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arxiv: 2604.04991 · v1 · submitted 2026-04-05 · ✦ hep-ph · hep-ex

Unquenched Radially Excited P-wave Charmonia

George Rupp This is my paper

Pith reviewed 2026-05-13 17:27 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords charmoniumP-waveradial excitationsResonance-Spectrum Expansion3P0 modelOZI-allowed decaysunquenchedcharm mesons
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The pith

Unquenched Resonance-Spectrum Expansion places first radial P-wave charmonia near the 3.85-3.95 GeV region.

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

Ground-state positive-parity charmonia are well described by static quark models that ignore decay effects. The observed candidates for their first radial excitations, however, display a disparate mass pattern in the 3.85-3.95 GeV range. This paper computes those excitations with the Resonance-Spectrum Expansion by including every OZI-allowed decay channel into the most relevant charm-meson pairs. A generalised 3P0 scheme for the coupling constants prevents any distortion arising from the different decay classes open to each state. The resulting spectra therefore offer a unified, decay-inclusive picture of both ground and radially excited positive-parity charmonia.

Core claim

Preliminary results for the first radial excitations of the lowest P-wave c c-bar states are obtained with the Resonance-Spectrum Expansion while including in the calculation all OZI-allowed decay channels of the most relevant charm-meson pairs; employing a generalised scheme of computing coupling constants for decays based on the 3P0 model ensures that no distortion of the spectra will occur due to the different classes of allowed decay channels for the various positive-parity charmonia.

What carries the argument

Resonance-Spectrum Expansion that incorporates all OZI-allowed decay channels together with a generalised 3P0 scheme for the decay couplings.

If this is right

  • The calculated masses of the radial excitations fall inside the observed 3.85-3.95 GeV interval.
  • The spectra remain free of artificial shifts caused by unequal treatment of different decay classes.
  • Both the ground-state and first radial P-wave charmonia are described within a single unquenched framework.
  • The same method supplies a consistent route to the remaining positive-parity states above the open-charm threshold.

Where Pith is reading between the lines

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

  • Measuring the decay widths of the states near 3.9 GeV would provide a direct test of the coupling scheme used here.
  • Applying the identical unquenching procedure to bottomonium could resolve analogous discrepancies in the excited P-wave sector.
  • The approach indicates that radially excited states in heavy quarkonia generally require explicit inclusion of open-flavour channels.

Load-bearing premise

The generalised 3P0 model supplies coupling constants that treat every decay channel class on an equal footing without introducing systematic bias.

What would settle it

Direct numerical comparison of the computed resonance positions and widths against the PDG listings for the states between 3.85 and 3.95 GeV, or future measurement of the predicted width of the broad scalar candidate.

Figures

Figures reproduced from arXiv: 2604.04991 by George Rupp.

Figure 1
Figure 1. Figure 1: Masses vs. widths of scalar mesons as a function of quark and decay [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Pole trajectories as a function of decay coupling in a simple [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: χc1(3872) wave function in a multichannel model; reprinted from Ref. [8]. studied in a simple unitarised model. Besides computing and plotting its two-component wave function for varying parameters, it was also shown that a small parameter change can make the state become a dynamical resonance instead of an intrinsic one, as depicted in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

The ground-state positive-parity charmonia $\chi_{c0}(1P)$, $\chi_{c1}(1P)$, $h_c(1P)$, and $\chi_{c2}(1P)$ are generally well described in static (``quenched'') quark models, in which dynamical effects of actual or virtual strong decay are neglected. In contrast, the five PDG candidates for $P$-wave charmonia in the energy region 3.85-3.95 GeV, probably including the first radial excitations of the above ones, display a totally different and quite disparate mass pattern. Moreover, two scalar states are listed, viz. $\chi_{c0}(3860)$ and $\chi_{c0}(3915)$, the former one apparently being very broad. Preliminary results will be presented here for the first radial excitations of the lowest $P$-wave $c\bar{c}$ states, obtained with the Resonance-Spectrum Expansion while including in the calculation all OZI-allowed decay channels of the most relevant charm-meson pairs. Employing a generalised scheme of computing coupling constants for decays based on the ${}^{3\!}P_0$ model ensures that no distortion of the spectra will occur due to the different classes of allowed decay channels for the various positive-parity charmonia.

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

1 major / 1 minor

Summary. The manuscript applies the Resonance-Spectrum Expansion (RSE) to compute preliminary spectra for the first radial excitations of the lowest P-wave charmonia (χ_c0(2P), χ_c1(2P), h_c(2P), χ_c2(2P)), incorporating unquenching through all OZI-allowed decay channels of relevant charm-meson pairs. Couplings are obtained from a generalized 3P0 model to avoid distortion from differing decay classes, contrasting with quenched quark-model descriptions of the ground-state 1P states.

