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$\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ productions in $\pi^{-} p$ scattering process

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The structure near 2.9 GeV in the D0p mass spectrum of pion–proton scattering should be Λc(2910), not Λc(2940).

desk verdict Workmanlike effective-Lagrangian calculation with a testable J-PARC prediction, but the 2910-over-2940 dominance claim rests on a cutoff that the authors themselves say should be smaller. read the letter →

arxiv 2502.03277 v2 pith:4Y5INKV4 submitted 2025-02-05 hep-ph hep-ex

Quan-Yun Guo , Dian-Yong Chen This is my paper · ORCID
classification hep-phhep-ex
keywords Λc(2910)Λc(2940)D*NmolecularstateseffectiveLagrangianpion-inducedreactionshadronmoleculesD0pinvariantmassJ-PARC
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 predicts which of the two nearly degenerate charmed-baryon candidates, $\Lambda_c(2910)$ and $\Lambda_c(2940)$, should appear as the structure near 2.9 GeV in the $D^0 p$ invariant mass spectrum of $\pi^- p \to D^- D^0 p$ at J-PARC. Treating both states as $D^* N$ molecules with $J^P = 1/2^-$ and $3/2^-$, the authors compute the production amplitudes with an effective Lagrangian approach and fix the cutoff by the measured upper limit on $\pi^- p \to D^{*-} \Lambda_c(2286)$. Their central numbers are a total cross section of $0.49^{+1.56}_{-0.38}$ nb at $p_\pi = 15$ GeV, dominated by $t$-channel $D^*$ exchange, and a $\Lambda_c(2910)$ signal in the $D^0 p$ spectrum about an order of magnitude larger than the $\Lambda_c(2940)$ signal. If correct, the prediction turns a spectroscopic ambiguity into a concrete peak-position measurement that the J-PARC pion beam can test.

What carries the argument

The argument is carried by effective-Lagrangian amplitudes for $s$-, $u$-, and $t$-channel exchange, with the $t$-channel $D^*$ meson exchange as the dominant mechanism. The central object is the form-factor cutoff $\Lambda_r$ appearing in $F(k_i, m_i, \Lambda_r) = \Lambda_r^4 / [\Lambda_r^4 + (k_i^2 - m_i^2)^2]$, fixed to 1.1 GeV by requiring the $\pi^- p \to D^{*-} \Lambda_c(2286)$ cross section to stay below its experimental upper limit, and then applied unchanged to the molecular-state vertices. The $\Lambda_c(2910)$ and $\Lambda_c(2940)$ couplings to their $D^* N$ constituents come from the compositeness condition with binding energies 32 MeV and 6.2 MeV, respectively, and the decay couplings into $D^0 p$ are set by the decay widths and branching fractions of the two states. The decisive feature is that the $t$-channel $D^*$ exchange that produces the molecular states and feeds their $D^0 p$ decay favours the lighter, wider $\Lambda_c(2910)$ over the heavier, narrower $\Lambda_c(2940)$.

What would settle it

Measure the $D^0 p$ invariant mass distribution of $\pi^- p \to D^- D^0 p$ at J-PARC with $p_\pi \approx 13$–15 GeV; the claim predicts a peak near 2914 MeV with a total cross section around 0.5 nb and a $\Lambda_c(2940)$ peak about ten times smaller. Finding the 2.9 GeV structure at the $\Lambda_c(2940)$ mass, or measuring an upper limit well below 0.1 nb at that energy, would falsify the prediction.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the expected 2.9 GeV enhancement in the $D^0 p$ invariant mass distribution of $\pi^- p \to D^- D^0 p$ should be attributed to $\Lambda_c(2910)$, not to $\Lambda_c(2940)$. With $\Lambda_r = 1.1$ GeV determined from the 7 nb upper limit for $\pi^- p \to D^{*-} \Lambda_c(2286)$ at $P_\pi = 13$ GeV, the two-body cross sections at $p_\pi = 30$ GeV stand in the ratios $1 : 4.8 : 1.42 : 0.26$ for $\pi^- p \to D^{*-} \Lambda_c(2286)$, $\pi^- p \to D^- \Lambda_c(2286)$, $\pi^- p \to D^- \Lambda_c(2910)$, and $\pi^- p \to D^- \Lambda_c(2940)$. In the three-body process, the intermediate $\Lambda_c(2910)$ dominates the $t$-channel contribution over $\Lambda_c(2940)$ by a factor of about 20, and in the final $D^0 p$ mass spectrum the $\Lambda_c(2910)$ peak is roughly an order of magnitude stronger, with $\Lambda_c(2286)$ serving as a smooth background. The authors conclude that a future J-PARC measurement of this reaction can distinguish the two molecular-state interpretations.

