Quarkoniumlike states above open-flavor thresholds in Born-Oppenheimer EFT

Abhishek Mohapatra; Fang-Zheng Peng; Nora Brambilla; Roberto Bruschini; Tommaso Scirpa

REVIEW 3 major objections 4 minor 1 cited by

Quarkoniumlike states above open-flavor thresholds in Born-Oppenheimer EFT

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that one calibrated adjoint-meson mass, inside a QCD-constrained Born–Oppenheimer effective field theory, organizes most quarkoniumlike states above open-flavor thresholds into heavy-quark-spin-symmetry multiplets.

desk verdict A serious QCD-constrained spectroscopy paper whose multiplet organization is likely robust, but whose headline X_b binding energy rest on an unconstrained potential that needs a sensitivity scan before the numbers are trusted. read the letter →

arxiv 2608.04105 v1 pith:IEAPIA7E submitted 2026-08-04 hep-ph hep-exhep-latnucl-th

Nora Brambilla , Roberto Bruschini , Abhishek Mohapatra , Fang-Zheng Peng , Tommaso Scirpa This is my paper · ORCID

classification hep-phhep-exhep-latnucl-th

keywords quantumchromodynamicsexotichadronsquarkoniumBorn-Oppenheimereffectivefieldtheoryheavy-quarkspinsymmetrytetraquarkshadronicmoleculesthresholdresonances

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper attempts to show that the many quarkoniumlike states observed above open-flavor thresholds are not a random collection of unrelated exotic mechanisms. It claims that a single leading-order Born–Oppenheimer effective field theory, with only one parameter calibrated to experiment, generates the hidden-charm and hidden-bottom spectrum between the spin–isospin averaged S+S and S+P thresholds. The result is a common heavy-quark-spin-symmetry multiplet organization: most poles are quarkonium-dominated resonances, while the same coupled equations also produce shallow, spatially extended, open-flavor-dominated states such as the multiplet associated with the chi_c1(3872) and a predicted bottomonium counterpart, X_b. If right, this would mean conventional quarkonia, molecular-like states, and hybrids are organized by the same QCD symmetries rather than by separate dynamical descriptions.

What carries the argument

The central object is the leading-order diabatic coupled Schrödinger equation in which the quarkonium static potential, carrying Sigma_g^+ quantum numbers, mixes through string breaking with tetraquark/open-flavor Born–Oppenheimer potentials of the same quantum numbers (Sigma_g^+' and Pi_g). The potentials are constrained by QCD symmetries, their short- and long-distance behavior, and lattice QCD static energies in the string-breaking region; the only calibrated parameter is the lowest 1-- adjoint meson mass. This single Hamiltonian, solved with T-matrix analytic continuation, K-matrix poles, and complex scaling, generates all the predicted bound states and resonance poles, with the string-breaking mixing potential and the adjoint meson mass carrying the main quantitative weight.

What would settle it

A lattice QCD determination of the lowest 1-- adjoint meson mass in a comparable heavy-light scheme would be decisive: if it disagrees substantially with the calibrated value, the predicted shallow binding energies, radii, and quarkonium probabilities of the chi_c1(3872) multiplet and the X_b would not survive.

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Extended reading notes

Core claim

The central claim is that, at leading order in the heavy-quark expansion, the coupled Born–Oppenheimer Schrödinger equations—with the quarkonium potential mixed through string breaking with the lowest tetraquark/open-flavor potentials—reproduce the isoscalar hidden-charm and hidden-bottom spectrum above the open-flavor thresholds. With only the lowest 1-- adjoint meson mass calibrated so that the spin-averaged 2P multiplet of the chi_c1(3872) binds at 96 keV below the spin-averaged D(*)D(*) threshold, the equations yield four charmoniumlike resonance multiplets (3P, 3S, 2D, 4P) and five bottomoniumlike resonance multiplets (3D, 5P, 5S, 4D, 6P) between the two thresholds. Most of these poles are predominantly quarkonium, with the largest open-flavor components closest to threshold; the same dynamics also generates a shallow 4P bottomonium multiplet, X_b, with binding energy 233 keV, root-mean-square heavy-quark separation 4.9 fm, and about 1% bottomonium probability. The paper argues that this global multiplet organization, together with uncoupled hybrid reference levels, accommodates most established isoscalar candidates, while the remaining ones point to hidden-strange and S+P tetraquark/open-flavor sectors and to hybrid–quarkonium or hybrid–tetraquark mixings.

