Predictions for Bottomonium from a Relativistic Screened Potential Model

Bhaghyesh; Chaitanya Anil Bokade

REVIEW 4 major objections 3 minor 87 references

Predictions for Bottomonium from a Relativistic Screened Potential Model

T0 review · 4 major / 3 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A relativistic screened potential model with S-D mixing assigns Υ(10355), Υ(10580), Υ(10860), and Υ(11020) — plus Υ(10753) — as conventional b-bbar states, reproducing their masses and di-leptonic widths.

desk verdict A useful bottomonium spectrum from a relativistic screened model, but the S-D mixing table is internally inconsistent (degrees vs radians) and the abstract contradicts the body on Upsilon(10753), so the headline interpretation needs major repair. read the letter →

arxiv 2501.03147 v2 pith:CC3O5RRN submitted 2025-01-06 hep-ph

Chaitanya Anil Bokade , Bhaghyesh This is my paper · ORCID

classification hep-ph PACS 12.39.Pn14.40.Pq

keywords bottomoniumrelativisticpotentialmodelscreenedS-DmixingUpsilonresonancesleptonicdecaywidthsradiativetransitionsquarkoniumspectroscopy

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 argues that five excited Upsilon resonances, several of which have been proposed as hybrids or tetraquarks, are in fact ordinary bottomonium (b-bbar) states once S-D mixing is included. Using a relativistic screened potential model, the authors compute the mass spectrum and decay properties and fix the two-state mixing angle by matching the measured di-leptonic widths. They assign Υ(10355) to 3S-2D, Υ(10580) and Υ(10753) to the two members of the 4S-3D pair, and Υ(10860) and Υ(11020) to the 5S-4D pair; the resulting masses and lepton-pair widths agree with experiment to within a few tens of MeV and a few percent, respectively. If this interpretation is correct, the conventional quark model, with screening and S-D mixing, is sufficient for these states, and the paper's extensive tables of radiative and annihilation widths become a practical guide for searching the still-unseen higher states.

What carries the argument

The engine of the calculation is the spinless Salpeter equation with a screened Coulomb-plus-linear potential, $V(r) = -\frac{4}{3}\frac{\alpha_s(r)}{r} + \lambda\frac{1-e^{-\mu r}}{\mu} + V_0$, whose screening parameter $\mu$ flattens the confining term at large distances. The wavefunctions are obtained by expanding in spherical Bessel functions on a finite interval and solving the resulting matrix eigenvalue equation, with spin-dependent corrections added perturbatively. On top of this, the S-D mixing ansatz $|\phi\rangle = \cos\theta\,|nS\rangle + \sin\theta\,|n'D\rangle$ (and its orthogonal partner) converts the pure-state masses and radial wavefunctions into the physical masses and leptonic widths; the angle $\theta$ is fixed by matching the measured $\Gamma_{ee}$ values. This two-state mixing, not the potential alone, carries the central claim.

What would settle it

Measure the $e^+e^-\to\Upsilon(10753)$ di-leptonic width and its radiative transitions: the model predicts $\Gamma_{ee}\approx 0.129$ keV and a D-dominated wavefunction, so a width near the S-wave scale or an E1 pattern characteristic of a pure 4S state would falsify the 4S-3D assignment. A lattice QCD calculation of the vector bottomonium spectrum above 10.5 GeV that includes $B^{(*)} \bar B$ thresholds would directly test whether these resonances contain significant non-$b\bar b$ components.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central result is that the persistent overestimation of the excited vector bottomonium masses by potential models disappears when each physical resonance is written as a linear combination of one S-wave and one D-wave component, $|\phi\rangle = \cos\theta\,|nS\rangle + \sin\theta\,|n'D\rangle$. The mixing angle $\theta$ is not chosen to fit masses: it is fixed by the measured di-leptonic widths $\Gamma_{ee}$, and the mixed-state masses then fall much closer to experiment than the pure states do. The assignments are $\Upsilon(10355)$ = 3S-2D, $\Upsilon(10580)$ = the lower 4S-3D state, $\Upsilon(10753)$ = the higher, D-dominated 4S-3D partner, and $\Upsilon(10860)$/$\Upsilon(11020)$ = the 5S-4D pair. The paper concludes that these resonances are conventional $b\bar b$ states and that the S-D admixture, rather than exotic degrees of freedom, accounts for their masses and widths.

Load-bearing premise

Each physical Upsilon above threshold is exactly one S-wave plus one D-wave $b\bar b$ component, with all coupled-channel, meson-loop, hybrid, and tetraquark effects ignored or absorbed into a single fitted angle $\theta$; if any of those extra components are significant, the state assignments in Table XXII do not follow.

