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Two nearby states in the $X(3872)$ region: Resolving the radiative-decay ratio tension with $\eta_{c2}$

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Satoshi X. Nakamura (Shandong University)

High Energy Physics - Phenomenology · Submitted 22 Feb 2026 · 73 references

Pith's verdict: Two-state X(3872)+eta_c2 explanation for the radiative-ratio tension is structurally clever and testable, but the decisive eta_c2 properties are fitted, not predicted, and the fitted production rates are never checked against existing Belle null searches.

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arXiv ID2602.19165 (version 2)
Pith IDUQLE5RI4, Pith's permanent record of this paper and its review
CitationSatoshi X. Nakamura (Shandong University). "Two nearby states in the $X(3872)$ region: Resolving the radiative-decay ratio tension with $\eta_{c2}$." arXiv:2602.19165 (2026). https://pith.science/paper/UQLE5RI4
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The paper

The paper claims

A second, unobserved charmonium state ηc2 sitting just above the D*0D̄0 threshold resolves the conflicting radiative-decay ratios in the X(3872) region.

The reading

This paper argues that the X(3872) region contains not one but two states: the established 1++ X(3872) and a so-far-unobserved 2−+ charmonium state, ηc2, slightly above the D*0D̄0 threshold. The authors show that assigning ψ′γ decays almost entirely to X(3872) and J/ψγ decays largely to ηc2, with ηc2 produced more strongly in e+e− annihilation than in B decays, reproduces the measured ratio R_B^{ψγ} ≈ 6.4 × R_{e+e-}^{ψγ}. A fit that includes ηc2 matches the data; a fit without it fails on the radiative ratios. If correct, this replaces the single-resonance interpretation of the X(3872) peak with a two-state picture and gives experiments a concrete target to search for the missing ηc2.

What carries the argument

A coupled-channel separable-potential model of {D*0D̄0}, {D*+D−}, J/ψω, J/ψρ, J/ψγ, and ψ′γ, in which X(3872) emerges as a 1++ pole and the unobserved 2−+ charmonium ηc2 is included as a Breit–Wigner excitation just above the D*0D̄0 threshold. The decisive element is the near-zero fitted coupling of ηc2 to ψ′γ with a non-zero coupling to J/ψγ, which gives each radiative channel a different dominant source.

Extended reading notes

Core claim

The paper's central claim is that two states occupy the 3871–3875 MeV window: the established 1++ X(3872), a shallow D*0D̄0 bound state, and a 2−+ charmonium candidate ηc2 with a pole at about 3874 − 0.25i MeV. In the coupled-channel model, ψ′γ events come almost entirely from X(3872), while J/ψγ events come largely from ηc2; because ηc2 is produced more readily in e+e− annihilations than in B decays, the measured radiative ratio in B decays ends up about 6.4 times larger than in e+e−. This separation reproduces the observed 1.67 vs −0.04 values, and removing ηc2 makes the model fail on the radiative ratios.

Load-bearing premise

The scenario stands or falls on the still-unobserved ηc2 having a nearly zero ψ′γ decay width and a narrow non-open-charm width (fixed at 0.5 MeV); if ηc2→ψ′γ is actually non-negligible, the clean separation of ψ′γ from X(3872) and J/ψγ from ηc2 breaks down.

Editorial extensions

If this is right

  • The 4.6σ radiative-ratio disagreement is not a systematic error but a physical signal: two states with different production rates across B decays and e+e− annihilation.
  • Helicity-angle distributions of J/ψγ and ψ′γ in the 3850–3890 MeV window are predicted to differ strongly, providing a direct experimental test.
  • The mass of the state seen in J/ψω and D*0D̄0 should be 2–3 MeV higher than the mass from J/ψπ+π−, because that higher value reflects the ηc2 contribution.
  • A search for ηc2 should find an enhancement in the D*0D̄0 invariant mass between 3872 and 3875 MeV and in the J/ψγ channel near 3874 MeV.
  • The predicted ratio R_B^{ψγ}/R_{e+e-}^{ψγ} ≈ 6.4 is a distinctive signature that future data can confirm or refute.

