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arxiv: 2606.09397 · v2 · pith:YCMJUIVEnew · submitted 2026-06-08 · ✦ hep-ph

Searching for the pseudoscalar partner of G(3900) via radiative Y(4230) decays

Vitor C. Premoli , Pedro Brand\~ao , Ya-Wen Pan , Li-Sheng Geng , Luciano M. Abreu This is my paper

Pith reviewed 2026-06-27 16:04 UTC · model grok-4.3

classification ✦ hep-ph
keywords molecular statesradiative decaysexotic hadronscharmonium-like statestriangle mechanismbranching fractionsY(4230)G(3900)
0
0 comments X

The pith

Radiative decay Y(4230) to gamma G0(3900) produces branching fractions between 3.8 times 10 to the minus 5 and 3.3 times 10 to the minus 4 when G0 is a P-wave molecular state.

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

The paper calculates the branching fraction for the radiative decay of the vector state Y(4230) into a photon and the pseudoscalar state G0(3900). It models G0(3900) as a P-wave molecular state with quantum numbers 0 to the minus plus, dominated by D D-bar star and D-bar D star components, and assumes the process occurs via a triangle loop mechanism. The resulting range of branching fractions supplies a concrete prediction for experimental searches and a consistency check on the molecular picture of both states.

Core claim

Assuming the triangle mechanism and the P-wave molecular interpretation of G0(3900) with J to the PC equal to 0 to the minus plus, the branching fraction B of Y(4230) to gamma G0(3900) lies between 3.8 times 10 to the minus 5 and 3.3 times 10 to the minus 4, depending on model parameters and the binding energy of G0(3900).

What carries the argument

Triangle mechanism, a loop diagram in which intermediate charmed-meson lines connect the initial Y(4230), the emitted photon, and the final G0(3900) state.

If this is right

  • Signatures of the G0(3900) state become accessible in radiative channels at current and future e-plus e-minus facilities.
  • The molecular description of the Y(4230) can be tested through the consistency of its loop-mediated radiative decays.
  • The calculated range supplies a quantitative target for dedicated searches in data samples already collected or planned.
  • Observation within the predicted window would link the vector G(3900) and its pseudoscalar partner through the same molecular components.

Where Pith is reading between the lines

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

  • Confirmation would favor molecular assignments over compact tetraquark or hybrid interpretations for this mass region.
  • Analogous triangle calculations could be applied to other radiative or hidden-charm decays of nearby exotic candidates.
  • The result connects to broader questions of how molecular binding energies influence electromagnetic transition rates in heavy-quark systems.

Load-bearing premise

The decay is assumed to proceed through a triangle mechanism with G0(3900) interpreted as a P-wave molecular state dominated by D D-bar star over D-bar D star components.

What would settle it

An experimental upper limit on the branching fraction below 3.8 times 10 to the minus 5, or a measured value significantly above 3.3 times 10 to the minus 4, in the mass region near the D D-bar star threshold.

Figures

Figures reproduced from arXiv: 2606.09397 by Li-Sheng Geng, Luciano M. Abreu, Pedro Brand\~ao, Vitor C. Premoli, Ya-Wen Pan.

Figure 1
Figure 1. Figure 1: FIG. 1: Triangle diagrams contributing to the decay [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Triangle diagrams contributing to the decay [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Partial decay width Γ as a function of Λ for fixed values of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Partial decay width Γ as a function of the binding energy [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Partial decay width Γ as a function of the invariant mass of the system [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
read the original abstract

Inspired by the $P$-wave molecular interpretation of the recently observed vector state $G(3900)$, we analyze the production of its possible pseudoscalar partner, denoted here as $G_0(3900)$, via the radiative decay $Y(4230) \to \gamma G_0(3900)$. The $G_0(3900)$ is interpreted as a $P$-wave molecular state with quantum numbers $J^{PC}=0^{-+}$, dominated by the $D\bar{D}^{\ast}/\bar{D}D^{\ast}$ components. Although not yet experimentally established, such a structure is expected to appear near the $D\bar{D}^*$ threshold and to exhibit characteristic production patterns. The decay is assumed to proceed through a triangle mechanism. Depending on the model parameters and the binding energy of $G_0(3900)$, the resulting branching fraction lies in the range $\mathcal{B}(Y(4230) \to \gamma G_0(3900)) = 3.8 \times 10^{-5} - 3.3 \times 10^{-4}$. Our results offer a pathway to search for signatures of $G_0(3900)$ in radiative channels and also provide a test of the consistency of loop-mediated radiative decays with a molecular description of the $Y(4230)$.

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

0 major / 2 minor

Summary. The manuscript analyzes the radiative decay Y(4230) → γ G₀(3900) under the assumption that G₀(3900) is a P-wave molecular state (J^{PC}=0^{-+}) dominated by D D-bar*/D-bar D* components. The decay is modeled via a triangle-loop mechanism, and the resulting branching fraction is reported to lie in the range 3.8 × 10^{-5} – 3.3 × 10^{-4} when model parameters and the binding energy of G₀(3900) are varied. The work positions this range as a guide for experimental searches and a consistency test of the molecular picture for both Y(4230) and G(3900).

Significance. If the central numerical range holds under the stated assumptions, the paper supplies a concrete, falsifiable target for radiative searches that can directly probe the molecular interpretation and the viability of triangle mechanisms in these states. The explicit dependence on binding energy and model parameters is transparently presented rather than hidden, which strengthens the result as a consistency check rather than an unconditional prediction. The stress-test concern on circularity does not land: the manuscript already frames the output as a scan over chosen inputs and does not claim parameter independence.

minor comments (2)
  1. Abstract: the final branching-fraction range is stated without any indication of the key loop integral, form-factor choice, or cutoff scheme used to generate it. Adding one sentence referencing the central formula would improve readability without altering the result.
  2. The manuscript would benefit from an explicit statement (perhaps in the introduction or conclusions) of how the quoted range maps onto specific variations in binding energy versus other model parameters, to allow readers to assess sensitivity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and significance assessment of our manuscript, as well as the recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper computes a model-dependent range for the branching fraction B(Y(4230) → γ G0(3900)) by varying parameters and binding energy inside an explicit triangle-loop mechanism and P-wave molecular ansatz for G0(3900). The abstract states the assumptions upfront and frames the output as a consistency test rather than an unconditional prediction. No equations, self-citations, or fitted inputs are shown to reduce the result to its inputs by construction; the range simply encodes the stated parameter variation. This is a standard model scan with transparent inputs, not a circular derivation.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the molecular interpretation of both states and the triangle-mechanism assumption for the decay; both are domain assumptions without independent evidence supplied in the abstract.

free parameters (2)
  • binding energy of G0(3900)
    Directly sets the numerical range of the branching fraction
  • model parameters
    Varied to produce the quoted interval
axioms (2)
  • domain assumption Decay proceeds via triangle mechanism
    Explicitly stated as the production mechanism
  • domain assumption G0(3900) is P-wave molecular state with J^{PC}=0^{-+}
    Core interpretation used to define the state
invented entities (1)
  • G0(3900) no independent evidence
    purpose: Pseudoscalar molecular partner of G(3900)
    Postulated on the basis of the P-wave molecular picture

pith-pipeline@v0.9.1-grok · 5799 in / 1438 out tokens · 34780 ms · 2026-06-27T16:04:43.257339+00:00 · methodology

discussion (0)

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