Editorial extensions

If this is right

If the assignments hold, Υ(10355), Υ(10580), Υ(10753), Υ(10860), and Υ(11020) are all conventional $b\bar b$ states, so hybrid and tetraquark explanations are not required for them.
The fitted di-leptonic widths match experiment closely: 0.440 keV vs 0.443 keV for Υ(10355), 0.272 vs 0.272 keV for Υ(10580), and 0.291 vs 0.31 keV and 0.142 vs 0.13 keV for the 5S-4D pair.
S-D mixing resolves part of the systematic overestimation of the pure 4S and 5S masses: the lower mixed state is pulled down by its D-wave admixture.
The E1 and M1 transition tables and annihilation widths give concrete guidance for Belle II, LHCb, and PANDA searches for the unobserved higher states such as 2D, 3P, F, and G waves.
For n ≥ 3 the di-leptonic width of the D-dominated partner becomes sensitive to even a small mixing angle, so the predicted $\Gamma_{ee}$ values distinguish the S-D assignment from a pure-state interpretation.

Reading between the lines

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

A decisive check is the di-leptonic width of Υ(10753), predicted here at 0.129 keV; because the state is mostly 3D, an experimental $\Gamma_{ee}$ near the S-wave scale would rule out the 4S-3D assignment.
The mixing angle is inferred from $\Gamma_{ee}$ alone; a coupled-channel calculation with explicit $B^{(*)} \bar B$ thresholds could reveal whether the residual mass gaps of tens of MeV are absorbed by $\theta$ or require further components.
The same screened-potential plus S-D mixing scheme, already applied to charmonium, should predict which higher states mix most strongly as a function of the screening parameter $\mu$; that is testable in lattice or experimental data.
The model's radiative-transition predictions, such as $\Upsilon(10753) \to \gamma \chi_b(3P)$, could be searched for in Belle II data and would distinguish a D-dominated from an S-dominated wavefunction.

Share X Bluesky LinkedIn Reddit HN

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

Quick take: this is a broad bottomonium catalog from a relativistic screened potential model, and the pure-spectrum part is a usable reference. But the S-D mixing section, which is the paper's headline, has a units problem that makes Table XXI internally inconsistent, and the abstract contradicts the body on Upsilon(10753). The mixing claims should not be taken as predictions until that is fixed.

What is new: the authors extend their charmonium model to bottomonium and give masses for S through G states, leptonic/radiative/annihilation widths, and mixing angles for the four Upsilon resonances. The eigenvalue calculation is a genuine solution of the spinless Salpeter equation, and the comparison tables with several other models are useful. For lower states the numbers are reasonable; the chi_b(1P,2P) splittings and several E1 widths track experiment well.

Soft spots: the central S-D mixing section. Eq. (35) and (36) do not reproduce Table XXI when the quoted mixing angles are read as degrees. With theta = 19.28 deg for 3S-2D, Eq. (35) gives about 10384 MeV, not 10374.9; with theta = 44.55 deg for 5S-4D, the mass split would be over a GeV. The table only works if the angles are in radians, but they are reported in degrees and compared with degree-valued angles from Ref. [61]. So the physical mixing amplitudes are misreported. On top of that, the abstract calls Upsilon(10753) a pure 3D state while the body and Table XXI treat it as the 4S-3D mixed partner. The mixing angles are also fit to the leptonic widths and then used to compute the mixed masses, so the agreement in Table XXII is not an independent test. Add to that deviations of 50-160 MeV in the pure S-wave masses, no uncertainty propagation, and the unstated potential constant V0, and the model's predictive weight rests mostly on the lower states.

Who it's for: hadron spectroscopists who want a broad set of bottomonium numbers for comparison; the mass and transition tables are worth having even if the mixing interpretation is not yet established.

Recommendation: send it to a competent referee, but with a direct request to check Table XXI. As written, the mixing section needs major revision; the rest is publishable after standard polishing.

Referee Report

4 major / 3 minor

Summary. The manuscript develops a relativistic screened potential model for bottomonium and computes the mass spectrum, decay constants, radiative (E1, M1) transitions, and annihilation widths for S, P, D, F, and G waves. Its main interpretive claim is that several observed vector resonances — Υ(10355), Υ(10580), Υ(10753), Υ(10860), and Υ(11020) — can be described as S–D mixed bottomonium states, with the mixing angles determined from leptonic widths. The paper contains an extensive set of tables comparing the model with experiment and with other potential-model calculations.

Significance. If the S–D assignments were established, the paper would support a conventional bottomonium interpretation of these resonances and provide a useful compendium of decay predictions for future searches. The pure-spectrum part is a genuine eigenvalue calculation and the decay tables are a potentially valuable resource. However, the central S–D mixing conclusion is not currently supported: the mixing angles are fitted to the same leptonic widths used in the comparison, the reported angles and masses are mutually inconsistent with the stated formulas, and the abstract and body disagree on the nature of Υ(10753). These issues affect the main novelty of the paper, not merely its presentation.

major comments (4)