Load-bearing premise

The calculation's load-bearing premise is that the two least-constrained open-flavor potentials—the unmeasured Pi_g potential and the modeled short-distance part of the tetraquark Sigma_g^+ potential—are parametrized accurately enough for quantitative predictions; the paper itself flags this as a model uncertainty.

Editorial extensions

If this is right

If the central claim is correct, the chi_c1(3872) sits in a spin-averaged 2P multiplet whose scalar and tensor partners are resolved only after spin-dependent corrections, leaving two possible assignments for the 0++ and 2++ candidates in that region.
A shallow bottomonium state X_b should exist as the 4P counterpart, with a binding energy of about 233 keV, an rms heavy-quark separation of about 4.9 fm, and a bottomonium probability of about 1%; its properties are highly sensitive to the adjoint meson mass.
The higher quarkonium-dominated multiplets are comparatively stable against changes in the adjoint meson mass, so their masses and dominant channel content are more reliable than the near-threshold states' binding energies and radii.
States such as the chi_c1(4140), psi(4230), and psi(4360) are not naturally accommodated by the included channels, which indicates that hidden-strange and S+P tetraquark/open-flavor sectors, plus hybrid mixing terms, are needed for a complete description.
The open-flavor pole widths are leading-order estimates only and may be qualitatively different from physical total widths, especially when the pole sits near a node of the transition amplitude.

Reading between the lines

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

The paper's logic implies that compact-tetraquark and molecular descriptions are not separate hypotheses: the same open-flavor Born–Oppenheimer channel interpolates from short-distance adjoint-hadron configurations to long-distance meson–antimeson pairs, so any state samples both regimes dynamically.
A lattice QCD determination of the lowest 1-- adjoint meson mass in a comparable scheme would turn the X_b prediction into a sharp test: if the lattice value differs from the calibration used here, the shallow binding energies and radii should change substantially while the higher spectrum remains stable.
The predicted non-vector bottomonium multiplets (for example, the 5P and 6P multiplets with no 1-- member) indicate that future searches in non-vector channels could discriminate between the proposed HQSS organization and alternative interpretations.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The thing to know up front: this is the first BOEFT calculation that carries the quarkonium–tetraquark coupled-channel machinery across the full S+S to S+P window and claims a common HQSS multiplet organization for most hidden-charm and hidden-bottom candidates. The calculation is done carefully, the paper is unusually explicit about what it does not include, and the X_b prediction is a real output of the framework rather than a hand-assembled molecule. That alone makes it worth a serious referee.

What the paper does well is the internal consistency work. T-matrix poles, K-matrix diagnostics, and complex scaling agree where they should; the effective-range analysis reproduces the bound-state binding momentum; the phase-shift and Argand-trajectory discussion tying the shallow 2P state to the broad 3P resonance is illuminating. The paper also repeatedly states that resonance composition is prescription dependent and that the quoted widths are not physical total widths. That level of honesty is genuine, not a disclaimer ritual.

The soft spot is exactly the one the authors name but do not quantify. V_Pi_g is completely unconstrained by lattice data, and the l=1 tetraquark S-wave potential that supports both the chi_c1(3872) multiplet and X_b is (1/3)V_Sigma_g' + (2/3)V_Pi_g. The calibration of the adjoint meson mass can absorb an overall shift in the charmonium 2P level, but it cannot correct a wrongly modeled V_Pi_g in the bottom sector or in the widths of quarkoniumlike resonances with large open-flavor components. The paper reports 233 keV binding for X_b as a central prediction, then does a sensitivity test on the adjoint meson mass only. A sensitivity scan over the V_Pi_g coefficients—even a crude one with the A and B parameters varied within a plausible range—would materially change how much weight the X_b prediction can carry. The absence of propagated uncertainties in the numerical tables is a related but secondary issue. No code or data release is included, which makes the sensitivity question harder to answer independently.

