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Lattice QCD study of $\Lambda_c \Lambda_c$ scattering

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

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Pith's one-line read This paper reports the first lattice QCD calculation of $\Lambda_c\Lambda_c$ scattering in the $I(J^P)=0(0^+)$ channel and finds the interaction is repulsive, with scattering length $a_0 = -0.21(4)(8)$ fm and no bound state in the studied…

desk verdict First lattice QCD study of Lambda_c Lambda_c scattering: a competent calculation with an honest error budget, but the repulsive conclusion leans on a qualitative no-mixing check rather than a quantitative coupled-channel bound. read the letter →

arxiv 2502.05546 v2 pith:JQK7HFM4 submitted 2025-02-08 hep-lat

Hanyang Xing , Yiqi Geng , Chuan Liu , Liuming Liu , Peng Sun , Jiajun Wu , Zhicheng Yan , Ruilin Zhu This is my paper · ORCID
classification hep-lat
keywords latticeQCDLambda_cscatteringLüscherfinite-volumemethodlengtheffectiverangeexpansionheavydibaryonsrepulsiveinteractionspectrum
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 aims to settle, with first-principles lattice QCD, a question on which quark-model and effective-field-theory studies disagree: whether two $\Lambda_c$ baryons attract strongly enough to form a double-charm dibaryon. Using two 2+1-flavor Wilson-Clover ensembles at pion mass $m_\pi \sim 303$ MeV and lattice spacing $a = 0.07746$ fm, it computes the finite-volume spectrum of the $I(J^P) = 0(0^+)$ $\Lambda_c\Lambda_c$ system and extracts the scattering parameters with L\"uscher's method. The result is a repulsive interaction, $a_0 = -0.21(4)(8)$ fm and $r_0 = -0.05(13)(25)$ fm, with no bound-state pole in the energy range studied. If this holds, the charmed analog of the $H$-dibaryon is not realized as a simple single-channel $\Lambda_c\Lambda_c$ bound state at these quark masses, and the numbers become the first lattice benchmark for double-charm baryon scattering.

What carries the argument

The method is L\"uscher's finite-volume formalism: the relation $k\cot\delta(k) = \frac{2\sqrt{\pi}}{L} Z_{00}(1;q^2)$ converts each finite-volume energy into the infinite-volume s-wave phase shift $\delta(k)$, with $Z_{00}$ the generalized zeta function encoding the box geometry. The phase shift is then parameterized by the effective range expansion $k\cot\delta = \frac{1}{a_0} + \frac{1}{2} r_0 k^2$. Energy shifts are extracted from ratios of the two-baryon correlation function to single-baryon correlators, and the free energies are evaluated with the continuum dispersion relation, a choice that reduces the impact of the observed roughly 4% deviation of the lattice speed-of-light parameter $c$ from unity.

What would settle it

A higher-statistics GEVP with additional $\Xi_{cc}N$ operators that reveals level repulsion between $\Lambda_c\Lambda_c$ and $\Xi_{cc}N$ states would refute the no-mixing assumption; alternatively, a second lattice spacing at the same pion mass that moves $a_0$ to a positive value would indicate that the repulsion is a discretization artifact.

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Extended reading notes

Core claim

The central claim is that the $\Lambda_c\Lambda_c$ interaction in the $I(J^P)=0(0^+)$ channel is repulsive near threshold. From seven finite-volume energy levels across two lattice volumes, the s-wave scattering length and effective range are determined as $a_0 = -0.21(4)(8)$ fm and $r_0 = -0.05(13)(25)$ fm, where the first error is statistical and the second systematic; no pole appears in the amplitude over the fitted energy range. The $\Xi_{cc}N$ channel is omitted because a GEVP including both $\Lambda_c\Lambda_c$ and $\Xi_{cc}N$ operators shows no mixing between the levels, and the $\Sigma_c\Sigma_c$ channel is omitted because the analyzed energies lie below its threshold. This is presented as the first lattice QCD constraint on double-charm baryon scattering.

