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REVIEW 3 major objections 6 minor 73 references

Decay constants of the two-pole D0*(2300) are tens of MeV, far below conventional c-qbar predictions, and can discriminate its internal structure.

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2026-07-31 11:49 UTC pith:GWG4C5ZL

load-bearing objection Clean, usable numbers for the two-pole D0* decay constants and Cabibbo-favored rates; the complex-pole → real-f step is underspecified and is the main soft spot. the 3 major comments →

arxiv 2607.24550 v1 pith:GWG4C5ZL submitted 2026-07-27 hep-ph

Decay constants of the two-pole D₀^*(2300)

Qi-Wei Yuan , Jia-Ting Zhang , Ming-Zhu Liu This is my paper
classification hep-ph
keywords D0*(2300)two-pole structuredecay constantshadronic moleculeschiral unitary approachfactorizationBs decaysbeauty baryon decays
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.

The scalar charmed meson D0*(2300) is widely argued to be two poles generated by coupled Dπ, Dη, DsKbar and Dη' channels, not a single ordinary c-qbar excitation. This paper computes the decay constants of those two poles in the molecular picture with an effective Lagrangian whose couplings come from the residues of a unitarized chiral amplitude. It finds f_lower ≈ 65 MeV and f_higher ≈ 81 MeV—several times smaller than the 100–370 MeV range quoted for conventional excited charmed mesons. Because production rates in weak decays scale with these constants, the authors also predict Cabibbo-favored branching fractions for Bs → Ds D0*, Λb → Λc D0* and Ξb → Ξc D0* at the few × 10^{-5} level. Measuring those rates, or the ratio of the two poles to the ground-state D, would test whether the two-pole molecular assignment is correct.

Core claim

In the two-pole molecular picture, the decay constants are f_D0*^(lower) = 64.6^{+0.9}_{-1.0} MeV and f_D0*^(higher) = 80.8^{+9.6}_{-5.3} MeV. These values are substantially smaller than conventional c-qbar excited-state estimates (roughly 107–373 MeV), so the decay constant itself is a structural discriminator. The same constants imply Cabibbo-favored b-hadron branching fractions of order 10^{-5}.

What carries the argument

The loop amplitude that defines the decay constant: each pole couples to its D(s)P constituents with strengths taken from the residues of the NLO chiral unitarized T-matrix; those couplings are folded with the known D(s)→P weak form factors and a dimensionally regularized two-point loop to yield f via the coefficient of p^μ.

Load-bearing premise

The whole result rests on treating D0*(2300) as a pure two-pole hadronic molecule whose couplings are exactly the residues of one particular unitarized chiral fit, with no compact quark-antiquark core.

What would settle it

Measure the Cabibbo-favored branching fractions Bs → Ds D0*, Λb → Λc D0* and Ξb → Ξc D0* (or the ratio of each pole to the corresponding ground-state D mode). Values near a few × 10^{-5} with the higher pole larger than the lower would support the claim; rates an order of magnitude higher would favor conventional decay constants.

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

If this is right

  • Decay constants become a practical observable for distinguishing molecular versus compact assignments of scalar charmed mesons.
  • The higher pole should be produced more copiously than the lower pole in factorization-allowed b-hadron decays because its decay constant is larger.
  • Branching fractions of order 10^{-5} for Bs, Λb and Ξc modes are concrete targets for LHCb and Belle II.
  • SU(3) partners such as the DK molecule are expected to have similarly small decay constants (~60 MeV), giving a coherent pattern across the multiplet.

Where Pith is reading between the lines

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

  • If future lattice or dispersive analyses prefer a sizable compact core, the residues (and therefore the quoted f values) would rise, erasing the numerical gap that the paper uses as a discriminator.
  • The same residue-to-decay-constant pipeline can be applied immediately to other two-pole candidates (e.g., the strange partners or the Λ(1405) sector) to generate parallel experimental tests.
  • A joint fit of the predicted weak branching fractions with existing angular-moment and femtoscopy constraints would tighten the allowed range on the higher-pole mass and width.

