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REVIEW 3 major objections 5 minor 2 cited by

Lattice QCD now yields first-principles charmed hadron interactions: a loosely bound T_cc^+ at the physical pion mass, an attractive nucleon-charmonium force, and a charm dibaryon near unitarity.

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2026-08-05 11:06 UTC pith:3WYKVHAO

load-bearing objection A competent, self-contained proceedings snapshot of three published HAL QCD results; worth reading as an entry point, but the T_cc extrapolation and the unshown local-potential truncation check are the soft spots. the 3 major comments →

arxiv 2509.03156 v1 pith:3WYKVHAO submitted 2025-09-03 hep-lat hep-phnucl-th

Recent progress on charmed hadron interactions from lattice QCD

Yan Lyu This is my paper
classification hep-lat hep-phnucl-th PACS 12.38.Gc
keywords charmed hadron interactionslattice QCDHAL QCD methodT_cc^+ tetraquarknucleon-charmonium scatteringOmega_ccc dibaryontwo-pion exchangenear-threshold states
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This review argues that lattice QCD, via the HAL QCD method on configurations with nearly physical quark masses, now supplies first-principles interactions among charmed hadrons — systems that scattering experiments can barely probe because the hadrons are unstable. Three results carry the argument. In the D*-D channel that produces the doubly charmed tetraquark T_cc^+, the extracted potential is attractive at all distances; at m_pi = 146.4 MeV the system appears as a near-threshold virtual state, and extrapolating the two-pion-exchange tail to m_pi = 135 MeV turns it into a loosely bound state whose D0D0pi+ line shape matches the measured spectrum semi-quantitatively. The nucleon-charmonium potential is likewise attractive at all distances with a two-pion-exchange tail, giving J/psi-nucleon scattering lengths around 0.3 fm and an in-medium J/psi mass shift near 19 MeV. The Omega_ccc-Omega_ccc potential supports a bound state in the 1S0 channel, but Coulomb repulsion lifts the system into the unitarity regime, placing the highest-charm dibaryon on the edge of existence.

Core claim

The paper's central claim is that the HAL QCD method — converting two-hadron correlation functions into an effective potential — now yields first-principles charmed hadron interactions near threshold. For T_cc^+ (D*-D, I=0, J^P=1+), the potential is attractive at all distances; the system is a virtual state at m_pi = 146.4 MeV and becomes loosely bound at the physical pion mass, reproducing the measured D0D0pi+ spectrum semi-quantitatively. The nucleon-charmonium potentials are attractive at all distances with two-pion-exchange tails, giving scattering lengths of 0.2-0.4 fm and a 19(3) MeV J/psi mass shift in nuclear matter. Omega_ccc-Omega_ccc binds in the 1S0 channel at 5.68 MeV until Coul

What carries the argument

The central object is the local potential V(r) extracted from the HAL QCD R-correlator, a spatiotemporal two-hadron correlation function whose Nambu-Bethe-Salpeter amplitudes encode the scattering information. From the R-correlator's integrodifferential evolution equation, the nonlocal potential U(r, r') is truncated at leading order to V(r) delta(r - r'), dropping the O(delta^2 d_t^3) term; the truncation error is estimated through the t-dependence of V(r). Phase shifts, scattering lengths, effective ranges, and poles then follow from solving the Schrodinger equation with V(r). Two further inputs carry the physics: a two-pion-exchange-motivated fit form, which lets the D*-D potential be ext

Load-bearing premise

Everything rests on truncating the nonlocal HAL QCD interaction to a single local potential V(r); if the dropped momentum-dependent terms are sizable in heavy-charm systems, every scattering length, binding energy, and mass shift moves. The T_cc^+ conclusion further assumes the two-pion-exchange fit form stays valid when extrapolated from m_pi = 146 to 135 MeV.