[Section IV, Eqs. (35)–(36) and Table XXI] The S–D mixing analysis is circular as presented. The mixing angle θ is obtained by fitting Eq. (36) to the experimental Γ_ee values, and that same θ is then inserted into Eq. (35) to compute the mixed masses in Table XXI. Consequently, the agreement of Mφ and Mφ′ with experiment is not an independent test of the S–D assignments; it is a consistency check at best. To support the claim that S–D mixing correctly reproduces the observed masses, the authors must either determine θ from a source that does not already enter the mass comparison (e.g., an independent coupled-channel or line-shape analysis) or explicitly reframe the analysis as a fit and propagate all correlations and uncertainties.
[Table XXI vs. Eq. (35)] The quoted mixing angles and mixed masses are arithmetically inconsistent. For the 3S–2D row, inserting θ=19.28° into Eq. (35) with M_S=10394.2 MeV and M_D=10467.3 MeV gives Mφ≈10384.0 MeV, not the tabulated 10374.9 MeV. For the 5S–4D row, θ=44.55° gives cos2θ≈0.016, which would produce a mass split of more than 1 GeV, whereas Table XXI shows a split of about 50 MeV. The tabulated values are reproduced only if the θ entries are interpreted as radians (e.g., 19.28 rad ≡ 0.430 rad). Since the adjacent column from Ref. [61] is explicitly in degrees, the physical mixing amplitudes (sinθ, cosθ) used in Eqs. (35)–(36) are misreported. This is a load-bearing error: every S–D assignment in Table XXII depends on these numbers, and the central claim is not assessable until the tables and formulas are brought into mutual consistency.
[Abstract vs. Section V and Table XXII] The abstract states that Υ(10753) is obtained as a purely Υ1(3D) bottomonium state, whereas Section V, Table XXI, and Table XXII treat Υ(10753) as the 4S–3D mixed partner with Mφ′=10772.9 MeV. This is not a cosmetic inconsistency: the nature of Υ(10753) is one of the paper's four central interpretive claims, and the reader cannot tell which assignment is being advocated. The abstract and body must be reconciled.
[Tables II and XXII; Conclusion] The conclusion that the computed masses exhibit strong agreement with experiment is not quantitatively supported for the states involved in the S–D analysis. The pure 4S1, 5S1, and 6S1 masses in Table II are 108.7, 53.7, and 160.9 MeV above the experimental values, and after mixing the 3S–2D and 4S–3D masses remain 19.8 and 77.0 MeV above the corresponding resonances. No uncertainties are propagated through Eqs. (35)–(36), so statements such as 'align closely' cannot be evaluated statistically. The authors should provide uncertainties on θ, Mφ, Mφ′, and Γφ, and should temper the agreement claim accordingly.

minor comments (3)

[Eq. (18)] The χ² definition uses artificial 0.1% mass errors rather than experimental uncertainties. This choice should be justified or replaced with a robust fitting procedure; as written, the quoted χ²=14.1 does not have the usual statistical interpretation.
[Table XXI] The table layout is confusing: the M_S/M_D and Mφ/Mφ′ entries are combined in single cells, and the negative values of θ[61] are not explained. A cleaner layout would separate the two masses and the two widths.
[Throughout] There are several typographical issues, including 'masess' (Section V), inconsistent spacing in 'E1' and 'M1' transitions, and the duplicated reference [30]/[13] for the Belle observation of Υ(10753). A careful proofreading pass is needed.

Circularity Check

2 steps flagged · score 6.0 of 10

S–D mixing angles are fitted to the experimental Γ_ee values, so the mixed-state leptonic widths are fitted inputs presented as predictions; the mass comparison retains partial independent content.

fitted input called prediction [Section IV (S-D Mixing), text immediately after Eq. (36); Table XXI]
"The leptonic decay of the mixed states is fitted to the experimental data to obtain the mixing angle, which is then used to calculate the masses of the mixed states."

Table XXI lists Γφ and Γφ′ against the experimental Γee values, and the surrounding text presents the agreement as support for the S–D assignments. But θ was obtained by fitting Eq. (36) to exactly those experimental di-leptonic widths, so the Γφ/Γφ′ entries are fit outputs, not predictions. The same fitted θ then enters Eq. (35) for the masses, making the mass values dependent on a parameter already determined by the data the table claims to reproduce.
fitted input called prediction [Section V, Table XXII and surrounding discussion]
"Table XXI presents the masses and leptonic decay widths of S−D mixed states, which are assigned to experimentally observed states."

The assigned states in Table XXII list Γee^cal values (e.g. 0.440 keV for Υ(10355), 0.272 keV for Υ(10580), 0.291 keV for Υ(10860)) as calculated predictions. These are the same di-leptonic widths used as fit input to fix θ for each nS–n′D pair. The conclusion that 'results align closely with experimental values' therefore rests on a quantity forced to agree by construction; only the mass columns provide a partly independent, though angle-dependent, test.