Load-bearing premise

The load-bearing premise is that the cutoff parameter $\Lambda_r = 1.1$ GeV, calibrated on the compact $\Lambda_c(2286)$ reference channel, also applies without reduction to the spatially larger $D^* N$ molecular states $\Lambda_c(2910)$ and $\Lambda_c(2940)$; the paper itself notes that a smaller cutoff would lower these cross sections and could change which resonance dominates the 2.9 GeV peak.

Editorial extensions

If this is right

  • At J-PARC pion momenta above roughly 13 GeV, the predicted $\pi^- p \to D^- D^0 p$ cross section is a few tenths of a nanobarn to a few nanobarns, so the process should be experimentally accessible.
  • The $D^0 p$ invariant mass spectrum should show its 2.9 GeV enhancement at the $\Lambda_c(2910)$ mass, near 2914 MeV, with any $\Lambda_c(2940)$ contribution about an order of magnitude smaller.
  • For the two-body channels at $p_\pi = 30$ GeV, $\Lambda_c(2940)$ production should be suppressed relative to $\Lambda_c(2910)$ by a factor of roughly 5.5, a pattern that can be checked through $\pi^- p \to D^- \Lambda_c(2910)$ versus $D^- \Lambda_c(2940)$.
  • Because the $t$-channel $D^*$ exchange dominates, the angular and pion-energy dependence of the cross section should follow the $t$-channel propagator rather than the $s$- or $u$-channel shapes.
  • The smooth $\Lambda_c(2286)$ contribution sits below the $D^0 p$ threshold and acts as a background, so subtracting it should cleanly expose the molecular-state peak.

Reading between the lines

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

  • If, as the authors themselves note, the cutoff for the spatially larger molecular states should be smaller than the 1.1 GeV value fixed from $\Lambda_c(2286)$, then all predicted $\Lambda_c(2910)$ and $\Lambda_c(2940)$ cross sections would shrink; whether $\Lambda_c(2910)$ still dominates the 2.9 GeV peak is not guaranteed and should be rechecked at $\Lambda_r \lesssim 1$ GeV.
  • The same calibrated amplitudes could be carried over to other production channels that populate these two states, such as photoproduction off a neutron or $\bar p p$ annihilation, where the predicted ratio pattern would serve as a cross-channel consistency test.
  • A line-shape analysis of the measured $D^0 p$ spectrum using the two resonances' widths (about 52 and 20 MeV) could distinguish a broad $\Lambda_c(2910)$ bump from the narrower $\Lambda_c(2940)$ even at modest statistics; the paper's claim implies the bump centroid sits near 2.91 GeV rather than 2.94 GeV.
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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 / 5 minor

Summary. The paper uses an effective Lagrangian approach to compute cross sections for π−p→D*−Λc(2286), π−p→D−Λc(2286)/Λc(2910)/Λc(2940), and the three-body process π−p→D−D0p, assuming Λc(2910) and Λc(2940) are D*N molecular states with J^P=1/2− and 3/2−, respectively. The cutoff Λr is fixed to 1.1 GeV by requiring the reference cross section π−p→D*−Λc(2286) to lie below the experimental upper limit of 7 nb at Pπ=13 GeV. With this parameter, the authors predict the ratio of two-body cross sections at Pπ=30 GeV to be 1:4.8:1.42:0.26 for the D*−Λc(2286), D−Λc(2286), D−Λc(2910), and D−Λc(2940) channels, and estimate the total three-body cross section at Pπ=15 GeV to be (0.49+1.56−0.38) nb. The central claim is that the structure near 2.9 GeV in the D0p invariant mass spectrum of π−p→D−D0p should correspond to Λc(2910) rather than Λc(2940), which is proposed as a testable signal at J-PARC.