What would settle it

Compute any of the three systems with the next, momentum-dependent term of the derivative expansion included, or run the D*-D calculation directly at m_pi = 135 MeV: if phase shifts and pole positions move beyond the quoted systematic errors, the local-potential truncation and the TPE extrapolation fail. On the experimental side, a precise J/psi-nucleon scattering length — current determinations differ by three orders of magnitude — would directly test the predicted value near 0.3 fm.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • The doubly charmed tetraquark T_cc^+ is a near-threshold state whose pole moves from the virtual to the bound side of threshold as the pion mass drops to its physical value.
  • The J/psi-nucleon scattering length of about 0.3 fm implies a roughly 19 MeV downward shift of the J/psi mass in normal nuclear matter, a concrete observable for heavy-ion and nuclear experiments.
  • The lattice determination of the nucleon-charmonium scattering length sits between two experimental estimates that differ by orders of magnitude and can help adjudicate between them.
  • Without Coulomb repulsion the Omega_ccc-Omega_ccc system would be a bound charmed dibaryon; with it, the system sits near unitarity, so the highest-charm dibaryon is right at the edge of existence.
  • The next step the paper identifies — direct lattice calculations at the physical pion mass — should settle whether the virtual-to-bound transition of T_cc^+ and the near-unitarity of Omega_ccc-Omega_ccc persist without extrapolation.

Where Pith is reading between the lines

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

  • If the leading-order local-potential truncation survives a next-order test, the same pipeline can be pointed at other experimentally blind charmed channels, such as D-D, D-D_s, and charmed-baryon pairs, where lattice potentials would be the only scattering information available.
  • The near-unitarity of Omega_ccc-Omega_ccc suggests that Coulomb repulsion, not QCD, is what prevents a stable highest-charm dibaryon; a variant with less electric charge could plausibly bind.
  • The two-pion-exchange tails seen in both meson-meson and baryon-meson channels suggest these lattice potentials could serve as inputs to heavy-quark effective field theories, extending chiral-EFT methods into the charm sector.
  • The extrapolation from 146.4 to 135.0 MeV makes a sharp prediction: a direct lattice run at the physical pion mass, or an independent finite-volume-method cross-check, should confirm the T_cc^+ binding near -45 keV.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This proceedings contribution by Y. Lyu reviews recent lattice QCD calculations of charmed hadron interactions using the HAL QCD method. The paper outlines the HAL QCD formalism (R-correlators, Nambu-Bethe-Salpeter amplitudes, and the effective-potential expansion leading to Eq. (4)) and then presents three representative systems: D*-D in the T_cc+ channel (an attractive potential, a near-threshold virtual state at m_pi = 146.4 MeV, and a TPE-motivated extrapolation to 135.0 MeV that turns it into a loosely bound state), N-charmonium (attractive N-J/psi and N-eta_c potentials with two-pion-exchange tails, scattering lengths around 0.2-0.4 fm, and a resulting J/psi mass shift in nuclear matter), and Omega_ccc-Omega_ccc (a bound 1S0 state that becomes near-unitary when a finite-size Coulomb potential is added). These are presented as evidence that lattice QCD with the HAL QCD method provides reliable first-principles charmed hadron interactions.

Significance. If the reported results hold, they are significant: they are among the first realistic QCD determinations of charmed hadron interactions that are poorly constrained experimentally. The D*-D analysis connects lattice QCD to the LHCb T_cc+ line shape; the N-c-bar-c scattering lengths could help resolve an order-of-magnitude experimental discrepancy; and the charmed dibaryon prediction is testable in future experiments. The review draws on peer-reviewed publications that include statistical and systematic errors, multiple fit forms, and cross-checks such as t-slice variation. However, because this is a review proceedings rather than an original calculation, several load-bearing technical justifications are only asserted, not demonstrated. The main weakness is the absence of explicit evidence for the convergence of the leading-order local-potential approximation and for the pion-mass extrapolation used in the D*-D system.