full rationale

The bulk of the paper is self-contained: the potential-model parameters are fitted by χ² to well-established low-lying bottomonium masses, and the resulting spectra, decay constants, and radiative widths are genuine model outputs compared with external data. No self-citation chain or imported uniqueness theorem is load-bearing: Ref. [36] is the authors' earlier charmonium application of the same model, and the S–D mixing formalism in Eqs. (34)–(36) is adopted from Ref. [61] with the two-state ansatz stated openly. The circularity is confined to the S–D mixing analysis: Eq. (36) is fitted to the experimental Γ_ee values to determine θ, and the same θ then enters Eq. (35) for the mixed masses. Consequently, the Γ_ee columns of Tables XXI–XXII are fitted inputs presented as calculated predictions; their agreement with Γ_exp is by construction. The masses are a partially independent prediction because the experimental masses of the assigned resonances were not used to determine θ, but the predictive power is weakened by the free θ and by the fact that the same data determine the assignments. Separately, the input contains internal inconsistencies that are not circularity: the supplied abstract says Υ(10753) is a pure 3D state while the full-text abstract, body, and Table XXII treat it as a 4S–3D mixed state; and Table XXI's θ values reproduce Eq. (35) only when read as radians, not degrees, making the reported mixing amplitudes irreproducible as written. These defects reduce confidence in the quantitative results but do not add circular steps beyond the fitted-input problem. On balance, the central S–D interpretation is partially circular: the leptonic-width 'predictions' reduce to the fit, while the mass comparison retains some independent content, giving a score of 6.

Assumptions & free parameters 10 free parameters · 8 assumptions · 0 invented entities

The model rests on five fitted potential and QCD parameters, three fitted mixing angles, and an unspecified potential constant V0. The pure mass spectrum is a genuine eigenvalue calculation, but the S-D mixed-state masses and widths quoted as predictions in Table XXII are largely generated by the fitted angles, not independently derived.

free parameters (10)

b-quark mass m_q = 4.744 GeV
Fitted by chi-square to nine low-lying bottomonium masses (Eq. 18); Table I.
Gaussian smearing width sigma = 4.967 GeV
Regulates the hyperfine delta-function in V_SS (Eq. 15); fitted in Table I.
confinement slope lambda = 0.240 GeV
Screened linear potential parameter (Eq. 3); fitted in Table I.
screening parameter mu = 0.039 GeV
Sets the distance at which the linear potential flattens (Eq. 3); fitted in Table I.
QCD scale Lambda = 0.17 GeV
Enters alpha_s(mu) through Eq. (27) for every annihilation width; fitted in Table I.
running-coupling shape parameters alpha_i, gamma_i = alpha_i = 0.15, 0.15, 0.20; gamma_i = 0.5, 1.581, 15.811
Taken from Ref. [39], not refitted here, but they set the short-distance force in Eq. (5).
mixing angle theta (3S-2D) = 19.28 degrees
Obtained by fitting Eq. (36) to the experimental Gamma_ee of Upsilon(10355); Table XXI.
mixing angle theta (4S-3D) = -28.82 degrees
Obtained by fitting Eq. (36) to Gamma_ee of Upsilon(10580) and Upsilon(10753); Table XXI.
mixing angle theta (5S-4D) = 44.55 degrees
Obtained by fitting Eq. (36) to Gamma_ee of Upsilon(10860) and Upsilon(11020); Table XXI.
potential constant V0 = unspecified (implicitly 0)
Appears in Eq. (3) but is absent from Table I; no value is quoted, so all results assume an unstated choice.

assumptions (8)

domain assumption The spinless Salpeter equation with an instantaneous potential adequately describes bottomonium.
Hamiltonian Eq. (1); neglects retardation and negative-energy components, standard for this class of model.
domain assumption The interaction is the screened Coulomb-plus-linear potential of Eqs. (2)-(4).
This form is assumed, not derived from QCD.
domain assumption Spin-dependent corrections can be treated perturbatively with the Gaussian-smeared delta function of Eq. (15).
Fine and hyperfine splittings are computed as first-order expectations on spin-averaged wavefunctions.
domain assumption Two-state S-D mixing with exactly one S and one D component per physical resonance.
Eq. (34); ignores coupled channels, hybrids, tetraquarks, and additional partial waves.
ad hoc to paper The chi-square fit uses 0.1% mass errors rather than experimental uncertainties.
Eq. (18); this choice changes the parameter values and is not externally motivated.
standard math The Bessel basis expansion converges for finite N and L.
Eqs. (10)-(12); the paper states stationarity for large N and L but reports no convergence tests.
ad hoc to paper alpha_i and gamma_i values from the charmonium fit of Ref. [39] transfer to bottomonium.
Eq. (5); no refit or uncertainty quoted.
domain assumption The vector decay width formula Eq. (22) applies without modification at these masses.
Relativistic phase space and higher-order QCD corrections are not included beyond the quoted factors.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Predictions for Bottomonium from a Relativistic Screened Potential Model." pith.science (2026). https://pith.science/paper/CC3O5RRN