Also worth noting: the assignment of X(3940) to the 3S multiplet is off by roughly 200 MeV, and the paper tolerates that with an order-of-magnitude band. The band is honestly labeled as not a statistical uncertainty, but the association is correspondingly weak. Similarly, the lattice comparison in the 0++/2++ sector shows that the number of scalar poles is not yet settled. These are not fatal; they are places where the framework's predictive power is currently limited.

Bottom line: the HQSS multiplet organization and the qualitative message—quarkonium-dominated resonances plus a few exceptional shallow open-flavor-dominated states from the same equations—are likely to survive improved modeling. The quantitative X_b binding energy and the near-threshold widths should not be quoted as predictions until the V_Pi_g sensitivity is explored. This paper deserves peer review, and the referee should ask for that sensitivity scan and at least an estimate of the model uncertainty in the quoted tables. I would take it to reading group.

Referee Report

3 major / 4 minor

Summary. The paper applies Born-Oppenheimer effective field theory (BOEFT) to isoscalar hidden-charm and hidden-bottom spectroscopy between the spin–isospin averaged nonstrange S+S and S+P open-flavor thresholds. At leading order in the heavy-quark expansion, heavy-quark spin decouples, and the quarkonium static potential mixes through string breaking with the lowest isoscalar tetraquark/open-flavor Born–Oppenheimer potentials of the same quantum numbers. The potentials are constrained by QCD symmetries, short- and long-distance behavior, and lattice data; the only parameter calibrated to experimental spectroscopy is the lowest 1−− adjoint meson mass, fixed so that the spin-averaged multiplet associated with the χc1(3872) lies 96 keV below the spin–isospin averaged D(*)D̄(*) threshold. Using analytic continuation of the T-matrix, K-matrix analysis, and complex scaling, the authors find four charmoniumlike and five bottomoniumlike resonance multiplets, together with shallow bound multiplets: the χc1(3872)-associated 2P multiplet (binding energy 96 keV, rms radius 10.8 fm, 3% quarkonium probability) and a predicted bottomoniumlike 4P multiplet X_b (binding energy 233 keV, radius 4.9 fm, 1% bottomonium probability). The paper also presents phase shifts, effective-range parameters, prescription-dependent composition measures, uncoupled hybrid reference levels, and comparisons with the experimental spectrum and lattice QCD.

Significance. If the quantitative predictions hold, the paper is significant: it offers a single QCD-constrained coupled-channel framework that organizes most established isoscalar hidden-charm and hidden-bottom candidates into HQSS multiplets, connects compact-quarkonium and molecular-open-flavor pictures within one dynamical setup, and makes a falsifiable prediction for X_b. The technical execution is strong in several respects: the pole extraction is cross-checked with three complementary methods (T-matrix, K-matrix, complex scaling), the complex-scaled eigenvalues agree with the analytically continued T-matrix poles, the K-matrix diagnostics behave as expected for broad resonances and threshold backgrounds, and the effective-range analysis correctly reproduces the bound-state binding momentum while demonstrating that inverting the leading Weinberg relation without finite-range corrections is unreliable. The paper is also careful to distinguish pole widths from physical total widths and to label resonance composition measures as prescription-dependent rather than probabilities.

major comments (3)