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 / 6 minor

Summary. The manuscript computes the decay constants of the two poles of the D0*(2300) in the hadronic-molecular picture. Starting from the NLO chiral unitarized amplitude for the coupled channels Dπ, Dη, DsK̄, Dη' (with the Fit-6C low-energy constants of Guo–Meißner–Yao 2015), the authors locate the two poles, extract complex pole residues g_i via Eq. (13), and insert them into a one-loop effective-Lagrangian expression (Eq. 6) together with weak D(s)→P transition form factors to obtain f^(lower) = 64.6 MeV and f^(higher) = 80.8 MeV. These are compared with conventional compact cq̄ predictions (107–373 MeV) and argued to discriminate internal structure. As an application, Cabibbo-favored Bs→Ds D0*, Λb→Λc D0*, and Ξb→Ξc D0* branching fractions of order 10^-5 are predicted in naive factorization. The algebraic framework (Eqs. 4–13, 14–22) is standard and internally consistent; pole positions and the Dπ scattering length agree with prior literature, and uncertainties from four NLO LECs are propagated with correlations.

Significance. If the numbers hold up, the result is phenomenologically useful: it provides (i) parameter-free-in-the-molecular-picture decay constants for each pole of the D0*(2300), computed from residues of a published amplitude rather than fitted to the quantity of interest; (ii) a concrete discriminating observable between molecular and compact cqbar interpretations, with external benchmarks (QCD sum rules, light-front, Salpeter, quark model) that are independent of the input fit; and (iii) falsifiable predictions for Cabibbo-favored Bs, Lambda_b, and Xi_b branching fractions at the 10^-5 level, within reach of LHCb. The two-pole-per-pole decomposition is a genuinely new element relative to prior molecular decay-constant calculations. The impact is tempered by the fact that the central numbers are conditional on the Fit-6C residue extraction and on an unstated complex-pole prescription, and by the very narrow quoted error bars, which currently reflect only four LECs.

major comments (3)
  1. [Sec. III, Eq. (6), Table III] Sec. III / Eq. (6): the prescription for extracting a real decay constant from a complex-pole quantity is never stated, and it is load-bearing for the headline numbers. Both poles lie deep in the complex plane (sqrt(s0) = (2102.8 - i 92.6) and (2437.3 - i 150.7) MeV), so the residues g_i from Eq. (13) are complex (Table III reports only |g_i|) and the loop integral in Eq. (6) is complex for any p^2 in the resonance region. Quoting real, positive f values requires a choice among inequivalent prescriptions: (a) evaluate at p^2 = s0 and take Re f or |f|; (b) evaluate the loop on the real axis at p^2 = M^2 with complex g_i; (c) insert |g_i| into a real loop at p^2 = M^2. For the higher pole, Im(sqrt(s0))/Re(sqrt(s0)) ~ 6% and the DsKbar threshold sits only ~28 MeV above the nominal mass, so the loop's imaginary part and the phase of g_{DsKbar} can shift the extracted real f at the tens-of-pe
  2. [Sec. III, footnote 1] Sec. III, footnote 1: the quoted errors on the decay constants (+0.9/-1.0 and +9.6/-5.3 MeV) propagate only the four LECs h24, h35, h4hat, h5hat. Several other inputs with non-negligible uncertainties enter Eq. (6) and Eqs. (19)-(21) and are held fixed: the weak transition form factors f_{D(s)P}(0) extracted from semileptonic branching fractions (Sec. II A), the renormalization scale mu and F (Table II), the eta-eta' mixing angle, a1 = 1.03, and the transition form-factor parameters F(0), a, b (Sec. II C, Tables V-VI). The extremely small lower-pole error (~1.5%) is presented in the abstract and Table IV alongside external determinations with 10-20% errors, which invites a comparison the error budget does not support. At minimum the authors should propagate the uncertainties on the f_{D(s)P}(0) (which enter linearly) and vary mu over a conventional range to give an honest systematic, or
  3. [Sec. III] Sec. III: the claim that the two-pole decay constant is independent of the renormalization scale mu is imported wholesale from Ref. [51] ('As shown in the analysis of Ref. [51]...'). That demonstration was made for the single-channel DK molecule; here the couplings g_i(mu) come from a four-channel NLO unitarized amplitude with a different DR convention for G(s) (Eq. 8), and mu-independence requires a specific cancellation between the mu-dependence of the residues and of the log in Eq. (6). Given that mu = 1.0 GeV is also an input to the LS equation that produces the poles, the authors should either show the cancellation numerically for this coupled-channel case (e.g., f at mu = 0.8-1.2 GeV) or soften the claim. This is a correctness-risk check, not a request for new physics.
minor comments (6)
  1. [Table IV] Table IV: the comparison would be more informative if it stated explicitly that the external values treat D0*(2300) as a single compact state, so they should be compared with an appropriate combination (or separately with each pole). As written, the single row 'Ours 64.6/80.8' against one number per external approach is slightly ambiguous about which pole each external value is being contrasted with.
  2. [Sec. II A] Sec. II A: the values f_{D(s)P}(0) are said to be extracted 'from their respective semileptonic decay branching fractions' [54], but no branching-fraction values, q^2 parametrization, or fit procedure is given. A short table or footnote with the inputs would aid reproducibility, and the experimental status of D -> eta' l nu specifically should be cited.
  3. [Table V] Table V: the 'Exp [54]' column for the Xi_b row gives 3.7 +/- 0.5 x 10^-4 for Xi_b -> Xi_c D; please clarify whether this is a measurement, an SM/factorization estimate, or derived via SU(3) from the Lambda_b mode, since the table layout implies an experimental value.
  4. [Eqs. (5)-(6)] Eq. (6) vs. Eq. (5): the relation between the loop tensor integral in Eq. (5) and the scalar decay-constant formula in Eq. (6) involves an on-shell projection p^2 = m_{D0*}^2 that is never written down; for complex poles this step is exactly where the prescription of major comment 1 enters. A line of derivation would help.
  5. [General] Typographical: missing space in the title/abstract rendering 'two-poleD*_0(2300)'; Introduction, 'quantitative understanding the production rates' should read 'quantitative understanding of the production rates'; Eq. (2) and Eq. (17) end with commas/periods inconsistently.
  6. [Sec. III] The SU(3)-breaking comparison in Sec. III (10% vs 11-45%) uses f_{DK} = 59 MeV from Ref. [51]; since that number carries its own unquantified systematics, the statement 'the two-pole assumption leads to the smallest SU(3)-flavor symmetry breaking' should be phrased more cautiously or accompanied by errors.

