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arxiv: 2503.00552 · v4 · submitted 2025-03-01 · ✦ hep-ph

Study of 1⁻⁻ P wave charmoniumlike and bottomoniumlike tetraquark spectroscopy

Zheng Zhao , Attaphon Kaewsnod , Kai Xu , Nattapat Tagsinsit , Xuyang Liu , Ayut Limphirat , Yupeng Yan This is my paper

Pith reviewed 2026-05-23 01:27 UTC · model grok-4.3

classification ✦ hep-ph
keywords tetraquarkscharmoniumbottomoniumP-wave statesconstituent quark modelexotic hadronsY statesspectroscopy
0
0 comments X

The pith

Constituent quark model assigns several Y states as P-wave tetraquarks with masses above 4.15 GeV.

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

The paper calculates the masses of 1-- P-wave charmonium-like and bottomonium-like tetraquarks using a constituent quark model with a Cornell-like potential and Breit-Fermi interactions. Parameters are taken directly from fits to conventional meson spectra without adjustment. It then computes two-body decay widths via the rearrangement mechanism and compares them to observed exotic states, proposing that ψ(4230), ψ(4360), ψ(4660), and Υ(10753) could be such tetraquarks, with possibly multiple states near 4.36 GeV. A sympathetic reader would care because this offers a unified explanation for several unexplained resonances using the same model that works for ordinary mesons.

Core claim

The masses of 1^{--} P-wave charmonium-like and bottomonium-like tetraquark states are calculated in a constituent quark model where the Cornell-like potential and Breit-Fermi interaction are employed with all model parameters imported from previous work on conventional mesons. The lowest 1^{--} tetraquark mass is predicted to be around 4.15 GeV. Decay widths are calculated for channels like ω χ_cJ and η J/ψ, and tentative assignments suggest that ψ(4230), ψ(4360), ψ(4660), and Υ(10753) may be P-wave tetraquark states with multiple states possibly existing around 4.36 GeV.

What carries the argument

constituent quark model with Cornell-like potential and Breit-Fermi interaction, parameters fixed from conventional S- and P-wave meson spectra, using rearrangement mechanism for decays

If this is right

  • ψ(4230) is interpreted as a P-wave tetraquark state
  • ψ(4360) and possibly another state around 4.36 GeV are tetraquarks
  • ψ(4660) and Υ(10753) fit as higher P-wave tetraquarks
  • Decay widths to ω χ_cJ and η J/ψ match observations for the assigned states

Where Pith is reading between the lines

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

  • If the model works, similar calculations could predict additional unobserved tetraquark states in other channels.
  • The success would suggest that tetraquarks share the same interquark potential as mesons, simplifying exotic hadron spectroscopy.
  • Experimental searches for multiple states near 4.36 GeV in charmonium-like sector could test this.

Load-bearing premise

The assumption that parameters predetermined solely from conventional S- and P-wave meson spectra can be transferred without modification to tetraquark wave functions and that the rearrangement mechanism suffices to compute the listed two-body decay widths.

What would settle it

A measurement showing that the decay width of ψ(4230) to ω χ_cJ or η J/ψ differs substantially from the model's prediction would falsify the tetraquark assignment.

Figures

Figures reproduced from arXiv: 2503.00552 by Attaphon Kaewsnod, Ayut Limphirat, Kai Xu, Nattapat Tagsinsit, Xuyang Liu, Yupeng Yan, Zheng Zhao.

Figure 1
Figure 1. Figure 1: FIG. 1. Quark rearranged diagram for Y tetraquark in the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

The masses of $1^{--}$ P-wave charmonium-like and bottomonium-like tetraquark states are calculated in a constituent quark model (CQM) where the Cornell-like potential and Breit-Fermi interaction are employed. All model parameters were imported from previous work, and predetermined by studying the low-lying conventional S- and P-wave light, charmed, bottom, charmonium, and bottomonium meson mass spectra. The lowest $1^{--}$ tetraquark mass is predicted to be around 4.15 GeV. The decay widths of $1^{--}$ P-wave tetraquark states are calculated for possible two-body strong decay channels within the rearrangement mechanism, including $\omega \chi_{cJ}$ and $\eta J/\psi$ for charmonium-like tetraquarks, and $\omega \chi_{bJ}$ for bottomonium-like tetraquarks. The theoretical results are compared with the selected exotic states, also known as Y states, and tentative assignments are suggested. This study suggests that $\psi(4230)$, $\psi(4360)$, $\psi(4660)$, and $\Upsilon$(10753) may be P-wave tetraquark states and that multiple states might exist around 4.36 GeV.

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 / 0 minor

Summary. The manuscript calculates masses of 1^{--} P-wave charmonium-like and bottomonium-like tetraquark states in a constituent quark model employing a Cornell-like potential plus Breit-Fermi interactions, with all six parameters imported unchanged from prior fits to conventional S- and P-wave meson spectra. Two-body decay widths are obtained via the rearrangement mechanism for channels including ω χ_{cJ}, η J/ψ (charmonium-like) and ω χ_{bJ} (bottomonium-like). The results are compared to selected Y states, yielding tentative assignments of ψ(4230), ψ(4360), ψ(4660) and Υ(10753) as P-wave tetraquarks together with the suggestion that multiple states exist near 4.36 GeV.

