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$\psi(3S)$ and $\eta_c(3S)$ production in the $B^+$ decay processes

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Zhuo Yu, Qi Wu, Man-Yu Duan, Zhou Rui, Dian-Yong Chen

High Energy Physics - Phenomenology · Submitted 16 Oct 2026 · 59 references

Pith's verdict: A solid but parameter-dependent explanation of the B+ -> K+ psi(4040) branching fraction, with a testable prediction for eta_c(3S).

T0 · AI review

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arXiv ID2610.23273 (version 1)
Pith IDJJFY3ACQ, Pith's permanent record of this paper and its review
CitationDian-Yong Chen, Man-Yu Duan, Qi Wu, Zhou Rui, Zhuo Yu. "$\psi(3S)$ and $\eta_c(3S)$ production in the $B^+$ decay processes." arXiv:2610.23273 (2026). https://pith.science/paper/JJFY3ACQ
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The paper

The paper claims

Long-distance meson loops resolve the anomalously large branching fraction of B+ → K+ ψ(4040) and predict η_c(3S) production.

The reading

The paper addresses the puzzle that the measured branching fraction of B+ → K+ ψ(4040) (where ψ(4040) is identified as the ψ(3S) charmonium state) is (1.6±0.5)×$10^{{-3}}$, about seven times larger than the short-distance perturbative QCD (pQCD) prediction of 2.4×$10^{{-4}}$. The authors argue that long-distance non-perturbative QCD effects, described phenomenologically by charmed-meson loops (e.g., $D_s^{{(*)}}$D̅^{(*)} intermediate states), are essential to bridge the gap. By introducing a monopole form factor with a cutoff parameter α expected to be of order unity, they fit the single experimental data point and find that α in the range 1.95–2.88 reproduces the observed branching fraction. Exploiting the structural similarity of η_c(3S) and ψ(3S), they then apply the same model parameters to predict the branching fraction of B+ → K+ η_c(3S) to be (0.$81^{{+0.31}}$_{-0.29})×$10^{{-3}}$. They suggest experimental searches for η_c(3S) in the J/ψ ω invariant mass distribution of B+ → J/ψ ω K+ at Belle II and LHCb. If correct, the work demonstrates that long-distance meson-loop contributions are crucial for understanding higher-excited charmonium production in B decays.

What carries the argument

The meson-loop mechanism: after the B+ weak decay produces a pair of charmed-strange and anti-charmed mesons (e.g., D_s^+ D̅^0), these mesons rescatter by exchanging a charmed meson to form the final-state ψ(3S) and K+. This hadron-level loop describes the long-distance non-perturbative QCD contribution. The coupling constants of ψ(3S) and η_c(3S) to charmed mesons are extracted from the open-charm decay widths computed in the 3P0 model. A monopole form factor F($q^{2}$,$m^{2}$) = ($m^{2}$-$Λ^{2}$)/($q^{2}$-$Λ^{2}$) with Λ = m + α Λ_QCD (Λ_QCD = 220 MeV) regularizes the loops; the cutoff parameter α is fitted to the single available experimental branching fraction of B+ → K+ ψ(3S).

Extended reading notes

Core claim

The authors find that the short-distance pQCD prediction for B+ → K+ ψ(3S) is (2.$4^{{+0.7}}$_{-0.5})×$10^{{-4}}$, far below the PDG average of (1.6±0.5)×$10^{{-3}}$. Including long-distance contributions from meson loops—where the B+ first decays weakly into a charmed-strange meson and an anti-charmed meson, which then rescatter via the exchange of a charmed meson to produce ψ(3S) and a kaon—and adjusting a single cutoff parameter α in the monopole form factor (expected to be of order unity), they reproduce the experimental value for α in the range 1.95–2.88. Using the same parameter range, they predict the branching fraction of B+ → K+ η_c(3S) to be (0.$81^{{+0.31}}$_{-0.29})×$10^{{-3}}$, which is larger than that of B+ → K+ η_c(2S) and similar in pattern to the vector sector. They note that the BaBar data on B+ → J/ψ ω K+ show an enhancement near 4.0 GeV in the J/ψ ω mass distribution that could be η_c(3S), and urge Belle II and LHCb to search for it.

Load-bearing premise

The model parameter α in the monopole form factor is determined by fitting the single experimental branching fraction of B+ → K+ ψ(3S), and this same α range is then used to predict the B+ → K+ η_c(3S) branching fraction without any independent constraint.