Circularity Check

1 steps flagged

No significant circularity: decay constants are computed from external Fit-6C residues and experimental weak form factors, then compared to independent compact-state benchmarks.

specific steps
  1. self citation load bearing [Sec. II A (after Eq. 6) and Sec. III (decay-constant paragraph); also Intro citing [50,51]]
    "Following Refs. [50, 51], we adopt the effective Lagrangian approach to compute the decay constant of the excited charmed meson D0*(2300)... As shown in the analysis of Ref. [51], the decay constant of the two-pole D0*(2300) is independent of the renormalization scale µ. We therefore adopt the same renormalization scale as that used for the loop function in the scattering equation [29]."

    The molecular decay-constant formula and the assertion that f is µ-independent are imported from Ref. [51] (Liu–Ling–Geng), which shares an author with the present work. This is a methodological self-citation, not a load-bearing uniqueness or fit-as-prediction step: the numerical f values still come from external Fit-6C residues plus experimental weak form factors, and the discrimination claim is against independent compact-state calculations. Minor only.

full rationale

The load-bearing numerical chain is: (i) adopt the NLO ChEFT potential and Fit-6C LECs from Guo–Meißner–Yao (external Ref. [29]); (ii) unitarize via the LS equation to obtain poles and residues g_i (Eqs. 7–13); (iii) insert those g_i plus experimental f_{D(s)P}(0) into the molecular loop (Eq. 6) to obtain real f values; (iv) compare to external QCD-sum-rule/quark-model numbers and feed f into factorization BRs. None of these steps defines the output in terms of itself, renames a fit as a prediction of the same observable, or imports a uniqueness theorem from the present authors. Using LECs constrained by scattering/lattice to compute a different matrix element (the vacuum-to-D0* current) is ordinary model application, not circularity. The only mild self-reference is methodological: the effective-Lagrangian molecular formula and the claim of µ-independence are taken from the overlapping-author Ref. [51] on Ds0*(2317). That citation supplies a calculational template, not the numerical result or a forced uniqueness claim, so it does not raise the score above the 0–2 band.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The central numbers rest on an upstream NLO ChEFT fit (many LECs), the pure-molecule hypothesis, standard effective-Lagrangian and factorization machinery, and external form-factor inputs. No new particles are postulated; the two poles are taken from the existing coupled-channel literature. The free-parameter count is dominated by the inherited Fit-6C constants and the transition form-factor parametrizations.