Significance. If the central prediction is reliable, it offers a concrete, falsifiable experimental signature that can distinguish between two molecular-state interpretations at J-PARC. The paper provides complete effective Lagrangians, explicit amplitudes, and a transparent parameter calibration, and it is commendable that the authors state the physical limitation that molecular states should have a smaller cutoff. However, the main prediction depends on two fragile inputs: the transferability of the cutoff Λr=1.1 GeV from a compact baryon to spatially larger molecular states, and the coupling constants inherited from the same authors' earlier model calculation (Ref. [57]). These dependencies are acknowledged or implicit in the manuscript but are not quantitatively explored, so the significance of the central claim is conditional rather than established.

major comments (3)
  1. [Section III.C, Eq. (9), Fig. 7] The central claim that the structure around 2.9 GeV should be assigned to Λc(2910) rather than Λc(2940) rests on the relative magnitude of the two signals in the D0p invariant mass distribution, which is controlled by the form factor F(k,m,Λr) of Eq. (8) applied to all vertices with a single cutoff Λr=1.1 GeV. The authors themselves state at the end of Section III.C that, as ND* molecular states, Λc(2910) and Λc(2940) should have a larger size and therefore a cutoff smaller than 1 GeV, which would reduce the cross sections. Because the two resonances have different D* virtualities and off-shell line shapes, a lower cutoff for the molecular vertices can change the relative 2910/2940 weight and thus the identity of the predicted peak. No sensitivity study of the differential spectrum, or of the dominance ratio, to Λr in the molecular-vertex range below 1 GeV is provided. This is load-bearing for the main conclusion and should be addressed with a quantitative scan or a robust argument that the dominance persists.
  2. [Section III.B, Fig. 4] The calibration of Λr uses only an upper limit, not a measured cross section, so it does not determine Λr uniquely; it merely imposes an inequality. Moreover, the uncertainty band quoted in Fig. 4(a) is not consistent with that upper limit: at Pπ=13 GeV the central value is 2.59 nb, but the +7.15 nb upper uncertainty reaches approximately 9.7 nb, exceeding the 7 nb bound from Ref. [66]. The range Λr=1.0–1.2 GeV is therefore only partially compatible with the reference data, and the corresponding uncertainty band in Fig. 8 for the three-body cross section overstates the allowed model variation. The authors should either restrict the admissible Λr range to values satisfying the bound or justify why including values above the bound is acceptable for estimating theoretical uncertainty.
  3. [Section III.A, Table I, Eq. (11)] The couplings g_Λc(2910)ND, g_Λc(2910)πΣc, g_Λc(2940)ND, and g_Λc(2940)πΣc are fixed by the branching fractions quoted in Eq. (11), which are taken from Ref. [57], a previous paper by the same group using the same D*N molecular assignments. Consequently, the relative strength of Λc(2910) versus Λc(2940) in the D0p spectrum is not an independent prediction of the present calculation but is inherited from those earlier model outputs. This is not an internal inconsistency, but it means the proposed J-PARC measurement would test the combined molecular model rather than the production mechanism alone. The manuscript should state this inheritance explicitly and avoid presenting the 2910/2940 dominance as a new result that is independent of the model assumptions.
minor comments (5)
  1. [Section III.C, Fig. 6(a)] The text says that the contributions from Λc(2286) and Λc(2940) are not shown in Fig. 6(a) because their cross sections are less than 1 fb, but the figure caption lists three curves corresponding to Λc(2286), Λc(2910), and Λc(2940). Please clarify which curves are actually plotted and why the caption is misleading.
  2. [Throughout] There are several typographical errors, including 'whlie' near Eq. (5), 'Λc((2940))' in Section III.A, and 'crosse an order of magnitude' near Fig. 8. These should be corrected.
  3. [Section III.B, Fig. 4] The statement that Λr=1.1 GeV is 'safely under the experimental upper limit' should be qualified, since the quoted uncertainty band extends above the 7 nb bound; the phrase 'safely' is only true for the central value.
  4. [Section II.B, Eq. (17)] The phase-space integral in Eq. (17) is written as dσ = ... d p0_5 d p0_3 d cosθ dη, but the integration limits and the definition of the five-body phase-space variables are not specified. Please provide the integration ranges or reference a standard phase-space parametrization so the numerical implementation is reproducible.
  5. [Abstract and Summary] The phrase 'should correspond to Λc(2910) rather than Λc(2940)' is presented as a definitive conclusion. Given the model dependence and the admitted cutoff uncertainty, a conditional formulation (e.g., 'within the present model') would be more appropriate and would better match the actual strength of the argument.

