^+$ assignment, the missing partner of $\Lambda_c(2860)^+$ may still be unobserved and should be looked for in $\Sigma_c^*\pi$, where the model predicts the $5/2^+$ state would dominantly decay.
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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 / 6 minor

Summary. The paper uses the quark pair creation (3P0) model in the j-j coupling scheme to compute OZI-allowed two-body strong decay widths of the low-lying 1P, 1D, 2S, and 2P excited Λ_c baryons, considering both λ-mode and ρ-mode excitations. It assigns the observed states as follows: Λ_c(2595) and Λ_c(2625) as the 1P λ-mode 1/2^- and 3/2^- states; Λ_c(2860) as the 1D λ-mode 3/2^+ state; Λ_c(2910) as either of the two 1P ρ-mode states with J^P=3/2^- or 5/2^-; Λ_c(2765) as a possible 2S λ-mode 1/2^+ state; and Λ_c(2940) as the 2P λ-mode 3/2^- state. It also reports that Λ_c(2880) is not well described as the 1D λ-mode 5/2^+ state and provides predictions for unobserved states. The central positive claim is that the Λ_c(2940) assignment is supported by the total width and the pD^0/Σ_cπ ratio.

Significance. If the assignments are correct, the paper would pin down the quark-model quantum numbers of several controversial Λ_c resonances, in particular Λ_c(2910) and Λ_c(2940), and it provides a concrete, testable observable (the Σ_cπ/Σ_c*π ratio) to distinguish the two Λ_c(2910) candidates. The study is systematic, covers ρ-mode excitations that are often omitted, and honestly reports a negative result for the Λ_c(2880) assignment. The model is standard and the calculations are of the kind commonly used in this field; the main value is phenomenological. However, the absolute width scale is calibrated with one fitted parameter and the central Λ_c(2940) claim is based on a subset of the available Belle data, so the significance is contingent on a more complete comparison.

major comments (3)
  1. [Sec. III.F, Table VIII] The paper claims that Λ_c1(3/2^-,1)_λ is in good agreement with the nature of Λ_c(2940) based on the total width and the pD^0/Σ_cπ ratio, citing Belle [16] as the 'more accurate reference'. However, the same Belle measurement also provides B(Λ_c(2940)→Λ_cη)/B(Λ_c(2940)→Σ_cπ), which the introduction explicitly mentions as part of the new data. Table VIII contains no Λ_cη partial width for either 2P λ candidate, and no selection rule is given to exclude this channel. The Λ_cη final state is kinematically open (threshold about 2834 MeV) and is allowed by parity and angular momentum for both the 3/2^- candidate (L=2) and the 1/2^- candidate (L=0). The authors should compute Γ(Λ_cη) for both 2P λ states and compare the resulting Λ_cη/Σ_cπ ratio with the Belle value; without this, the claimed 'good agreement' is incomplete and the assignment is not secured by the full dataset.
  2. [Sec. III.A, Table III] The predicted total width of Λ_c(2595) as the 1P λ-mode 1/2^- state is 7.07 MeV, while the experimental value is 2.59 ± 0.30 ± 0.47 MeV, i.e. a factor of about 2.7 larger. The text states this is 'roughly consistent' with the observations, but the discrepancy is much larger than the combined experimental uncertainty. Because this state is the primary calibration check for the model's absolute width scale, the authors should either quantify the theoretical uncertainties that could justify this level of agreement or soften the abstract's claim that the 1P λ-mode assignments 'reproduce the experimental data well'. This matters for the later use of total widths (e.g. for Λ_c(2940)) as supporting evidence.
  3. [Sec. III.B] The paper drops the ND and D*N decay channels for all ρ-mode excitations based on the statement that these decays 'are forbidden due to the orthogonality of spatial wave functions'. No derivation or reference is given, and the statement is not obvious in the 3P0 model because the vertex contains the solid harmonic Y_1^m((p4-p5)/2), which can supply the odd momentum needed to connect orthogonal harmonic-oscillator states. The external form factor of Eq. (9) multiplies the amplitude after the spatial integral and does not by itself preserve or break this orthogonality. This selection rule is load-bearing for the Λ_c(2910) assignment: it is what restricts the decays to Σ_cπ and Σ_c*π and therefore determines the total widths and the discriminating ratio Γ(Σ_cπ)/Γ(Σ_c*π). The authors should show explicitly that the overlap vanishes for the ND channels in the harmonic-oscillator limit, or provide a reliable reference for this rule, and discuss how robust the Λ_c(2910) predictions are if the rule is only approximate.
minor comments (6)
  1. [Abstract and Sec. III.F] The phrase 'mostly likely to be a good assignment' should read 'most likely'; the same typo appears in the abstract and in Sec. III.F.
  2. [Sec. III.F, Eq. (36) and Eq. (39)] The text attributes the measured ratio 3.59 ± 0.21 ± 0.56 to 'the LHCb Collaboration [16]', but Ref. [16] is a Belle publication. Please correct the attribution.
  3. [Sec. III.F, Eq. (39)] The statement that the predicted ratio 4.48 is 'close to the upper limit of the measurement' should be made quantitative. The 1σ upper limit from 3.59 ± 0.21 ± 0.56 is about 4.36 (adding the two uncertainties linearly) or about 4.19 (adding in quadrature), so 4.48 lies somewhat above the 1σ range. Please state the significance of the difference.
  4. [Table IV] The two columns for the Λ_c(2910) candidates under the J^P=3/2^-,2 and J^P=5/2^-,2 rows are visually confusing, since each candidate is evaluated both at the predicted mass and at the experimental mass. Please add subheadings or separate rows that clearly distinguish M=2885, M=2914, M=2900, and M=2914.
  5. [Sec. III.B, Eq. (13)] The 'mixing angle θ' is mentioned in the text and used in Fig. 2, but Eq. (13) is just the standard recoupling between j-j and L-S bases and does not define θ. Please define θ explicitly and state how the physical states are parametrized in terms of it.
  6. [Sec. II] The pair-creation strength γ=11.51 is said to be fixed by fitting Σ_c(2520)→Λ_cπ, but the input width used for this fit is not reported. Please give the experimental or fitted value of Γ[Σ_c(2520)→Λ_cπ] so that the normalization of the absolute widths can be reproduced.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the only fitted constant γ is calibrated externally to Σ_c(2520)→Λ_cπ, the discriminating comparisons are γ-independent ratios, and the central J^P assignments remain falsifiable model predictions.