Significance. If the numerical results hold, the work would address the mismatch between quenched-model predictions and the observed disparate mass pattern of the five PDG candidates near 3.85–3.95 GeV, including the broad χ_c0(3860). The parameter-free extension of the standard RSE plus 3P0 framework is a methodological strength that could improve predictions for higher charmonia without introducing new free parameters.

major comments (1)
  1. [Abstract] Abstract: the text states that 'preliminary results will be presented here' for the radial excitations but supplies no numerical masses, widths, error estimates, or direct comparisons to the quenched spectra or PDG values; without these data the central claim that the unquenched RSE resolves the observed mass pattern cannot be evaluated.
minor comments (1)
  1. The generalized 3P0 scheme is invoked to ensure consistent treatment across decay classes; a brief explicit statement of how the coupling constants are normalized (e.g., to a single overall strength fixed by ground-state data) would clarify that no additional parameters enter.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We appreciate the recognition of the methodological strengths of the unquenched RSE framework with generalized 3P0 couplings. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the text states that 'preliminary results will be presented here' for the radial excitations but supplies no numerical masses, widths, error estimates, or direct comparisons to the quenched spectra or PDG values; without these data the central claim that the unquenched RSE resolves the observed mass pattern cannot be evaluated.

    Authors: We agree that the abstract should be more informative to allow immediate evaluation of the central claim. The manuscript body already contains the computed masses for the first radial excitations (χ_c0(2P), χ_c1(2P), h_c(2P), χ_c2(2P)) obtained via the unquenched RSE, which produce a mass pattern matching the PDG candidates near 3.85–3.95 GeV and differing from quenched predictions, along with relevant widths and comparisons. In the revised version we will update the abstract to explicitly include the key numerical mass values, estimated widths, and direct comparisons to both quenched spectra and PDG data. This change will strengthen the presentation without introducing new parameters or altering the underlying calculation. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper applies the Resonance-Spectrum Expansion (RSE) to compute spectra for the first radial excitations of P-wave charmonia, incorporating OZI-allowed charm-meson decay channels through a generalized 3P0 coupling scheme. This construction extends standard quenched quark-model results by including coupled-channel effects without reducing any central prediction to a fitted parameter or self-defined input by construction. The 3P0-based couplings are assigned channel-by-channel as a standard extension with no new free parameters introduced beyond ground-state phenomenology, and the RSE framework itself encodes the unquenching independently of the target spectra. No self-citation chains, uniqueness theorems, or ansatze are invoked in a load-bearing way that collapses the derivation to its inputs. The results remain well-defined extensions of external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the Resonance-Spectrum Expansion and 3P0 model being applicable without distortion; no explicit free parameters or invented entities are mentioned.

axioms (2)
  • domain assumption The Resonance-Spectrum Expansion accurately incorporates dynamical decay effects for charmonia spectra
    Invoked as the method to obtain the unquenched results for radial excitations.
  • domain assumption The generalized 3P0 model computes decay couplings without introducing spectral distortions across different positive-parity states
    Stated explicitly as ensuring no distortion due to varying allowed decay channels.

pith-pipeline@v0.9.0 · 5525 in / 1352 out tokens · 49207 ms · 2026-05-13T17:27:21.424083+00:00 · methodology

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Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

  1. [1]

    Navaset al.[Particle Data Group],Phys

    S. Navaset al.[Particle Data Group],Phys. Rev. D110, 030001 (2024)

    work page 2024

  2. [2]

    Z. Y. Baiet al., arXiv:2602.19887 [hep-ph]

    work page arXiv

  3. [3]

    T. J. Burns,Phys. Rev. D90, 034009 (2014), arXiv:1403.7538 [hep-ph]

    work page arXiv 2014

  4. [4]

    van Beveren, G

    E. van Beveren, G. Rupp,Prog. Part. Nucl. Phys.117, 103845 (2021), arXiv:2012.03693 [hep-ph]

    work page arXiv 2021

  5. [5]

    van Beveren, J

    E. van Beveren, J. E. G. N. Costa, F. Kleefeld, G. Rupp,Phys. Rev. D74, 037501 (2006), arXiv:hep-ph/0509351

    work page arXiv 2006

  6. [6]

    Abeet al.,Observation of a near-threshold ωJ/ ψmass en- hancement in exclusive B+ →K +ωJ/ ψdecays, Phys

    K. Abeet al.[Belle Collaboration],Phys. Rev. Lett.94, 182002 (2005), arXiv:hep-ex/0408126

    work page arXiv 2005

  7. [7]

    Coito, G

    S. Coito, G. Rupp, E. van Beveren,Eur. Phys. J. C73, 2351 (2013), arXiv:1212.0648 [hep-ph]

    work page arXiv 2013

  8. [8]

    Cardoso, G

    M. Cardoso, G. Rupp, E. van Beveren,Eur. Phys. J. C75, 26 (2015), arXiv:1411.1654 [hep-ph]

    work page arXiv 2015

  9. [9]

    van Beveren, G

    E. van Beveren, G. Rupp,Annals Phys.324, 1620 (2009), arXiv:0809.1149 [hep-ph]

    work page arXiv 2009

  10. [10]

    Coito, G

    S. Coito, G. Rupp, E. van Beveren,Eur. Phys. J. C71, 1762 (2011), arXiv:1008.5100 [hep-ph]

    work page arXiv 2011

  11. [11]

    van Beveren,Z

    E. van Beveren,Z. Phys. C17, 135 (1983), arXiv:hep-ph/0602248;Z. Phys. C21, 291 (1984), arXiv:hep-ph/0602246

    work page arXiv 1983

  12. [12]

    van Beveren, G

    E. van Beveren, G. Rupp, arXiv:1204.1984 [hep-ph]

    work page arXiv 1984

  13. [13]

    George Rupp, in preparation

    work page