[Section II C, Eq. (2.11), and Tables II, III, XII] The central quantitative claims for open-flavor-dominated states rest on the unconstrained V_Πg potential. In Eq. (2.11), the parameters A_Πg and B_Πg are not constrained by lattice data, and the text explicitly states that the parametrization of V_Πg and of the short-distance part of V_Σg′ introduces a model uncertainty. The l=1 shallow multiplets that produce the χc1(3872) and X_b are supported by the combination (1/3)V_Σg′ + (2/3)V_Πg, so the shape and depth of V_Πg directly control the X_b binding energy, radius, and quarkonium probability reported in Table XII. The calibration of the adjoint meson mass can absorb an overall shift of the charmonium 2P level, but it cannot compensate for a materially different V_Πg in the bottomonium sector or in the widths and compositions of the 3P and 3D resonances. The paper acknowledges this limitation, but it does not provide a sensitivity scan over A_Πg, B_Πg, or the matching radius R_Πg. A quantitative assessment of how the X_b binding and the 3P/3D pole widths vary under plausible variations of these parameters is required before these are presented as central predictions.
[Section V A, Tables II and III] The quoted pole widths and compositions carry no uncertainty estimates, yet the T-matrix and K-matrix determinations differ substantially for two of the most open-flavor-sensitive multiplets: the charmoniumlike 3P width is 28 MeV from the T-matrix versus 50 MeV from the K-matrix, and the bottomoniumlike 3D width is 32 MeV versus 58 MeV. The paper attributes these differences to nonresonant threshold background, which is physically plausible, but the central values are then used in the experimental comparisons as if they had no systematic uncertainty. In addition, the model uncertainty from V_Πg is not propagated into any of the numerical tables. The paper should state the dominant systematic uncertainty on the pole masses, widths, and composition measures, at least in the form of a range obtained from varying the unconstrained potential parameters and from the T/K prescription difference.
[Section II C and Section V D] The claim that the same equations 'generate' the shallow charmoniumlike multiplet associated with χc1(3872) should be formulated more carefully. The adjoint meson mass is calibrated so that this multiplet lies 96 keV below threshold, so the shallow charmonium 2P binding is an input constraint rather than an independent output. The genuine predictions are the higher quarkonium-dominated spectrum, the X_b multiplet, the compositions, and the relative organization. The distinction is stated in Section V D, but the abstract and conclusions sometimes present the 2P multiplet as a dynamical output of the coupled equations. Rephrasing these passages would avoid giving the impression that the χc1(3872) binding energy is predicted rather than imposed.

minor comments (4)

[Tables II and III] The notation g²_{l−1} is not defined for the l=0 multiplets 3S and 5S, where there is only a single open channel with l_QbarQ = l+1; the columns should be labeled consistently for the l=0 case.
[Section II C] The phrase 'the only calibrated parameter' is potentially misleading: V_Σg′, V_Πg, and the mixing-potential parameters are modeling inputs that are not independently constrained by data, even if they are not calibrated to experimental spectroscopy. The sentence at the end of Section II C clarifies this, but the abstract and introduction could state 'only parameter calibrated to experimental spectroscopy' more consistently.
[Section V C] The effective-range fit interval k ∈ [1.4 keV, 14.0 keV] is extremely narrow and close to threshold; it would be helpful to show explicitly that the phase shift is numerically stable in this regime and that the extraction of a0 = 15.2 fm is not dominated by numerical artifacts at such low momenta.
[Section VII A] The scalar and tensor assignments in the 2P/3P region are presented as ambiguous, which is appropriate. However, the text says one organization 'may be somewhat preferred based on the mass' without giving a quantitative measure of preference; adding the mass differences in MeV would make this statement more concrete.

Circularity Check

1 steps flagged · score 4.0 of 10

The χc1(3872) binding energy is a calibration input relabeled as a prediction; the HQSS multiplet organization, X_b, and the higher spectrum are genuine outputs.

fitted input called prediction [Section II C, Eq. (2.20), and Section V D (adjoint-meson sensitivity discussion)]
"The lowest 1−− adjoint meson mass has not yet been determined in lattice QCD and is therefore calibrated phenomenologically. ... We therefore require the spin-averaged 2P multiplet associated with the χc1(3872) to lie 96 keV below the static spin–isospin averaged D(∗) ¯D(∗) threshold. ... The central prediction of the present work is the 96 keV result obtained with ¯ΛHL 1−− = −0.113 GeV."