Significance. If the direct transfer of meson-tuned parameters remains valid for four-quark systems, the calculation supplies a uniform framework that links predicted masses (lowest ~4.15 GeV) and widths to specific experimental candidates and forecasts additional states, thereby contributing concrete, falsifiable input to the interpretation of exotic vector states.

major comments (1)
  1. The central mass and width results rest on the assumption that the Cornell-like potential and Breit-Fermi coefficients, fixed exclusively on conventional qq-bar S- and P-wave spectra, can be transferred without adjustment or sensitivity scan to tetraquark color and spatial wave functions. This assumption is load-bearing for the reported masses around 4.15 GeV and the subsequent state assignments; the manuscript provides no re-optimization, variation of string tension or spin-dependent terms, or test against known tetraquark candidates to quantify possible corrections from color-octet or diquark effects.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript. We address the major comment in detail below.

read point-by-point responses

  1. Referee: The central mass and width results rest on the assumption that the Cornell-like potential and Breit-Fermi coefficients, fixed exclusively on conventional qq-bar S- and P-wave spectra, can be transferred without adjustment or sensitivity scan to tetraquark color and spatial wave functions. This assumption is load-bearing for the reported masses around 4.15 GeV and the subsequent state assignments; the manuscript provides no re-optimization, variation of string tension or spin-dependent terms, or test against known tetraquark candidates to quantify possible corrections from color-octet or diquark effects.

    Authors: We agree that the transfer of parameters without adjustment is a key assumption of our calculation. The constituent quark model employed here is designed to use the same Cornell-like potential and Breit-Fermi terms as determined from meson spectra to explore their applicability to tetraquark systems. Performing a re-optimization or sensitivity analysis would require introducing new parameters or varying them specifically for four-quark states, which would undermine the goal of testing the direct transferability. The manuscript explicitly states that all parameters are imported unchanged, and the results are presented as predictions under this framework. While we recognize that color-octet or diquark effects might necessitate corrections, our calculation is based on the standard four-body treatment with the given interactions. We do not plan to modify the manuscript to include such variations, as they fall outside the scope of the current study. revision: no

Circularity Check

0 steps flagged

No significant circularity; parameters transferred from independent meson fits

full rationale

The paper states that all six parameters of the Cornell-like potential plus Breit-Fermi terms were predetermined exclusively from fits to conventional S- and P-wave meson spectra in prior work, then held fixed while solving the four-body Schrödinger equation for 1-- P-wave tetraquarks. The resulting masses (~4.15 GeV lowest state) and rearrangement-mechanism widths are therefore model outputs for a distinct system (color and spatial wave functions extended to four quarks), not algebraic reductions or statistical re-fits of the original meson data. No equation in the derivation equates a tetraquark observable directly to a meson observable by construction, and the cited prior work supplies an external benchmark. This is standard parameter transfer, not circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The calculation rests on parameters fitted to meson data and on the domain assumption that those parameters remain valid for four-quark systems; no independent evidence is supplied for the transferability.

free parameters (2)
  • Cornell-like potential parameters
    Imported from previous work on light, charmed, bottom, charmonium, and bottomonium meson spectra
  • Breit-Fermi interaction parameters
    Predetermined by studying low-lying conventional meson mass spectra
axioms (2)
  • domain assumption Parameters fixed on conventional mesons apply unchanged to tetraquarks
    Explicitly stated in the abstract as the basis for the tetraquark calculation
  • domain assumption Rearrangement mechanism governs the two-body strong decays
    Used to compute widths for channels such as omega chi_cJ and eta J/psi
invented entities (1)
  • 1-- P-wave tetraquark states no independent evidence
    purpose: To account for selected Y resonances as four-quark configurations
    Postulated to match experimental masses and suggested decay modes

pith-pipeline@v0.9.0 · 5778 in / 1559 out tokens · 48644 ms · 2026-05-23T01:27:55.489902+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Open-flavor threshold effects on quarkonium spectrum in the BOEFT

    hep-ph 2026-04 unverdicted novelty 7.0

    BOEFT quantifies threshold-induced shifts in quarkonium masses below threshold by solving coupled Schrödinger equations using lattice potentials and one parameter fixed to the χ_c1(3872) mass.

  2. Search for $e^+ e^- \to \gamma\chi_{bJ}$ ($J$ = 0, 1, 2) near $\sqrt{s} = 10.746$ GeV at Belle II

    hep-ex 2025-08 unverdicted novelty 5.0

    Belle II sets 90% CL upper limits on the Born cross sections for e+e−→γχbJ near √s=10.746 GeV, with those for χb1 being significantly smaller than for ωχb1 and π+π−Υ(2S).

  3. Improved measurement of Born cross sections for $\chi_{bJ}\,\omega$ and $\chi_{bJ}\,(\pi^+\pi^-\pi^0)_{\rm non-\omega}$ ($J$ = 0, 1, 2) at Belle and Belle II

    hep-ex 2025-10 accept novelty 4.0

    Improved cross-section measurements reveal Υ(10753) decays to χ_bJ ω but not non-ω three-pion states, while Υ(10860) shows the reverse pattern, plus updated mass 10756.1 ± 3.4 ± 2.7 MeV and width 32.2 ± 11.3 ± 14.9 Me...

  4. Systematic study of exotic $1^{-+}$ tetraquark spectroscopy

    hep-ph 2025-11 unverdicted novelty 3.0

    A constituent quark model predicts masses of 1.9, 4.2, and 6.6 GeV for light, charmonium-like, and fully-charm 1^{-+} tetraquarks along with decay ratios for specific two-body channels and rules out η1(1855) as a comp...

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