full rationale

The decay calculation is a genuine model prediction rather than a repackaging of its inputs. The single global parameter γ is fitted to the external channel Σ_c^{++}(2520)→Λ_c^+π^+ (Sec. II) and is never adjusted to the target resonances; the assignments for Λ_c(2910) and Λ_c(2940) are tested chiefly through partial-width ratios such as Γ(Σ_cπ)/Γ(Σ_c^*π) (Eq. (15)) and Γ(pD^0)/Γ(Σ_cπ) (Eq. (39)), in which γ cancels by construction. Fixing candidate masses at the observed values sets phase space, but it does not define the predicted width ratios on which the spin-parity conclusions rest. The model parameters α_ρ, Λ, and R, including values taken from Refs. [45] and [62] with overlapping authorship, are stated inputs rather than conclusions forced by those citations; they do not encode the paper's J^P assignments. The omission of the Λ_cη/Σ_cπ ratio from Ref. [16] is a possible completeness or correctness concern, not a circularity, because no equation reduces a target prediction to the data used to fix it.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

No new particles, fields, forces, or conserved quantities are introduced; all assignments refer to existing quark-model states and observed resonances. The free parameters are the standard inputs of the quark-pair-creation model, mostly inherited from prior literature, with only gamma freshly fitted to one external datum.