Load-bearing premise

The extraction assumes the measured finite-volume levels are purely $\Lambda_c\Lambda_c$ states and are not secretly mixed with the $\Xi_{cc}N$ channel; if a weak coupling is hiding below the statistical noise, the quoted scattering length would be biased and the repulsive conclusion could change.

Editorial extensions

If this is right

  • At $m_\pi \sim 303$ MeV, the single-channel $\Lambda_c\Lambda_c$ system in this quantum number is unbound, so any double-charm dibaryon in this channel would have to arise from coupled-channel effects rather than from the $\Lambda_c\Lambda_c$ attraction alone.
  • The quoted $a_0$ and $r_0$ give the first lattice-QCD numbers for double-charm baryon scattering, giving model calculations a concrete target to reproduce.
  • The observed absence of mixing between $\Lambda_c\Lambda_c$ and $\Xi_{cc}N$ operators supports the single-channel analysis only within current statistical precision; a stronger coupled-channel study would be needed near the $\Xi_{cc}N$ threshold.
  • Because the calculation uses one lattice spacing and one pion mass, these parameters are not yet the physical-point values; the paper quotes systematic errors from the effective-range expansion and fit-range choices but not a continuum-extrapolation error.

Reading between the lines

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

  • If the repulsion persists toward the physical pion mass, the most plausible route to a double-charm dibaryon in this channel runs through the $\Sigma_c\Sigma_c$ channel, and a future calculation with levels above that threshold would test that scenario.
  • The roughly 4% deviation of the lattice dispersion coefficient $c$ from 1 suggests charm-quark discretization effects; a second lattice spacing could turn the quoted one-point result into a continuum-extrapolated value.
  • The same correlation functions could be re-analyzed with a coupled-channel L\"uscher treatment or an alternative potential method; agreement between independent extractions would strengthen confidence in the repulsion, while disagreement would expose a systematic not covered by the quoted errors.
  • The no-mixing observation is consistent with a genuinely weak coupling or with operators that do not overlap the mixed state; adding higher-momentum $\Xi_{cc}N$ operators and more statistics would discriminate between these readings.
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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. This paper presents a lattice QCD study of ΛcΛc scattering in the I(J^P)=0(0+) channel using two N_f=2+1 Wilson-Clover ensembles with pion mass mπ≈303 MeV and lattice spacing a=0.07746 fm (L/a=32 and 48). The authors compute the finite-volume spectrum from GEVP and diagonal correlation functions, extract energy shifts from ratio fits, and apply Lüscher's finite-volume method with an effective-range expansion to obtain a0=-0.21(4)(8) fm and r0=-0.05(13)(25) fm. They interpret the negative scattering length as evidence for a repulsive interaction and thus the absence of a ΛcΛc bound state in this channel. The coupled channels ΞccN and ΣcΣc are argued to be negligible based on the observed absence of operator mixing and the energy window below the ΣcΣc threshold, respectively.

Significance. If the result holds, this is the first lattice QCD constraint on double-charm baryon scattering and provides a useful benchmark for phenomenological models, which currently disagree on whether ΛcΛc is bound. The paper benefits from a transparent analysis: the GEVP fits, the ratio method for energy shifts, the covariance-matrix fits, and the systematic-error estimates from fit-range variations and the ERE are all described in detail, and the absence of input-output circularity is clear. The main sources of concern are the unquantified effect of the open ΞccN channel and the mixing of continuum and lattice dispersion conventions in Eq. (12); both bear directly on the central quantitative claim. The single-lattice-spacing and single-pion-mass setup is acknowledged and limits the conclusions to the simulated quark masses.