The 96 keV binding energy of the 2P multiplet is not an output of the calculation: it is the single condition used to fix the only calibrated parameter, ΛHL 1−−. The paper then refers to this same value as a 'central prediction' and lists the shallow 2P multiplet among the bound states 'obtained' from the equations, even though its shallow character was imposed by construction. The mass listed in Table IV (3946 MeV) is just the spin-averaged threshold minus the imposed 96 keV. What remains genuinely predictive is the rest of the spectrum, the X_b binding, the widths, and the composition measures, all of which follow from the same equations after the calibration.

full rationale

The only circular step found is the treatment of the χc1(3872) 2P binding energy as a prediction when it is the calibration constraint. This is disclosed explicitly, and the paper is careful to call ΛHL 1−− the only calibrated parameter, so the issue is a labeling/emphasis problem rather than a hidden fit. The central claim of the paper, the global HQSS multiplet organization, is not reduced to this input: the charmonium 3P, 3S, 2D, 4P multiplets, the bottomonium multiplets, and the predicted X_b state all emerge from solving the coupled Schrödinger equations after the single calibration. The V_Pi_g and short-distance V_Sigma_g' model dependence is a genuine correctness risk, but it is stated openly as model uncertainty, not disguised as data or imported from a self-citation. No load-bearing self-citation chain, uniqueness argument, or ansatz-smuggling-via-citation is present. Thus the appropriate finding is partial, localized circularity, not a derivation that is equivalent to its inputs.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central calculation rests on one spectroscopy-tuned parameter plus several potential-modeling inputs, especially the unconstrained Pi_g tetraquark potential. The paper's 'only calibrated parameter' claim refers to tuning against experimental masses; the potential parameters are fitted to lattice data or chosen by hand, so they still count as free parameters for the ledger. No new fundamental entity is introduced; the predicted X_b is an output state, not an input.

free parameters (6)

Adjoint meson mass (Lambda^HL_{1--}) = -0.113 GeV (central), -0.134 GeV (sensitivity test)
The only parameter calibrated to experimental spectroscopy; fixed so the spin-averaged 2P multiplet associated with chi_c1(3872) lies 96 keV below the spin-isospin averaged D(*)Dbar(*) threshold. Used in Eqs. (2.20) and (2.11).
Pi_g tetraquark potential coefficients A_Pi_g, B_Pi_g = A=0.0726 GeV^3, B=-0.0051 GeV^5
V_Pi_g is not constrained by lattice QCD; its short-distance polynomial is modeled on the quenched hybrid form in Eq. (2.11), introducing model dependence for states with open-flavor components.
Sigma_g' tetraquark potential coefficients A_Sigma_g', B_Sigma_g' = A=0.0065 GeV^3, B=0.0018 GeV^5
Chosen to satisfy short- and long-distance constraints and reproduce lattice string-breaking data around 1-1.5 fm; not derived from first principles.
Asymptotic offset E1 of tetraquark potentials = 0.005 GeV
Constant shift in Eq. (2.11) used in the mass convention M_l=E_l+2m_HL_Q-E1; chosen by hand.
Mixing potential plateau radii r1, r2 and decay range r0 = r1=0.95 fm, r2=1.51 fm, r0=0.5 fm
Chosen to localize the string-breaking mixing in the region where lattice data exist; g=0.05 GeV is taken from Ref. [43], but the radius choices are modeling inputs.
Hybrid matching shift delta_g = -1.232 +/- 0.100 GeV
Fixes the absolute normalization of the uncoupled hybrid reference levels by matching ABM and quarkonium potentials over 0.4-0.9 fm; affects hybrid reference multiplets rather than coupled quarkonium-tetraquark poles.