free parameters (7)
  • vacuum pair-creation strength gamma = 11.51
    Fit to the measured Sigma_c(2520) to Lambda_c pi width (Sec. II). Absolute widths scale as gamma^2; the ratios used for assignments are independent of gamma.
  • rho-mode oscillator parameter alpha_rho = 0.4 GeV
    Chosen (Sec. II) for the light-diquark relative-motion wave function; sets the node positions that control the rho-mode decay amplitudes, including the orthogonality that suppresses ND channels.
  • form-factor cutoff Lambda = 780 MeV
    Adopted from Ref. [62] to soften the quark-pair-creation vertex (Eq. 9). Affects absolute widths and some ratios.
  • meson oscillator parameters R = 2.5 GeV^-1 (light), 1.67 GeV^-1 (D), 1.94 GeV^-1 (D*)
    Taken from Ref. [64] for ground-state meson wave functions (Eq. 6).
  • light-heavy oscillator parameter alpha_lambda = derived via Eq. (12)
    alpha_lambda = (3 m_Q / (2 m_q + m_Q))^{1/4} alpha_rho with m_q = 330 MeV and m_c = 1700 MeV; determines the lambda-mode wave-function scale.
  • j-j / L-S mixing angle theta = about 35 degrees (central value)
    Used for rho-mode state decomposition (Eq. 13, Fig. 2); the paper varies theta but the central value is an input from heavy-quark-symmetry considerations.
  • constituent quark masses = m_u = m_d = 330 MeV, m_s = 450 MeV, m_c = 1700 MeV
    Standard constituent masses adopted in Sec. II for the wave-function scales and the alpha_lambda relation.
assumptions (5)
  • domain assumption The quark-pair-creation (3P0) model describes OZI-allowed two-body strong decays of hadrons.
    The entire calculation rests on this phenomenological model (Sec. II, Eqs. 1-11). Its accuracy is not derived from QCD.
  • domain assumption Baryon and meson wave functions are non-relativistic simple harmonic oscillator states.
    Eqs. (2)-(6) use SHO wave functions; node structure and orthogonality of rho-mode excitations (Sec. III.B) follow from this choice.
  • ad hoc to paper The form factor e^{-p^2/(2 Lambda^2)} with Lambda = 780 MeV regularizes the high-momentum vertex.
    Eq. (9) modifies the pair-creation vertex; the cutoff value is taken from Ref. [62], not derived in this work.
  • domain assumption Heavy-quark symmetry and the j-j coupling scheme with mixing angle theta about 35 degrees classifies the states.
    Used to express states in the j-j basis (Eq. 13) and to discuss the Lambda_c(1/2-,0)_rho state (Fig. 2).
  • domain assumption Masses of initial and final hadrons can be taken from experiment or from Capstick-Isgur [30] predictions.
    Tables I-II; the paper fixes many initial masses at observed values, and uses predicted masses for unobserved states, acknowledging sensitivity near thresholds.

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Cite this review

Pith. "Pith review of Possible explanations of the observed $\Lambda_c$ resonances." pith.science (2026). https://pith.science/paper/3DNZ5AHH

@misc{pith2026250100268,
  author       = {Pith},
  title        = {Pith review of: Possible explanations of the observed $\Lambda_c$ resonances},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3DNZ5AHH}},
  note         = {Machine review of arXiv:2501.00268}
}
abstract

Inspired by the latest experimental progress, we systematically study the OZI-allowed two-body strong decay properties of $1P$-, $1D$-, $2S$- and $2P$-wave $\Lambda_c$ baryons within the $j $-$j$ coupling scheme in the framework of the quark pair creation model. The calculations indicate that: (i) Taking the observed states $\Lambda_c(2595)^+$ and $\Lambda_c(2625)^+$ as the $1P$-wave $\lambda$-modes states $\Lambda_c|J^P=1/2^-,1\rangle_{\lambda}$ and $\Lambda_c|J^P=3/2^-,1\rangle_{\lambda}$, respectively, we can reproduce the experimental data well in theory. (ii) Combining with the measured mass and the decay properties of $\Lambda_c(2860)^+$, this excited state can be explained as $1D$-wave $\lambda$-mode state $\Lambda_c|J^P=3/2^+,1\rangle_{\lambda\lambda}$. (iii) The newly observed state $\Lambda_c(2910)^+$ may be assigned as one of the $1P$-wave $\rho$-mode states $\Lambda_c|J^P=3/2^-,2\rangle_{\rho}$ or $\Lambda_c|J^P=5/2^-,2\rangle_{\rho}$. Meanwhile, we notice that the partial decay width ratio between $\Sigma_c\pi$ and $\Sigma_c^*\pi$ for the two candidates is significantly different. Hence, experimental progress in this ratio measurement may shed light on the nature of $\Lambda_c(2910)^+$. (iv) According to the properties of $\Lambda_c(2765)^+$, we find that the $2S$-wave $\lambda$-mode state $\Lambda_{c1}|J^P=1/2^+,0\rangle_{\lambda}$ may be a potential candidate. (v) The $2P$-wave $\lambda$-mode state $\Lambda_{c1}|J^P=3/2^-,1\rangle_{\lambda}$ is mostly likely to be a good assignment of the controversial state $\Lambda_c(2940)^+$. Both the total decay width and partial decay ratio between $pD^0$ and $\Sigma_c\pi$ are in good agreement with the observations. (vi) In addition, for the missing $\Lambda_c$ excitations, we obtain their strong decay properties and hope that's useful for future experimental exploration.

Figures

Figures reproduced from arXiv: 2501.00268 by the authors.

Figure 1
Figure 1. FIG. 1: Possible decay ways for the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Partial and total strong decay widths of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Partial and total strong decay widths of the two [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Partial and total strong decay widths of the two 2 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Partial and total strong decay widths of the two [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Partial and total strong decay widths of the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

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