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arxiv: 2503.03555 · v2 · submitted 2025-03-05 · ✦ hep-ph

Analysis of molecular state {{η}_cD^*} and {J/psi D^*} in the effective Lagrangian approach

Na Li , Ye Xing , Jing-Rui Shi This is my paper

Pith reviewed 2026-05-23 01:09 UTC · model grok-4.3

classification ✦ hep-ph
keywords molecular stateseffective LagrangianB_c decayseta_c D*J/psi D*exotic hadronsSU(3) symmetrybranching ratios
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The pith

Molecular states η_c D* and J/ψ D* show production branching ratios from B_c of order 10^{-4} and 10^{-5} under effective Lagrangian analysis.

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

The paper investigates the production and decay properties of possible molecular states formed by η_c D* and J/ψ D* pairs, both carrying J^P = 1^+. It applies an effective Lagrangian framework after using SU(3) flavor symmetry to select dominant channels, then computes numerical rates assuming the molecular picture. The results show sizable production from B_c decays and narrow total widths of a few MeV. A sympathetic reader would care because these numbers supply concrete targets for experimental searches that could distinguish molecular interpretations of exotic four-quark states from other pictures.

Core claim

Assuming the states η_c D* and J/ψ D* exist as molecular bound states with J^P = 1^+, the effective Lagrangian analysis yields branching ratios for their production in B_c decays that reach 10^{-4} and 10^{-5} respectively, while the decay widths of both configurations remain at the level of O(MeV).

What carries the argument

Effective Lagrangian approach under explicit molecular assumptions for the η_c D* and J/ψ D* configurations, combined with SU(3) flavor symmetry to identify golden production and decay channels.

If this is right

  • Production branching ratio of the η_c D* molecular state from B_c reaches order 10^{-4}.
  • Production branching ratio of the J/ψ D* molecular state from B_c reaches order 10^{-5}.
  • Decay widths of both molecular configurations stay at the level of O(MeV).
  • SU(3) flavor symmetry selects specific golden channels for both production and decay.

Where Pith is reading between the lines

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

  • Current B-physics experiments could target the predicted branching ratios in dedicated searches for these four-quark candidates.
  • The calculated MeV-scale widths imply the states would appear as relatively narrow structures in invariant-mass distributions rather than broad enhancements.
  • The same framework could be extended to other hidden-charm molecular combinations to generate additional testable rates.

Load-bearing premise

The states η_c D* and J/ψ D* exist as molecular bound states with J^P = 1^+, which allows the effective Lagrangian analysis and numerical estimates to proceed.

What would settle it

Failure to observe signals in B_c meson decays at branching ratios near 10^{-4} for η_c D* or 10^{-5} for J/ψ D* in the channels selected by SU(3) symmetry, or measurement of decay widths much larger than a few MeV.

Figures

Figures reproduced from arXiv: 2503.03555 by Jing-Rui Shi, Na Li, Ye Xing.

Figure 1
Figure 1. Figure 1: FIG. 1: The internal W-emission(A) and external W-emission diagra [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Diagrams(a,b) represent two-body decays of the triply ch [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
read the original abstract

In this work, we investigate the production and decay of the molecular states $cc\bar c\bar q$ with $J^P=1^+$ using the phenomenological analysis and effective Lagrangian approach. Based on an SU(3) flavor symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of ${\eta_c D^*}$ and ${J/\psi D^*}$. Our results indicate that the production branching ratio from $B_c$ meson is sizable, it can reach the order of $10^{-4}$ for the molecular configuration ${{\eta}_cD^*}$, and $10^{-5}$ for molecule ${J/\psi D^*}$. In addition, we find that the decay widths of the two molecular configurations ${{\eta}_cD^*}$ and ${J/\psi D^*}$ are not significant, being at level of $\cal{O}$($\rm {MeV}$).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper investigates the production and decay of putative molecular states η_c D* and J/ψ D* (cc cbar qbar with J^P=1^+) via the effective Lagrangian approach after an SU(3) flavor symmetry analysis to identify channels. It reports that the branching ratios for production from B_c decays reach O(10^{-4}) for the η_c D* configuration and O(10^{-5}) for J/ψ D*, while the decay widths of both configurations are O(MeV).