Reading between the lines

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

  • If confirmed, ηc2 would be the first observed 1D charmonium state, and its near-zero ψ′γ width would become a strong constraint on quark-model radiative-transition calculations.
  • The same two-state logic may apply to other 'tension' observables in the XYZ sector: overlapping spin-parity partners near thresholds can generate process-dependent ratios that look like inconsistencies.
  • The fitted ηc2 production strengths sit uneasily with current null searches from Belle; reconciling the two would require additional production or detection suppressions beyond the model.
Original abstract

Recently, LHCb reported the radiative-decay ratio ${\cal R}^{\psi\gamma}\equiv {\cal B}[X(3872)\to \psi'\gamma]/{\cal B}[X(3872)\to J/\psi\gamma]=1.67\pm 0.25$ extracted from $B^+\to K^+(J/\psi\gamma, \psi'\gamma)$. This result differs markedly ($\sim4.6\sigma$) from the BESIII value obtained from $e^+e^-\to \gamma(J/\psi\gamma, \psi'\gamma)$, ${\cal R}^{\psi\gamma}=-0.04\pm 0.28$. Such a significant tension suggests that more than one state in the $X(3872)$ region contributes to the processes. We therefore propose a two-state scenario: a shallow $D^{*0}\bar{D}^0$ bound state with $J^{PC}=1^{++}$ and a $2^{-+}$ charmonium candidate, $\eta_{c2}$, slightly above the $D^{*0}\bar{D}^0$ threshold. We show that this hypothesis consistently describes these ratios along with other branching fractions and lineshapes across multiple processes. By contrast, fits without the $\eta_{c2}$ component fail to reproduce the radiative-ratio data. We also predict helicity-angle distributions that motivates the future experiments to test the two-state hypothesis and search for the so-far missing $\eta_{c2}$.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,002 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.02 · controlled comparison 0.24 · randomized assignment 0.01 · states quantitative result 0.83 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Recently, LHCb reported the radiative-decay ratio ${\cal R}^{\psi\gamma}\equiv {\cal B}[X(3872)\to \psi'\gamma]/{\cal B}[X(3872)\to J/\psi\gamma]=1.67\pm 0.25$ extracted from $B^+\to K^+(J/\psi\gamma, \psi'\gamma)$. This result differs markedly ($\sim4.6\sigma$) from the BESIII value obtained from $e^+e^-\to \gamma(J/\psi\gamma, \psi'\gamma)$, ${\cal R}^{\psi\gamma}=-0.04\pm 0.28$. Such a significant tension suggests that more than one state in the $X(3872)$ region contributes to the processes. We therefore propose a two-state scenario: a shallow $D^{*0}\bar{D}^0$ bound state with $J^{PC}=1^{++}$ and a $2^{-+}$ charmonium candidate, $\eta_{c2}$, slightly above the $D^{*0}\bar{D}^0$ threshold. We show that this hypothesis consistently describes these ratios along with other branching fractions and lineshapes across multiple processes. By contrast, fits without the $\eta_{c2}$ component fail to reproduce the radiative-ratio data. We also predict helicity-angle distributions that motivates the future experiments to test the two-state hypothesis and search for the so-far missing $\eta_{c2}$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Recently, LHCb reported the radiative-decay ratio ${\cal R}^{\psi\gamma}\equiv {\cal B}[X(3872)\to \psi'\gamma]/{\cal B}[X(3872)\to J/\psi\gamma]=1.67\pm 0.25$ extracted from $B^+\to K^+(J/\psi\gamma, \psi'\gamma)$. background 0.95 0.04 0.03 asserted 1.00
s1 This result differs markedly ($\sim4.6\sigma$) from the BESIII value obtained from $e^+e^-\to \gamma(J/\psi\gamma, \psi'\gamma)$, ${\cal R}^{\psi\gamma}=-0.04\pm 0.28$. background 0.88 0.05 0.04 asserted 1.00
s2 Such a significant tension suggests that more than one state in the $X(3872)$ region contributes to the processes. interpretation 0.91 0.13 0.14 hedged possibility 1.00
s3 We therefore propose a two-state scenario: a shallow $D^{*0}\bar{D}^0$ bound state with $J^{PC}=1^{++}$ and a $2^{-+}$ charmonium candidate, $\eta_{c2}$, slightly above the $D^{*0}\bar{D}^0$ threshold. contribution 0.90 0.54 0.48 speculative 0.44
s4 We show that this hypothesis consistently describes these ratios along with other branching fractions and lineshapes across multiple processes. result 0.85 0.92 0.63 asserted 1.00
s5 By contrast, fits without the $\eta_{c2}$ component fail to reproduce the radiative-ratio data. result 0.93 0.88 0.21 asserted 1.00
s6 We also predict helicity-angle distributions that motivates the future experiments to test the two-state hypothesis and search for the so-far missing $\eta_{c2}$. future work 0.97 0.84 0.11 asserted 0.77

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from analysis of existing data 0.83.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 2. FIG. 2. (a)-(e) Invariant mass
Figure 3. FIG. 3. Invariant mass (
Figure 4. FIG. 4. Helicity angle distributions predicted by the defau

Showing 3 of the paper's 4 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2602.19165 by the authors.

References
How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 3 sentences without a confident label

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Discussion

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