assumptions (4)

domain assumption BOEFT static-potential framework and leading-order heavy-quark spin decoupling hold in the S+S to S+P window.
Invoked throughout Sections II and V; spin-averaged HQSS multiplets are the organizing output, and spin corrections are treated only as broad bands.
domain assumption Lattice QCD static energies from the D200 ensemble [43] reliably constrain the quarkonium-tetraquark potentials and mixing in the string-breaking region.
Used to fix V_Sigma+g, V_Sigma+g', and the mixing potential in Section II C.
ad hoc to paper The modeled V_Pi_g and the modeled short-distance part of V_Sigma+g' are sufficiently accurate for the predicted spectra.
Equation (2.11) is not derived from first principles; no lattice data constrain V_Pi_g, and the paper explicitly flags the resulting model uncertainty.
domain assumption Hidden-strange, S+P, and hybrid mixing effects omitted from the coupled equations do not qualitatively alter the main multiplet organization.
The paper uses non-accommodated experimental states to argue these omitted sectors are needed, but the central multiplet assignments assume the omissions do not reshuffle the included levels.

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Pith. "Pith review of Quarkoniumlike states above open-flavor thresholds in Born-Oppenheimer EFT." pith.science (2026). https://pith.science/paper/IEAPIA7E

@misc{pith2026260804105,
  author       = {Pith},
  title        = {Pith review of: Quarkoniumlike states above open-flavor thresholds in Born-Oppenheimer EFT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IEAPIA7E}},
  note         = {Machine review of arXiv:2608.04105}
}

abstract

Many quarkoniumlike states have been observed above open-flavor thresholds, but their organization and internal structure remain unsettled. We study the isoscalar hidden-charm and hidden-bottom sectors in Born--Oppenheimer effective field theory (BOEFT), between the spin--isospin averaged $S+S$ and $S+P$ thresholds. At leading order, heavy-quark spin decouples, and the quarkonium static potential mixes through string breaking with the lowest tetraquark/open-flavor BO potentials of the same quantum numbers. These potentials are constrained by QCD symmetries, their short- and long-distance behavior, and lattice-QCD data. The only calibrated parameter is the lowest $1^{--}$ adjoint meson mass, fixed from the shallow multiplet associated with the $\chi_{c1}(3872)$. Using $T$-matrix, $K$-matrix, and complex-scaling methods, we determine bound states and resonance poles, their masses, pole widths from the included nonstrange $S+S$ channels, normalized pole couplings, and prescription-dependent quarkonium--open-flavor composition measures. Uncoupled hybrid BOEFT multiplets are included as reference levels. The spectrum exhibits a common heavy-quark-spin-symmetry multiplet organization. Most poles are predominantly quarkonium resonances localized at short distances, with the largest open-flavor components closest to threshold. The same equations also generate shallow, spatially extended, open-flavor-dominated states with molecular long-distance characteristics. Their binding energies, radii, and small quarkonium components are highly sensitive to the adjoint meson mass, whereas the higher spectrum is more stable. Together with the hybrid reference levels, the spectrum provides multiplet assignments for most candidates. States not naturally accommodated point to the need for hidden-strange and $S+P$ tetraquark/open-flavor BO sectors and for hybrid--tetraquark and hybrid--quarkonium mixings.

Figures

Figures reproduced from arXiv: 2608.04105 by the authors.

**Figure 2.** The pole width of the charmoniumlike 3S multiplet generated by the included open-charm channels as a function of its mass relative to the spin–isospin averaged D (∗)D¯(∗) threshold. The scan is obtained by adding a constant shift to the quarkonium potential and is used to display the nodal dependence of the transition amplitude. The red dashed line marks the central pole position obtained with the potential paramete… view at source ↗