Significance. If the molecular bound-state premise were independently established and the effective-Lagrangian couplings were fixed by external data or first-principles input, the reported branching ratios would indicate that these states could be searched for in B_c decays at current or future facilities. The work supplies concrete numerical targets under the molecular hypothesis, but its significance is limited by the absence of any binding-energy calculation or lattice input to justify the existence of the bound states below threshold.

major comments (2)
  1. [Abstract and introduction] The central numerical claims (BR ~10^{-4}, 10^{-5} and widths O(MeV)) rest entirely on the unverified premise that η_c D* and J/ψ D* form J^P=1^+ molecular bound states. No binding-energy calculation, potential-model solution, or lattice QCD input is supplied to establish that a bound state forms; the effective Lagrangian and all subsequent results are conditional on this external hypothesis rather than derived from the dynamics.
  2. [Abstract] The abstract presents final numerical results for branching ratios and decay widths without derivation steps, explicit parameter values, error bars, or comparison to data, so that the quoted numbers cannot be checked or reproduced from the provided text.
minor comments (1)
  1. [Title and abstract] Notation for the molecular configurations (η_c D* vs. η_cD*) is used inconsistently between the title and abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and valuable comments on our manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and introduction] The central numerical claims (BR ~10^{-4}, 10^{-5} and widths O(MeV)) rest entirely on the unverified premise that η_c D* and J/ψ D* form J^P=1^+ molecular bound states. No binding-energy calculation, potential-model solution, or lattice QCD input is supplied to establish that a bound state forms; the effective Lagrangian and all subsequent results are conditional on this external hypothesis rather than derived from the dynamics.

    Authors: Our study is conducted under the explicit assumption that η_c D* and J/ψ D* are molecular states with J^P = 1^+, as indicated in the title and throughout the text. The effective Lagrangian approach is applied to compute production branching ratios from B_c decays and decay widths within this framework. We do not provide a binding energy calculation or lattice QCD input, as the work is phenomenological and focuses on the consequences of the molecular hypothesis rather than establishing the existence of the states. We will add a clarifying statement in the introduction to emphasize the conditional nature of the results and reference prior works that motivate the molecular interpretation. revision: partial

  2. Referee: [Abstract] The abstract presents final numerical results for branching ratios and decay widths without derivation steps, explicit parameter values, error bars, or comparison to data, so that the quoted numbers cannot be checked or reproduced from the provided text.

    Authors: The abstract is a concise overview of the key results. The full derivations, including the SU(3) flavor symmetry analysis, effective Lagrangian constructions, coupling constants, and numerical evaluations, are detailed in the main body of the paper. To address this, we will revise the abstract to briefly mention the main assumptions and direct readers to the relevant sections for the parameter values and methods. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are conditional on explicit molecular assumptions.

full rationale

The paper states it explores dynamics 'under the molecular assumptions of η_c D* and J/ψ D*' and computes branching ratios and widths via effective Lagrangian and SU(3) analysis. No quoted step shows a fitted parameter renamed as prediction, a self-definitional loop, or load-bearing self-citation that reduces the central claim to its own inputs. The derivation remains self-contained under the stated premise that the states exist as J^P=1^+ bound states; the numerical estimates follow from that assumption rather than deriving or presupposing it circularly.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 2 invented entities

The central claim rests on the molecular interpretation of the states and on the effective Lagrangian whose couplings are not specified in the abstract; SU(3) symmetry is invoked to select channels but its applicability to these heavy-quark systems is an additional assumption.

free parameters (1)
  • effective Lagrangian couplings
    Numerical values for interaction strengths are required to obtain the quoted branching ratios and widths; these are not reported in the abstract.
axioms (2)
  • domain assumption SU(3) flavor symmetry can be used to identify golden channels for these processes
    Invoked explicitly in the abstract to select channels.
  • ad hoc to paper The states η_c D* and J/ψ D* are molecular bound states with J^P=1^+
    The entire analysis is performed under this molecular assumption.
invented entities (2)
  • molecular state η_c D* no independent evidence
    purpose: Model for the cc cbar qbar exotic state
    Postulated as the physical configuration whose production and decay are calculated.
  • molecular state J/ψ D* no independent evidence
    purpose: Model for the cc cbar qbar exotic state
    Postulated as the physical configuration whose production and decay are calculated.

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Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages · 12 internal anchors

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    diquarks in flavor subspace |{cc}1[¯c¯q]3⟩f lavor, then the S-wave Tcc¯c¯q can only be spin-1 with spin-parity J P = 1 +, |{cc}1[¯c¯q]0⟩spin ⊗ |{cc}1[¯c¯q]3⟩f lavor ⊗ |[cc]¯3[¯c¯q]3⟩color, (1) here the {} and [] indicate the symmetry and antisymmetry of the diquark in different spaces respectively. According to configuration of S-wave triply c harmed four-qu...

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    The production process es of molecular states TJ/ψD ∗ and TηcD∗ can be pictured as triangle diagram drawn in Fig

    Production of four-quark molecular states from Bc meson Based on the discussion from SU(3) symmetric analysis, we fu rther investigate the dynamics of molecular states TJ/ψD ∗ andTηcD∗ by the effective Lagrangian approach. The production process es of molecular states TJ/ψD ∗ and TηcD∗ can be pictured as triangle diagram drawn in Fig. 1.D, the expression c...

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    +iε∗ µ(mBc +mV )A1(k2 2) 5 − i ε∗ ·k2 mBc +mV (pBc +pJ/ψ)µA2(k2

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