Circularity Check

1 steps flagged · score 6.0 of 10

The central claim that the 2.9 GeV structure is Λc(2910) rather than Λc(2940) is largely inherited from the same-group model's branching fractions in Ref. [57] via Table I and Eq. (9); the new scattering calculation repackages those prior decay inputs.

  1. self citation load bearing [Section III.A (Coupling Constants), around Eqs. (10)-(11) and Table I; applied in Eq. (9) and Fig. 7]
    "in Ref. [57], the decay properties of Λc(2910) and Λc(2940) were investigated, and the estimations indicated that the branching fractions of ND and πΣc channels for Λc(2910) and Λc(2940) are about, Br(Λc(2910)→ ND) = 40%, Br(Λc(2910)→πΣ) = 60%, Br(Λc((2940))→ ND) = 11%, Br(Λc(2940)→πΣ) = 12.5%. With the above branching fractions, the central values of the widths of Λc(2940) and Λc(2910) and the formula in Eq. (10), one can obtain the coupling constants gΛ∗ c1ND, gΛ∗ c1Σcπ, gΛ∗ c2ND, and gΛ∗ c2Σcπ, which are listed in Table I."

    Ref. [57] is by the same group (Zi-Li Yue, Quan-Yun Guo, Dian-Yong Chen), and it is the only stated source for the branching fractions that fix the Λc(2910)/Λc(2940)→ND couplings. Those couplings enter the D0p decay amplitudes of Eq. (9), and since Br(Λc(2910)→ND) is about 40% while Br(Λc(2940)→ND) is about 11%, the 2910 signal in the D0p spectrum is predicted to be roughly an order of magnitude larger than the 2940 signal (Fig. 7). The paper's central conclusion that the 2.9 GeV structure corresponds to Λc(2910) rather than Λc(2940) is therefore a direct propagation of the same authors' earlier model outputs, not an independent consequence of the new π−p production calculation.

full rationale

The paper does contain genuinely independent elements: the calibration of the cutoff Λr to the external upper limit on π−p→D*−Λc (Ref. [66]), the s/u/t-channel decomposition, and the absolute cross-section predictions that could be tested at J-PARC. However, the central claim identifying the 2.9 GeV structure with Λc(2910) over Λc(2940) is not an independent result of this calculation. The relative D0p signal strengths are governed by the couplings in Table I, which are derived in Sec. III.A from the branching fractions that the same group estimated in Ref. [57]. The measured masses and widths supply only the overall normalization and line-shape positions; they do not determine which state dominates the D0p spectrum. The paper itself also notes that the 1.1 GeV cutoff may be too large for the spatially extended molecular states, which is a robustness concern rather than a circularity, but it reinforces that the relative signal prediction is not strongly constrained by the new channel. Because the headline claim reduces, through Eq. (9) and Table I, to the authors' prior decay-model outputs, a circularity score of 6 is appropriate: the derivation is not vacuous, but one of its principal predictions is inherited by construction from a self-citation chain.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central claim rests on several modeled inputs: the cutoff Λr, the molecular assignment and branching fractions from the authors' own prior work, SU(4)-based couplings, and the tree-level truncation. No new particles or forces are introduced. The most fragile input is the transferability of Λr to molecular-state vertices, which the paper itself questions.