free parameters (6)
  • NLO LECs h0,h1,h2,h3,h4,h5,h24,h35,ĥ4,ĥ5 (Fit-6C) = h0=0.033, h1=0.43, h2=0.08, h3=3.79, h4≃−0.057 GeV^{-2}, h5≃−0.484 GeV^{-2}, h24=−0.13^{+0.05}_{-0.06}, h35=0.23±0.06, ĥ
    Low-energy constants of the ChEFT potential; values and a subset of errors taken from Guo–Meißner–Yao 2015 Fit-6C without refit. They fix the poles and residues that enter the decay-constant integral.
  • Renormalization scale μ and decay constant F = μ=1.0 GeV, F=92.2 MeV
    Fixed inputs of the dimensional-regularization loop; chosen equal to the scattering-equation scale of the reference fit.
  • η–η' mixing angle θ = θ≃−19.0°
    Enters the SU(3) coefficients of the coupled-channel potential (Table I).
  • Weak transition form factors f_Dπ(0), f_Dη(0), f_DsK̄(0), f_Dη'(0) = 0.71, 0.39, 0.71, 0.34
    Extracted from experimental semileptonic branching fractions and inserted as constants into the molecular loop.
  • Effective Wilson coefficient a1 = a1=1.03
    Overall factor in the factorization amplitudes for b-hadron decays.
  • Bs→Ds and Λb/Ξb→Λc/Ξc transition form-factor parameters F(0), a, b = F(0)_BsDs=0.67, a=0.69, b=0.07; baryon F(0),a,b in Table VI
    Phenomenological dipole-like parametrizations taken from external quark-model/LFQM fits; they convert decay constants into branching fractions.
axioms (6)
  • domain assumption D0*(2300) is a pure two-pole hadronic molecule generated by unitarized coupled-channel Dπ, Dη, DsK̄, Dη' dynamics with no compact c¯q core contribution to the decay constant.
    Stated in the abstract and Sec. I–II; the entire calculation of f via Eq. (6) assumes the state is exhausted by the molecular loop of Fig. 1.
  • domain assumption Molecular couplings equal the residues of the NLO ChEFT unitarized T-matrix (Eq. 13).
    Standard in the hadronic-molecule literature; invoked in Sec. II B to feed g_i into the decay-constant formula.
  • domain assumption Cabibbo-favored b→c transitions with external W-emission are adequately described by naive factorization with a universal a1.
    Sec. II C; nonfactorizable corrections are asserted to be small for these modes but not quantified.
  • domain assumption Dimensional regularization with the same subtraction scale for the scattering loop and the weak-production loop yields a μ-independent decay constant.
    Claimed via citation to Ref. [51] in Sec. III; not re-derived here.
  • domain assumption SU(3) flavor symmetry relates Ξb→Ξc form factors to Λb→Λc form factors and organizes the two poles into 3-bar and 6 representations.
    Used for Ξb rates and for the qualitative comparison of the lower-pole f to the DK molecule.
  • standard math Lippmann–Schwinger / Bethe–Salpeter unitarization of the NLO chiral potential is a valid nonperturbative resummation for these channels near the poles.
    Standard tool in the coupled-channel chiral program; Eq. (7).

pith-pipeline@v1.2.0-grok45-kimik3 · 19079 in / 4349 out tokens · 81110 ms · 2026-07-31T11:49:27.618045+00:00 · methodology

0 comments
read the original abstract

The nature of the scalar charmed meson $D_0^*(2300)$ remains one of the most intriguing states in hadron spectroscopy. A prominent interpretation is a two-pole structure generated by the coupled channels $D\pi$, $D\eta$, $D_s\bar K$, and $D\eta'$, in which the lower pole couples mainly to $D\pi$ and the higher pole to $D_s\bar K$. Following this picture, we calculate the decay constants of these two poles using the effective Lagrangian approach. The resulting values, $f_{D_0^*}^{(\mathrm{lower})}=64.6^{+0.9}_{-1.0}\,\mathrm{MeV}$ and $f_{D_0^*}^{(\mathrm{higher})}=80.8^{+9.6}_{-5.3}\,\mathrm{MeV}$, are substantially smaller than those predicted by conventional $c\bar q$ excited-state scenarios. This difference suggests that decay constants can serve as a sensitive probe to discriminate between different internal structures of the $D_0^*(2300)$. As a phenomenological application, we further predict the branching fractions for the Cabibbo-favored decays $B_s \to D_s D_0^*$, $\Lambda_b \to \Lambda_c D_0^*$, and $\Xi_b \to \Xi_c D_0^*$ within the factorization approach. These predictions provide crucial tests to validate the two-pole interpretation of the $D_0^*(2300)$.

Figures

Figures reproduced from arXiv: 2607.24550 by Jia-Ting Zhang, Ming-Zhu Liu, Qi-Wei Yuan.

Figure 1
Figure 1. Figure 1: FIG. 1. Feynman diagrams for the transition of the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. External [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

discussion (0)

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