Editorial extensions

If this is right

  • The predicted branching fraction of B+ → K+ η_c(3S) is (0.81^{+0.31}_{-0.29})×10^{-3}, providing a clear target for experimental searches at Belle II and LHCb in the B+ → J/ψ ω K+ channel.
  • Long-distance meson-loop contributions are shown to be essential for reproducing the branching fraction of B+ → K+ ψ(3S), indicating that pure pQCD calculations are insufficient for higher-excited charmonium production in B decays.
  • A similar meson-loop mechanism may be important for other B decays to excited charmonia, such as ψ(4S) or ψ(4415), and should be included in future theoretical analyses.
  • If η_c(3S) is observed with a branching fraction consistent with the prediction, it would support the identification of ψ(4040) as the dominant ψ(3S) state and validate the long-distance approach employed here.

Reading between the lines

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

  • Because the cutoff parameter α is determined solely from one data point, the uncertainty in the predicted η_c(3S) branching fraction may be underestimated; future experimental measurement will serve as a stringent test of the model.
  • If η_c(3S) is not found or its branching fraction differs significantly from the prediction, the meson-loop model might require revision (e.g., inclusion of additional intermediate states or a different form factor), or the identification of ψ(4040) as the pure ψ(3S) could be questioned.
  • The framework can be applied to decays of bottom baryons (e.g., Λ_b) to excited charmonia, where long-distance effects might also be significant and observable at LHCb.
Original abstract

In the present work, we investigate the production of psi(4040) in the B+ -> K+ psi(4040) process. Our estimations indicate that the unexpectedly large branching fraction could be well reproduced by taking both the short-range perturbative and long-range non-perturbative QCD contributions into account, where the long-range non-perturbative part plays an important role. Considering the structural similarity of eta_c(3S) and psi(3S), we apply the same model parameters to investigate the production of eta_c(3S) in the B+ decay process, and the branching fraction is predicted to be (0.81 +0.31 -0.29) x 10^-3. Based on the estimations in the present work and the relevant experimental measurements, we suggest that the experimentalists search for eta_c(3S) in the J/psi omega invariant mass distributions of B+ -> J/psi omega K+ process at Belle II and LHCb Collaborations.

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, 2026-10-20: 1 request, 3,899 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.46 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In the present work, we investigate the production of psi(4040) in the B+ -> K+ psi(4040) process. Our estimations indicate that the unexpectedly large branching fraction could be well reproduced by taking both the short-range perturbative and long-range non-perturbative QCD contributions into account, where the long-range non-perturbative part plays an important role. Considering the structural similarity of eta_c(3S) and psi(3S), we apply the same model parameters to investigate the production of eta_c(3S) in the B+ decay process, and the branching fraction is predicted to be (0.81 +0.31 -0.29) x 10^-3. Based on the estimations in the present work and the relevant experimental measurements, we suggest that the experimentalists search for eta_c(3S) in the J/psi omega invariant mass distributions of B+ -> J/psi omega K+ process at Belle II and LHCb Collaborations.

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 In the present work, we investigate the production of psi(4040) in the B+ -> K+ psi(4040) process. contribution 1.00 0.82 0.05 asserted 0.84
s1 Our estimations indicate that the unexpectedly large branching fraction could be well reproduced by taking both the short-range perturbative and long-range non-perturbative QCD contributions into account, where the long-range non-perturbative part plays an important role. interpretation 0.50 0.88 0.36 hedged possibility 1.00
s2 Considering the structural similarity of eta_c(3S) and psi(3S), we apply the same model parameters to investigate the production of eta_c(3S) in the B+ decay process, and the branching fraction is predicted to be (0.81 +0.31 -0.29) x 10^-3. result 0.93 0.91 0.27 asserted 0.91
s3 Based on the estimations in the present work and the relevant experimental measurements, we suggest that the experimentalists search for eta_c(3S) in the J/psi omega invariant mass distributions of B+ -> J/psi omega K+ process at Belle II and LHCb Collaborations. future work 1.00 0.33 0.42 hedged possibility 0.99

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from simulation or computation 0.86.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
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 1. FIG. 1: Typical short distance diagrams contributing to
Figure 2. FIG. 2: Typical diagrams contributing to
Figure 3. FIG. 3: (Color online.) Branching fractions of
Figure 4. FIG. 4: (Color online.) Branching fractions of
Figure 6. FIG. 6: Diagrams contributing to

Showing 5 of the paper's 6 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2610.23273 by the authors.

References

Discussion

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