free parameters (2)
  • Λr (form-factor cutoff) = 1.1 GeV, varied from 1.0 to 1.2 GeV
    Phenomenological cutoff in F(k_i, m_i, Λr) = Λr^4/(Λr^4 + (k_i^2 - m_i^2)^2); chosen so the computed π−p→D*−Λc(2286) cross section at 13 GeV (2.59 nb) lies below the experimental upper limit of 7 nb. An upper limit is an inequality, so Λr is not uniquely determined.
  • g_Λc(2910)ND, g_Λc(2940)ND, g_Λc(2910)πΣc, g_Λc(2940)πΣc = 0.99, 0.84, 2.22, 1.35 respectively
    Derived from assumed branching fractions from Ref [57] (40%, 11%, 60%, 12.5%) together with experimental total widths, using Eq. (10). These couplings largely set the relative resonance contributions in the final prediction.
assumptions (6)
  • domain assumption Λc(2910) and Λc(2940) are D*N molecular states with JP = 1/2− and 3/2−, respectively.
    Adopted from the authors' previous decay analysis (Ref [57]) and other molecular studies; underpins the effective Lagrangians in Eq. (3).
  • domain assumption Branching fractions of Λc(2910) and Λc(2940) to ND and πΣc are 40%/60% and 11%/12.5%, respectively.
    Taken from Ref [57], a paper by the same group, and used to fix the couplings in Table I. These branching fractions are not independently measured.
  • domain assumption SU(4) flavor symmetry determines the light-heavy meson-baryon coupling constants.
    The paper acknowledges that large mass differences between charmed and light quarks significantly break SU(4) symmetry, but invokes it because no alternative systematic method is available.
  • ad hoc to paper The same cutoff Λr = 1.1 GeV applies to vertices involving the spatially larger molecular states as to ordinary hadron vertices.
    Required to keep the model predictive. The authors themselves state the cutoff should be smaller than 1 GeV for molecular states, which would reduce the central cross sections.
  • domain assumption The Weinberg compositeness condition in the non-relativistic limit (Eq. 12) gives the couplings g_Λ*_c1ND* and g_Λ*_c2ND*.
    Used to set g_Λ*_c1ND* = 3.55 and g_Λ*_c2ND* = 2.34 from the binding energies of the two molecular states.
  • domain assumption Only tree-level s, u, and t-channel diagrams are included, with no final-state interactions or additional background parameterization.
    The amplitudes in Eqs. (4), (5), and (9) sum the selected tree diagrams; Λc(2286) is treated as a smooth background because it lies below the D0p threshold.

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Pith. "Pith review of $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ productions in $\pi^{-} p$ scattering process." pith.science (2026). https://pith.science/paper/4Y5INKV4

@misc{pith2026250203277,
  author       = {Pith},
  title        = {Pith review of: $\Lambda_c(2910)$ and $\Lambda_c(2940)$ productions in $\pi^- p$ scattering process},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4Y5INKV4}},
  note         = {Machine review of arXiv:2502.03277}
}
abstract

In the present work, we propose to investigate the productions of $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ in the $\pi^{-} p \rightarrow D^{-} D^{0} p$ processes by utilizing an effective Lagrangian approach, where $\Lambda_c(2910)$ and $\Lambda_c(2940)$ are considered as $D^\ast N$ molecular states with $J^P$ quantum numbers to be $1/2^-$ and $3/2^-$, respectively. With the cutoff parameter determined by the upper limit of the cross sections for $\pi^- p \to D^{\ast-} \Lambda_c(2286)$, the ratios of the cross sections for $\pi^- p \to D^{\ast-} \Lambda_c(2286)$, $\pi^- p \to D^{-} \Lambda_c(2286)$, $\pi^- p \to D^{-} \Lambda_c(2910)$, and $\pi^- p \to D^{-} \Lambda_c(2940)$ are estimated to be $1:4.8:1.42:0.26$ at $p_\pi=30$ GeV. Considering that the $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ state can further decay into $D^{0}p$, we estimate the cross sections for $\pi^{-} p \rightarrow D^{-} D^{0} p$ process and the differential cross sections depending on the $D^0 p$ invariant mass spectrum. Our estimations indicate that the total cross sections are $(0.49^{+1.56}_{-0.38})$ nb when $p_{\pi}=15~\mathrm{GeV}$, where the uncertainties result from the variation of the $\Lambda_{r}$. By comparing the contributions of the $s$, $u$, and $t$-channels, we conclude that the $t$-channel plays the predominant role. Moreover, the present estimations suggest that the structure around 2.9 GeV in the $D^0 p$ invariant mass spectrum of the $\pi^{-} p \rightarrow D^{-} D^{0} p$ process should correspond to $\Lambda_c(2910)$ rather than $\Lambda_c(2940)$, which can be tested by further experimental measurements at J-PARC in the future.

Figures

Figures reproduced from arXiv: 2502.03277 by the authors.

Figure 1
Figure 1. FIG. 1: Diagrams contributing to the process of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Diagrams contributing to the process of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Diagrams contributing to the process of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: (Color online) The cross sections for the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) The cross sections for the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: (Color online) The cross sections for the [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: (Color online) The [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: (Color online) The total cross sections for the [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

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