major comments (3)
  1. [Sec. III.B and Figs. 2, 5] The argument for neglecting the open ΞccN channel is not quantitative. The observation that the ΛcΛc and ΞccN operators have small overlap with the eigenstates does not imply that the ΛcΛc → ΞccN scattering coupling is negligible, because the energy shift of a finite-volume level depends on the coupled-channel T-matrix and the phase space, not directly on the operator overlaps. Since mΞcc + mN ≈ 4.817 GeV is about 9 MeV below 2mΛc ≈ 4.826 GeV (Table II), ΞccN is open throughout the fitted energy range, and a weak coupling could shift the single-channel levels by more than the statistical errors. Please provide a quantitative bound, for example by performing a two-channel Lüscher fit or by inserting a test coupling and showing that the resulting shifts are within the quoted errors.
  2. [Sec. IV, Eq. (12) and Table II] The free energies used in Eq. (12) are computed with the continuum dispersion relation, while the measured Λc dispersion relation has c ≈ 0.99 (Table II). Because the ΔEn values in Eq. (11) are extracted from the ratio to the single-baryon correlators at the actual lattice momenta, the combination in Eq. (12) mixes the lattice and continuum dispersion conventions. This mismatch enters the Lüscher analysis and can bias a0 and r0. The expectation that this effect is smaller than the statistical error should be demonstrated numerically, e.g., by repeating the fits using the measured dispersion relation in the quantization condition or by assigning a systematic error from the difference.
  3. [Sec. IV, Eq. (16) and Table III] The evidence for a repulsive interaction, which is the central quantitative claim, has limited statistical strength when the quoted systematic error is included: a0 = -0.21(4)(8) fm is only about 2.3σ from zero, and the ground-state energy shift on F32P30 is 0.00085(47) in lattice units, i.e., about 1.8σ. Please state the significance of the repulsive sign explicitly, for example by giving the probability that a0 is negative, and temper the abstract and conclusions accordingly if that probability is not high.
minor comments (5)
  1. [Abstract and Sec. V] The abstract and summary should explicitly state that the repulsive interaction and the scattering parameters are obtained at mπ ≈ 303 MeV, since no chiral extrapolation is performed.
  2. [Eqs. (7)-(8)] Equations (7) and (8) contain an extra closing parenthesis in the definitions of OΞccN and OΣcΣc.
  3. [Sec. III.B] The notation 'p2' in the operator labels is ambiguous; using 'n' or '|p|^2' would be clearer.
  4. [Fig. 6] The axis label of Fig. 6 appears truncated ('0/') and should be completed, e.g., 'δ0 (rad)' or 'δ0/π'.
  5. [Sec. IV] The statement that the effect of the c≈0.99 dispersion should be 'much smaller than the statistical error' is an estimate; please either provide a numerical estimate or move this caveat to the systematic-error discussion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the scattering parameters are extracted from independent lattice finite-volume spectra via the external Lüscher relation; no fitted input is fed back into the spectrum.

full rationale

The paper's central result, a0 = -0.21(4)(8) fm and r0 = -0.05(13)(25) fm, is obtained by (i) computing finite-volume two-baryon energies from lattice correlation functions (Sec. III), and (ii) inverting the standard Lüscher quantization condition (Eq. 13) with an effective-range parameterization (Eq. 14) via a chi-square fit to those energies (Eq. 15). Nothing in the input encodes the sign or magnitude of the scattering length: the input is the set of measured energy shifts in Table III, and the output is a fit to those independent lattice data. The use of the continuum dispersion relation in Eq. (12) is an explicit consistency choice, not a fitted parameter recycled as a prediction. The omission of the Xi_ccN and Sigma_cSigma_c channels is justified by observed level shifts and thresholds, and the paper explicitly acknowledges in Sec. V that a quantitative coupled-channel study would require more operators and three-body treatments; that is a systematic-uncertainty concern, not circularity. The CLQCD ensemble citation is data provenance, and the Lüscher and distillation references are external standard methods. No self-citation is load-bearing, and no derivation step reduces by construction to its inputs.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The analysis is a standard single-channel Lüscher extraction. The free parameters are the ERE coefficients, which are the physical outputs of the fit, plus one hand-chosen energy cut. The axioms are standard relations and inputs from the CLQCD ensembles. No new entities are introduced.