major comments (3)
  1. [Section 2, Eq. (4)] The leading-order local-potential truncation is load-bearing for all three systems. The paper states that the truncation error from higher-order derivative terms is 'quoted into systematic errors by an estimation through the t dependence of V(r)' citing Refs. [15,16], but no such estimation is shown in this manuscript. The t-dependence of V(r) is primarily a probe of excited-state contamination, not of the convergence of the derivative expansion in U(r,r'). For heavy-charm systems with strong short-range interactions, the omitted V_1, V_2 terms could shift the extracted scattering parameters and pole classifications. Please either summarize the convergence checks from the original papers or add an explicit caveat about the unquantified truncation error.
  2. [Section 3, Eq. (6) and Table 1] The physical-point prediction that T_cc+ becomes bound relies on extrapolating V_B(r; m_pi) from 146.4 to 135.0 MeV by substituting m_pi into the TPE-motivated functional form while holding all other parameters fixed. No uncertainty is assigned to this extrapolation, and no alternative extrapolation is discussed. Because the near-threshold pole position and the D0D0pi+ mass spectrum depend sensitively on this step, the review should explicitly state the model dependence (e.g., from the original paper) or provide a sensitivity estimate.
  3. [Section 5, Eqs. (7)-(10)] The 'near-unitarity' conclusion for Omega_ccc-Omega_ccc is obtained by adding a model Coulomb potential (Eq. (9)) to a strong-interaction potential computed in pure QCD. This is a delicate cancellation: without Coulomb the system is bound with B = 5.68 MeV; with Coulomb it is unbound with a_0^C = 19(7) fm. The review does not discuss the systematic uncertainty of this two-step procedure, including the validity of adding the Coulomb potential linearly and the uncertainty in the finite-size charge radius r_d. A small change in either potential could move the system away from unitarity. Please quote the relevant error analysis from the original publication or add an explicit caveat.
minor comments (5)
  1. [Section 2, lattice setup] The text 'L4 = 964' should read 'L^4 = 96^4'; the superscript formatting was lost. Please correct.
  2. [Section 3, Fig. 2] The two fit functions V_A and V_B are said to describe the lattice data equally well, but the bands in Fig. 2 are visually almost indistinguishable. A residual plot or a quantitative chi^2 comparison would help the reader evaluate this statement.
  3. [Section 3, text near Table 1] The phrase 'm_D*+, D0, pi+' is ambiguous. It should be 'm_{D^{*+}}, m_{D^0}, m_{\pi^+}'.
  4. [Section 5, Eq. (9)] The symbol alpha_e is used without definition. Presumably it is the fine-structure constant; please state this explicitly.
  5. [Section 6] Item (i) calls the D0D0pi+ spectrum a 'semi-quantitative description' of LHCb data. It would be useful to specify in what sense it is only semi-quantitative (e.g., peak position offset, width, or overall normalization).

Circularity Check

0 steps flagged

No significant circularity: lattice QCD potentials are fitted to correlation functions, and the reported scattering parameters/binding energies are derived outputs, not fitted to target observables. Minor concern: the derivative-expansion truncation error is delegated to self-citations [15,16] without demonstration here.

full rationale

The paper's derivation chain for each highlighted system is: lattice QCD correlation functions -> HAL QCD potential V(r) -> solve Schrödinger equation -> scattering parameters, pole positions, binding energies. The lattice potentials are obtained from first-principles lattice QCD (configurations from Refs [17,18]) and fitted to phenomenological forms; the target observables (e.g., the Tcc pole, the N-J/psi scattering length, the Omega_ccc-Omega_ccc binding energy) are not used as inputs to these fits. For the D*-D system, the physical-point prediction is an extrapolation using the explicit m_pi dependence of the TPE ansatz (Eq. 6), which is a model assumption but is transparently stated and not a fit to the LHCb data. The LHCb comparison is a postdiction. Similarly, the N-cbar-c and Omega_ccc-Omega_ccc results are derived from the lattice potentials and do not reduce to input observables. The one notable self-citation is the claim that the derivative-expansion truncation error is 'quoted into systematic errors by an estimation through the t dependence of V(r) [15,16]'; refs [15,16] are authored by the present author, and no such estimation is shown in this proceedings. However, this is a systematic-error justification that is ancillary to the central qualitative results (attraction, bound-state candidates), and no mathematical reduction of an output to an input is exhibited. The paper is self-contained against external benchmarks (LHCb data for Tcc, experimental N-J/psi scattering length estimates), supporting the conclusion of no significant circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The analysis relies on multiple phenomenological fits to lattice QCD potentials. These fits introduce a large number of shape parameters (Gaussians and TPE tails). None of these parameters are fitted to the physics targets (T_cc pole, scattering lengths, dibaryon binding); they are fitted to the lattice-derived potentials, which themselves are defined by the HAL QCD local equation. This is a moderate model-dependence burden, distinct from circularity.