**Figure 3.** Inelasticity parameter η (top panels) and phase shifts δ0 and δ2 (bottom panels) in the l = 1 coupled-channel sector. The left panels (a-b) show D (∗)D¯(∗) scattering and the right panels (c-d) show B (∗)B¯(∗) scattering. The two open channels have heavy-pair orbital angular momenta lQQ¯ = 0 and lQQ¯ = 2. Departures of η from unity quantify transitions between these two included channels. The phase shifts are displa… view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Argand trajectories of the diagonal T matrix elements for the coupled S - and D-wave D (∗)D¯(∗) channels. Panel (a) shows the S -wave amplitude T11 and panel (b) shows the D-wave amplitude T22. For the normalization S = I + 2iT, the dashed circle is the elastic-unitari…

**Figure 5.** Figure 5: Comparison between the charmoniumlike multiplets predicted in BOEFT (shaded boxes) by solv [PITH_FULL_IMAGE:figures/full_fig_p039_5.png]

**Figure 6.** Figure 6: Comparison between the bottomoniumlike multiplets predicted in BOEFT (shaded boxes) by [PITH_FULL_IMAGE:figures/full_fig_p040_6.png]

**Figure 7.** Figure 7: Comparison between the charmoniumlike multiplets predicted in BOEFT (shaded boxes) by [PITH_FULL_IMAGE:figures/full_fig_p041_7.png]

**Figure 8.** Figure 8: Comparison between the bottomoniumlike multiplets predicted in BOEFT (shaded boxes) by [PITH_FULL_IMAGE:figures/full_fig_p042_8.png]

**Figure 9.** Figure 9: Comparison of the lattice QCD results of Refs. [31, 32] with the corresponding spin-averaged [PITH_FULL_IMAGE:figures/full_fig_p056_9.png]

**Figure 10.** Figure 10: Comparison between the charmoniumlike multiplets predicted in BOEFT (shaded boxes) by [PITH_FULL_IMAGE:figures/full_fig_p062_10.png]

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Reference graph

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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51 The BOEFT4Smultiplet has a calculated spin-averaged mass of10593 MeVand lies below the common spin–isospin averagedB (∗) ¯B(∗) threshold

Quarkonium-dominated BOEFT multiplets BOEFT multiplet4S(quarkonium multiplet4S),J PC = 0−+,1 −− 1−−→Υ(4S) :M=10579.4±1.2MeVΓ =20.5±2.5MeV. 51 The BOEFT4Smultiplet has a calculated spin-averaged mass of10593 MeVand lies below the common spin–isospin averagedB (∗) ¯B(∗) threshold. The well-establishedΥ(4S)is the natural physical candidate for its spin-tripl...

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Tetraquark/open-flavor-dominated BOEFT multiplets BOEFT multiplet4P(X b and its HQSS partners),J PC = 1+−,0 ++,1 ++,2 ++ No established candidates. With the central adjoint-meson calibration adopted in this work, ¯ΛHL 1−− =−0.113 GeV, the bot- tomoniumlike BOEFT4Pmultiplet forms a shallow bound state233 keVbelow the common spin– isospin averagedB (∗) ¯B(∗...

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TheΥ(10753)was seen by Belle ine +e−→Υ(nS)π +π− [116]

Uncoupled hybrid BOEFT reference multiplets Hybrid multipletH 1(10749),J PC = 1−−,0 −+,1 −+,2 −+ 1−−→Υ(10753) :M=10756.6±2.8MeV,Γ =29±9MeV. TheΥ(10753)was seen by Belle ine +e−→Υ(nS)π +π− [116]. The measured mass of theΥ(10753) lies only about8 MeVabove the centralH 1 reference level. This is the closest central mass agree- ment between an established bot...

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probabilities

Experimental candidate not uniquely accommodated by the included channels Υ(11020):J PC =1−−,M=11000±4MeV,Γ =24 +8 −6 MeV. TheΥ(11020)is not assigned uniquely within the present spin-averaged calculation. Its mass lies near theH′ 1 hybrid reference level, above the predominantly quarkonium4Dpole, and close to the first spin-averagedB (∗) ¯B(∗) J threshold...

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