@misc{pith2026250103147,
  author       = {Pith},
  title        = {Pith review of: Predictions for Bottomonium from a Relativistic Screened Potential Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CC3O5RRN}},
  note         = {Machine review of arXiv:2501.03147}
}

abstract

In this work, a comprehensive analysis of the mass spectra and decay properties of bottomonium states using a relativistic screened potential model is carried out. The mass spectrum, decay constants, $E1$ transitions, $M1$ transitions, and annihilation decay widths are evaluated. The interpretation of $\Upsilon(10355)$, $\Upsilon(10580)$,$\Upsilon(10860)$, and $\Upsilon(11020)$ as $S-D$ mixed bottomonium states are analysed. The $\Upsilon(10355)$ state is considered to be $3S-2D$, $\Upsilon(10580)$ state is considered to be $4S-3D$ mixed state, the $\Upsilon(10753)$ is obtained as purely $\Upsilon_{1}(3D)$ bottomonium state, and the $\Upsilon(10860)$ and $\Upsilon(11020)$ are deemed to be $5S-4D$ mixed states.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

87 extracted references · 79 canonical work pages

[61]

S. F. Radford and W. W. Repko, Potential model calculati ons and predictions for heavy quarkonium, Phys. Rev. D 75, 074031 (2007). 22

work page 2007
[1]

F.-K. Guo, H. Peng, J.-J. Xie, and X. Zhou, Hadron spectro scopy at STCF, arXiv 10.48550/arXiv.2203.07141 (2022), 2203.07141

arXiv doi:10.48550/arxiv.2203.07141 2022
[2]

D. M. Asner, H. Atmacan, S. Banerjee, J. V. Bennett, M. Ber temes, et al. , Belle II Executive Summary, arXiv 10.48550/arXiv.2203.10203 (2022), 2203.10203

work page Pith review arXiv doi:10.48550/arxiv.2203.10203 2022
[3]

Brambilla, S

N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P . Shen, et al. , The XYZ states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020)

2020
[4]

S. W. Herb, D. C. Hom, L. M. Lederman, J. C. Sens, H. D. Snyde r, et al. , Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-Nucleus Collisions, Phys. Rev. Lett. 39, 252 (1977)

1977
[5]

W. R. Innes, J. A. Appel, B. C. Brown, C. N. Brown, K. Ueno, et al. , Observation of Structure in the Υ Region, Phys. Rev. Lett. 39, 1240 (1977)

1977
[6]

K. Han, T. B¨ ohringer, P. Franzini, G. Mageras, D. Peters on, et al. , Observation of P -Wave b¯b Bound States, Phys. Rev. Lett. 49, 1612 (1982)

1982
[7]

Eigen, G

G. Eigen, G. Blanar, H. Dietl, E. Lorenz, F. Pauss, et al. , Evidence for χ ′ b Production in the Exclusive Reaction Υ ′′ → γχ ′ b → (γγ Υ ′ or γγ Υ), Phys. Rev. Lett. 49, 1616 (1982)

1982

Show all 87 references

[8]

Klopfenstein, J

C. Klopfenstein, J. E. Horstkotte, J. Lee-Franzini, R. D . Schamberger, M. Sivertz, et al. , Observation of the Lowest P -Wave b¯b Bound States, Phys. Rev. Lett. 51, 160 (1983)

1983
[9]

Pauss, H

F. Pauss, H. Dietl, G. Eigen, E. Lorenz, G. Mageras, et al. , Observation of χb production in the exclusive reaction Υ ′ → γγχ b → γγ Υ → γγ (e+e− or µ+µ− ), Phys. Lett. B 130, 439 (1983)

1983
[10]

Artuso, C

CLEO Collaboration, M. Artuso, C. Boulahouache, S. Blu sk, J. Butt, et al. , Photon Transitions in Υ(2 S) and Υ(3 S) Decays, Phys. Rev. Lett. 94, 032001 (2005)

2005
[11]

Andrews, K

D. Andrews, K. Berkelman, R. Cabenda, D. G. Cassel, J. W. DeWire, et al. , Observation of a Fourth Upsilon State in e+e− Annihilations, Phys. Rev. Lett. 45, 219 (1980)

1980
[14]

Bonvicini, D

G. Bonvicini, D. Cinabro, M. Dubrovin, A. Bornheim, E. L ipeles, et al. , First observation of a Υ(1 D) state, Phys. Rev. D 70, 032001 (2004)

2004
[15]

del Amo Sanchez, J

BABAR Collaboration, P. del Amo Sanchez, J. P. Lees, V. P oireau, E. Prencipe, et al. , Observation of the Υ(1 3DJ ) bottomonium state through decays to π+π− Υ(1 S), Phys. Rev. D 82, 111102 (2010)

2010
[16]

Aubert, M

BABAR Collaboration, B. Aubert, M. Bona, Y. Karyotakis , J. P. Lees, et al. , Observation of the Bottomonium Ground State in the Decay Υ(3 S) → γηb, Phys. Rev. Lett. 101, 071801 (2008)

2008
[17]

Dobbs, Z

S. Dobbs, Z. Metreveli, A. Tomaradze, T. Xiao, and K. K. S eth, Observation of the ηb(2S) Meson in Υ(2 S) → γηb(2S), ηb(2S) → Hadrons and Conﬁrmation of the ηb(1S) Meson, Phys. Rev. Lett. 109, 082001 (2012)