free parameters (5)
  • V_A Gaussian parameters = 8 params (a_i, b_i, i=1..4)
    Fitted to the lattice D*-D potential in the T_cc channel (Eq. 5, Fig. 2); used to compute scattering parameters and poles.
  • V_B TPE-motivated parameters = 6 params (a_1, a_2, b_1, b_2, a_3, b_3)
    Fitted to the lattice D*-D potential with an explicit two-pion-exchange tail (Eq. 6); chosen as an alternative to V_A and also used for the m_pi extrapolation.
  • N-c bar c three-range Gaussian parameters = 6 params per channel
    Fitted to lattice N-J/psi(3/2), N-J/psi(1/2), and N-eta_c potentials (Fig. 4); feeding the scattering length extraction.
  • Omega_ccc three-range Gaussian parameters = 6 params
    Fitted to the lattice Omega_ccc-Omega_ccc 1S0 potential (Fig. 6); used for phase shifts and bound-state extraction.
  • D D pi production amplitude U and vertex P = Not quoted in text
    Constants entering the D0D0pi+ mass spectrum calculation (Fig. 3 inset); the absolute normalization is not specified, so the claimed semi-quantitative agreement with LHCb data may partly reflect a normalization choice.
axioms (5)
  • domain assumption The R-correlator satisfies the HAL QCD integrodifferential equation for t >> 1/Delta E* (Eq. 3).
    Basis of the HAL QCD method; quoted from Ref. [14] without derivation in this manuscript (Section 2).
  • domain assumption The nonlocal potential can be truncated to a local potential at leading order in the derivative expansion (Eq. 4).
    The paper states the O(delta^2 d_t^3) term vanishes for equal masses and is numerically negligible otherwise, but the convergence of the expansion is asserted, not demonstrated (Section 2).
  • domain assumption The TPE form V = -alpha e^{-2 m_pi r}/r^2 describes the long-range part of N-c bar c and D*-D potentials.
    Used to justify fits (Eq. 6 and Fig. 5); adapted from Refs. [39,40] and carried into the m_pi extrapolation.
  • domain assumption Pole positions are unaffected by the left-hand cut (lhc).
    Stated in Section 3 with a pointer to Ref. [24]; needed for interpreting kappa_pole as a virtual or bound-state pole.
  • ad hoc to paper The extrapolation V_B(r; m_pi = 146.4 -> 135.0 MeV) preserves the functional form.
    The TPE tail parameters are extrapolated by shifting m_pi inside Eq. (6); no additional lattice data at physical pion mass is used (Section 3).

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Cite this review

Pith. "Pith review of Recent progress on charmed hadron interactions from lattice QCD." pith.science (2026). https://pith.science/paper/3WYKVHAO

@misc{pith2026250903156,
  author       = {Pith},
  title        = {Pith review of: Recent progress on charmed hadron interactions from lattice QCD},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3WYKVHAO}},
  note         = {Machine review of arXiv:2509.03156}
}
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read the original abstract

Recent years have witnessed rapid progress in charmed hadron physics, driven by numerous experimental discoveries of exotic states such as $T^+_{cc}$ and $P_c$. These findings have highlighted the importance of understanding charmed hadron interactions. With significant advances in theory and computation, lattice QCD has become a reliable tool for studying nonperturbative dynamics of low-energy QCD. In this talk, I review recent lattice QCD studies of charmed hadron interactions, focusing on three representative systems: $D^*$-$D$, $N$-$c\bar c$, and $\Omega_{ccc}$-$\Omega_{ccc}$.