free parameters (3)
  • a0 (s-wave scattering length) = -0.21(4)(8) fm
    Leading effective range expansion parameter obtained by fitting Eq. (15) to the finite-volume energies from both ensembles. This is the target observable, not a nuisance parameter.
  • r0 (effective range) = -0.05(13)(25) fm
    Subleading effective range expansion parameter in the same fit; weakly constrained and consistent with zero within errors.
  • Energy window cut (aE <= 1.98) = 1.98 (lattice units)
    Chosen to exclude the highest F32P30 level lying near the Sigma_c Sigma_c and Xi_cc N pi thresholds. The authors test sensitivity with fit2, which removes two high levels and shifts a0 to -0.28(6) fm.
assumptions (6)
  • standard math Lüscher's finite volume formula (Eq. 13) with the A1+ irrep and neglect of partial waves l >= 4 connects the finite-volume spectrum to the infinite-volume phase shift.
    Standard result from Refs. [31-33]; used without modification. It assumes the box levels are dominated by s-wave scattering and that higher partial waves are negligible.
  • domain assumption The CLQCD ensembles provide Nf=2+1 dynamical QCD with the stated bare quark masses, lattice spacing a = 0.07746(18) fm, and pion mass 303 MeV.
    Ensemble parameters and scale setting are taken from prior CLQCD work (Ref. [34]); the present paper does not independently calibrate the ensembles.
  • domain assumption The valence charm quark mass is tuned to reproduce the spin-averaged eta_c and J/psi mass, as stated in Sec. II.
    This tuning is standard, but uncertainties in the charm mass feed into baryon masses and energy levels.
  • domain assumption The effective range expansion truncated at O(k^2) describes the phase shift in the fitted energy window.
    Standard low-energy parameterization; the paper probes sensitivity by dropping the two highest levels but does not test higher-order terms.
  • ad hoc to paper The continuum dispersion relation E^2 = m^2 + p^2 is used to build finite-volume energies in Eq. (12), even though the measured Lambda_c dispersion has c ~ 0.99.
    This is a deliberate choice to align with Lüscher's derivation; the residual lattice artifact is estimated to be a few percent in c^2 but is not quantified in the final error.
  • domain assumption The off-diagonal elements of the Lambda_c Lambda_c correlation matrix are negligible, so the F48P30 spectrum can be extracted from diagonal correlators alone.
    The authors observe small off-diagonal elements on F32P30 (Sec. III.B); on F48P30 only diagonal correlators are computed, so the assumption is not directly checked there.

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Pith. "Pith review of Lattice QCD study of $\Lambda_c \Lambda_c$ scattering." pith.science (2026). https://pith.science/paper/JQK7HFM4

@misc{pith2026250205546,
  author       = {Pith},
  title        = {Pith review of: Lattice QCD study of $\Lambda_c \Lambda_c$ scattering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JQK7HFM4}},
  note         = {Machine review of arXiv:2502.05546}
}
abstract

We present the first lattice result of the near threshold $\Lambda_c\Lambda_c$ scattering with $I(J^P) = 0(0^+)$. The calculation is performed on two $N_f = 2+1$ Wilson-Clover ensembles with pion mass $m_\pi \sim 303$\,MeV and lattice spacing $a = 0.07746$\,fm. The L\"uscher's finite volume method is utilized to extract the scattering parameters from the finite-volume spectrum. The coupled channel $\Xi_{cc}N$ is ignored in the scattering analysis based on the observation that the energy levels computed from the $\Lambda_c\Lambda_c$ and $\Xi_{cc}N$ operators do not mix. The $\Sigma_c\Sigma_c$ channel is not included either since the energy range explored in this study is well below its threshold. Our results indicate that the interaction in the $\Lambda_c\Lambda_c$ single channel is repulsive, and the scattering length is determined to be $a_0 = -0.21(4)(8)$\,fm, where the first error is the statistical error and the second is the systematic error.

Figures

Figures reproduced from arXiv: 2502.05546 by the authors.

Figure 1
Figure 1. FIG. 1: Left: the effective mass of Λ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (a) Comparison of the energies using both Λ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Comparison of the energies using both Λ [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Effective mass calculated from the ratio defined in Eq. 11. The red horizontal bands indicate the fitted [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Finite-volume spectrum of Λ [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Energy dependence of the phase shift. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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