2012
[18]

Dobbs and The CLEO Collaboration, A New Measurement o f ηb(1S) From Υ(3 S) Radiative Decay at CLEO, AIP Conf

S. Dobbs and The CLEO Collaboration, A New Measurement o f ηb(1S) From Υ(3 S) Radiative Decay at CLEO, AIP Conf. Proc. 1257, 408 (2010)

2010
[19]

Mizuk, D

Belle Collaboration, R. Mizuk, D. M. Asner, A. Bondar, T . K. Pedlar, et al. , Evidence for the ηb(2S) and Observation of hb(1P ) → ηb(1S)γ and hb(2P ) → ηb(1S)γ, Phys. Rev. Lett. 109, 232002 (2012). 21

2012
[20]

The BABAR Collaboration, J. P. Lees, V. Poireau, E. Pren cipe, V. Tisserand, et al. , Evidence for the hb(1P ) meson in the decay Υ(3 S) → π0hb(1P ), Phys. Rev. D 84, 091101 (2011)

2011
[21]

Adachi, H

Belle Collaboration, I. Adachi, H. Aihara, K. Arinstei n, D. M. Asner, et al. , First Observation of the P -Wave Spin-Singlet Bottomonium States hb(1P ) and hb(2P ), Phys. Rev. Lett. 108, 032001 (2012)

2012
[22]

ATLAS Collaboration, G. Aad, B. Abbott, J. Abdallah, A. A. Abdelalim, et al., Observation of a New χb State in Radiative Transitions to Υ(1 S) and Υ(2 S) at ATLAS, Phys. Rev. Lett. 108, 152001 (2012)

2012
[23]

D0 Collaboration, V. M. Abazov, B. Abbott, B. S. Acharya , M. Adams, et al. , Observation of a narrow mass state decaying into Υ(1 S) + γ in pp collisions at √ s = 1.96 TeV, Phys. Rev. D 86, 031103 (2012)

2012
[24]

CMS Collaboration, A. M. Sirunyan, A. Tumasyan, W. Adam , F. Ambrogi, et al. , Observation of the χb1(3P ) and χb2(3P ) and Measurement of their Masses, Phys. Rev. Lett. 121, 092002 (2018)

2018
[25]

Bondar, A

Belle Collaboration, A. Bondar, A. Garmash, R. Mizuk, D . Santel, et al. , Observation of Two Charged Bottomoniumlike Resonances in Υ(5 S) Decays, Phys. Rev. Lett. 108, 122001 (2012)

2012
[26]

F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, et al. , Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018)

2018
[27]

Q. Wang, V. Baru, A. A. Filin, C. Hanhart, A. V. Nefediev, et al. , Line shapes of the Zb(10610) and Zb(10650) in the elastic and inelastic channels revisited, Phys. Rev. D 98, 074023 (2018)

2018
[28]

E. S. Swanson, Zb and Zc exotic states as coupled channel cusps, Phys. Rev. D 91, 034009 (2015)

2015
[29]

Maiani, A

L. Maiani, A. D. Polosa, and V. Riquer, A theory of X and Z m ultiquark resonances, Phys. Lett. B 778, 247 (2018)

2018
[30]

Mizuk, A

R. Mizuk, A. Bondar, I. Adachi, H. Aihara, D. M. Asner, et al. , Observation of a new structure near 10.75 GeV in the energy dependence of the e+e− → Υ( nS)π+π− (n = 1, 2, 3) cross sections, J. High Energy Phys. 2019 (10), 1

2019
[31]

Dong, X.-H

X.-K. Dong, X.-H. Mo, P. Wang, and C.-Z. Yuan, Hadronic c ross section of e+e− annihilation at bottomonium energy region, Chin. Phys. C 44, 083001 (2020)

2020
[32]

Hou, Searching for the bottom counterparts of X(3872) and Y (4260) via π+π− Υ, Phys

W.-S. Hou, Searching for the bottom counterparts of X(3872) and Y (4260) via π+π− Υ, Phys. Rev. D 74, 017504 (2006)

2006
[33]

A. Ali, C. Hambrock, I. Ahmed, and M. J. Aslam, A case for h idden b¯b tetraquarks based on e+e− → b¯b cross section between √ s = 10.54 and 11.20 GeV, Phys. Lett. B 684, 28 (2010)

2010
[34]

F.-K. Guo, C. Hidalgo-Duque, J. Nieves, and M. Pav´ on Va lderrama, Consequences of heavy-quark symmetries for hadr onic molecules, Phys. Rev. D 88, 054007 (2013)

2013
[35]

Mezzadri and S

G. Mezzadri and S. Spataro, XYZ states: An experimental point-of-view, Rev. Phys. 8, 100070 (2022)

2022
[36]

C. A. Bokade and Bhaghyesh, Conventional and XY Z charmonium states in a relativistic screened potential mod el, Phys. Rev. D 111, 014030 (2025)

2025
[37]