Figures

Figures reproduced from arXiv: 2509.03156 by Yan Lyu.

Figure 1
Figure 1. Figure 1: A comparison on single-hadron masses between the experiment and the lattice calculations. The experimental values represented by black lines are from the PDG [19], while the red dots are from our lattice QCD calculations. Two lattice data for each charmed hadron correspond to two sets of parameters in the charmed quark action [18], and are linearly extrapolated to the physical charm quark mass. The masses … view at source ↗
Figure 2
Figure 2. Figure 2: The potential between a 𝐷 meson and a 𝐷 ∗ meson in the 𝑇 + 𝑐𝑐 channel (𝐼 = 0, 𝐽𝑃 = 1 + ). The lattice data for 𝑟 < 0.8 fm show monotonically decreasing towards the origin, where 𝑉(𝑟 = 0) ≃ −500 MeV. The two bands are the fitted results using fit functions in Eqs. (5) and (6). by 𝑉 𝐵 fit(𝑟; 𝑚𝜋 = 146.4 → 135.0 MeV). Using such a potential together with the physical hadron masses, we found that 𝑇 + 𝑐𝑐 evolves… view at source ↗
Figure 3
Figure 3. Figure 3: (Left) The inverse of scattering length 1/𝑎0 for the 𝐷 ∗𝐷 scattering in the 𝑇 + 𝑐𝑐 channel obtained from lattice QCD simulations by Refs. [25](blue square), [26](green diamond), and [27](yellow triangle). Our result [22](magenta circle) and the real part of the experimental value by LHCb (red star) [21] are also shown. (Right) The 𝐷 0𝐷 0𝜋 + mass spectrum calculated using 𝑉 𝐵 fit (𝑟; 𝑚𝜋) with 𝑚𝜋 = 146.4 MeV… view at source ↗
Figure 4
Figure 4. Figure 4: The 𝑁-𝑐𝑐¯ potential in the 𝑆 wave for 𝑁-𝐽/𝜓 with spin 3/2 (upper left), with spin 1/2 (upper right), and for 𝑁-𝜂𝑐 (lower left). The red bands show the fitted results with a phenomenological three-range Gaussian at 𝑡/𝑎 = 14. The three potentials at 𝑡/𝑎 = 14 are also shown (lower right) for a direct comparison. A magnification is shown in the inset for each panel. In [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (Left) The TPE function 𝑉(𝑟) = −𝛼𝑒−2𝑚𝜋𝑟 /𝑟 2 fitted to the long-range 𝑁-𝑐𝑐¯ potentials. The gray dashed line is the best fit with 𝑉(𝑟) = −𝛼/𝑟 7 for comparison. (Right) The 𝑁-𝑐𝑐¯ scattering phase shifts. 5. The Ω𝑐𝑐𝑐-Ω𝑐𝑐𝑐 interaction The deuteron, composed of a proton and a neutron, is the only known stable dibaryon. In principle, QCD allows for the existence of other dibaryons. This has motivated a broad an… view at source ↗
Figure 6
Figure 6. Figure 6: (Left) The Ω𝑐𝑐𝑐-Ω𝑐𝑐𝑐 potential in the 1𝑆0 channel. (Right) The Ω𝑐𝑐𝑐-Ω𝑐𝑐𝑐 scattering phase shifts in the 1𝑆0 channel. 6. Summary In summary, we have reviewed recent progress on lattice QCD studies of charmed hadron interactions. Special attention has been paid to three representative channels investigated using lattice configurations with nearly physical quark masses (𝑚𝜋 ≃ 146 MeV) within the HAL QCD approa… view at source ↗

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Forward citations

Cited by 2 Pith papers

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