The parameters values are taken as α1 = 0.15, α2 = 0 .15, α3 = 0 .20, and γ1 = 1/2, γ2 = √ 10/2, γ3 = √ 1000/2 [39]

and is given by αs(r) = ∑ i αi 2√π ∫ γir 0 e−x2 dx , (5) where α′ is are the free parameters to imitate the short-distance behaviour of αs ( Q2) as predicted by QCD. The parameters values are taken as α1 = 0.15, α2 = 0 .15, α3 = 0 .20, and γ1 = 1/2, γ2 = √ 10/2, γ3 = √ 1000/2 ...
[38]

Godfrey and N

S. Godfrey and N. Isgur, Mesons in a relativized quark mo del with chromodynamics, Phys. Rev. D 32, 189 (1985)

1985
[39]

Yibing, C

D. Yibing, C. Kuangta, and Q. Danhua, Screened Q − ¯Q Potential and Spectrum of Heavy Quarkonium, Chin. Phys. Lett. 10, 460 (1993)

1993
[40]

Liu and M.-Z

J.-B. Liu and M.-Z. Yang, Spectrum of the charmed and b-ﬂ avored mesons in the relativistic potential model, J. High Energy Phys. 2014 (7), 1

2014
[41]

Yang, Wave functions and decay constants of B and D mesons in the relativistic potential model, Eur

M.-Z. Yang, Wave functions and decay constants of B and D mesons in the relativistic potential model, Eur. Phys. J. C 72, 1 (2012)

2012
[42]

Eichten and F

E. Eichten and F. Feinberg, Spin-dependent forces in qu antum chromodynamics, Phys. Rev. D 23, 2724 (1981)

1981
[43]

M. B. Voloshin, Charmonium, Prog. Part. Nucl. Phys. 61, 455 (2008)

2008
[44]

Barnes, S

T. Barnes, S. Godfrey, and E. S. Swanson, Higher charmon ia, Phys. Rev. D 72, 054026 (2005)

2005
[45]

R. F. Lebed and E. S. Swanson, Quarkonium h states as arbiters of exoticity, Phys. Rev. D 96, 056015 (2017)

2017
[46]

Li and K.-T

B.-Q. Li and K.-T. Chao, Higher charmonia and X, Y , Z states with screened potential, Phys. Rev. D 79, 094004 (2009)

2009
[47]

Wang, Z.-F

J.-Z. Wang, Z.-F. Sun, X. Liu, and T. Matsuki, Higher bot tomonium zoo, Eur. Phys. J. C 78, 1 (2018)

2018
[48]

Van Royen and V

R. Van Royen and V. F. Weisskopf, Hardon decay processes and the quark model, Nuovo Cimento A (1965-1970) 50, 617 (1967)

1967
[49]

Braaten and S

E. Braaten and S. Fleming, QCD radiative corrections to the leptonic decay rate of the Bc meson, Phys. Rev. D 52, 181 (1995)

1995
[50]

J. P. Lansberg and T. N. Pham, Eﬀective Lagrangian for tw o-photon and two-gluon decays of P -wave heavy quarkonium χc0, 2 and χb0, 2 states, Phys. Rev. D 79, 094016 (2009)

2009
[51]

Akbar, Decay Properties of Conventional and Hybrid C harmonium Mesons, J

N. Akbar, Decay Properties of Conventional and Hybrid C harmonium Mesons, J. Korean Phys. Soc. 77, 17 (2020)

2020
[52]

Kwong and J

W. Kwong and J. L. Rosner, D-wave quarkonium levels of th e Υ family, Phys. Rev. D 38, 279 (1988)

1988
[53]

Kwong, P

W. Kwong, P. B. Mackenzie, R. Rosenfeld, and J. L. Rosner , Quarkonium annihilation rates, Phys. Rev. D 37, 3210 (1988)

1988
[54]

V. A. Novikov, L. B. Okun, M. A. Shifman, A. I. Vainshtein , M. B. Voloshin, et al. , Charmonium and gluons, Phys. Rep. 41, 1 (1978)

1978
[55]

Godfrey and K

S. Godfrey and K. Moats, Bottomonium mesons and strateg ies for their observation, Phys. Rev. D 92, 054034 (2015)

2015
[56]

B´ elanger and P

G. B´ elanger and P. Moxhay, Three-gluon annihilation o f D-wave quarkonium, Phys. Lett. B 199, 575 (1987)

1987
[57]

W. A. Bardeen, E. J. Eichten, and C. T. Hill, Chiral multi plets of heavy-light mesons, Phys. Rev. D 68, 054024 (2003)

2003
[58]

Pandya, M

B. Pandya, M. Shah, and P. C. Vinodkumar, Importance of c onﬁnement in instanton induced potential for bottomonium spectroscopy, Eur. Phys. J. C 81, 1 (2021)

2021
[59]

Eichten, K

E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T .-M. Yan, Charmonium: The model, Phys. Rev. D 17, 3090 (1978)

1978
[60]

V. Kher, R. Chaturvedi, N. Devlani, and A. K. Rai, Bottom onium spectroscopy using Coulomb plus linear (Cornell) potential, Eur. Phys. J. Plus 137, 1 (2022)

2022
[62]

Z. Zhao, K. Xu, A. Limphirat, W. Sreethawong, N. Tagsins it, et al. , Mass spectrum of 1 −− heavy quarkonium, Phys. Rev. D 109, 016012 (2024)

2024
[63]

Heikkil¨ a, N

K. Heikkil¨ a, N. A. T¨ ornqvist, and S. Ono, Heavy cc and bb quarkonium states and unitarity eﬀects, Phys. Rev. D 29, 110 (1984)

1984
[64]

Y. Lu, M. N. Anwar, and B.-S. Zou, Coupled-channel eﬀect s for the bottomonium with realistic wave functions, Phys. Rev. D 94, 034021 (2016)

2016
[65]

Machleidt, K

R. Machleidt, K. Holinde, and Ch. Elster, The bonn meson -exchange model for the nucleon-nucleon interaction, Phys. Rep. 149, 1 (1987)

1987
[66]

L. Ya. Glozman and D. O. Riska, The spectrum of the nucleo ns and the strange hyperons and chiral dynamics, Phys. Rep. 268, 263 (1996)

1996
[67]

Wang and X

J.-Z. Wang and X. Liu, Identifying a characterized ener gy level structure of higher charmonium well matched to the p eak structures in e+e− → π+D0D∗− , Phys. Lett. B 849, 138456 (2024)

2024
[68]

Particle Data Group, R. L. Workman, V. D. Burkert, V. Cre de, E. Klempt, et al. , Review of Particle Physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022)

2022
[69]

Liang, N

W.-H. Liang, N. Ikeno, and E. Oset, Υ( nl) decay into B(∗ ) ¯B(∗ ), Phys. Lett. B 803, 135340 (2020)

2020
[70]

van Beveren and G

E. van Beveren and G. Rupp, Production of hadron pairs in e+e− annihilation near the K +K − , DD, BB, and Λ + c Λ − c thresholds, Phys. Rev. D 80, 074001 (2009)

2009
[71]

Besson, J

D. Besson, J. Green, R. Namjoshi, F. Sannes, P. Skubic, et al. , Observation of New Structure in the e+e− Cross Section above the Υ(4 S), Phys. Rev. Lett. 54, 381 (1985)

1985
[72]

Bruschini and P

R. Bruschini and P. Gonz´ alez, A plausible explanation of Υ(10860), Phys. Lett. B 791, 409 (2019)

2019
[73]

Bicudo, N

P. Bicudo, N. Cardoso, L. Mueller, and M. Wagner, Study o f I = 0 bottomonium bound states and resonances in S, P , D, and F waves with lattice QCD static-static-light-light potenti als, Phys. Rev. D 107, 094515 (2023)

2023
[74]

Li, M.-S

Q. Li, M.-S. Liu, Q.-F. L¨ u, L.-C. Gui, and X.-H. Zhong, C anonical interpretation of Y (10750) and Υ(10860) in the Υ family, Eur. Phys. J. C 80, 1 (2020)

2020
[75]

W.-J. Deng, H. Liu, L.-C. Gui, and X.-H. Zhong, Spectrum and electromagnetic transitions of bottomonium, Phys. Rev. D 95, 074002 (2017)

2017
[76]

Karliner and J

M. Karliner and J. L. Rosner, X(3872), Xb, and the χb1(3P ) state, Phys. Rev. D 91, 014014 (2015)

2015
[77]

B. Chen, A. Zhang, and J. He, Bottomonium spectrum in the relativistic ﬂux tube model, Phys. Rev. D 101, 014020 (2020)

2020
[78]

A. Ali, L. Maiani, A. Y. Parkhomenko, and W. Wang, Interp retation of Yb(10750) as a tetraquark and its production mechanism, Phys. Lett. B 802, 135217 (2020)

2020
[79]

Wang, Vector hidden-bottom tetraquark candidat e: Y (10750), Chin

Z.-G. Wang, Vector hidden-bottom tetraquark candidat e: Y (10750), Chin. Phys. C 43, 123102 (2019)

2019
[80]

van Beveren and G

E. van Beveren and G. Rupp, Observation of the Upsilon(2 3D1) and indication of the Upsilon(1 3D1), arXiv 10.48550/arXiv.1009.4097 (2010), 1009.4097

2010 doi arXiv
[81]

N. R. Soni, B. R. Joshi, R. P. Shah, H. R. Chauhan, and J. N. Pandya, Q ¯Q (Q ∈ { b, c}) spectroscopy using Cornell potential, Eur. Phys. J. C 78, 1 (2018)

2018
[82]

Patel and P

B. Patel and P. C. Vinodkumar, Properties of Q ¯Q (Qǫb, c) mesons in Coulomb plus Power potential, J. Phys. G: Nucl. Part. Phys. 36, 035003 (2009)

2009
[83]

A. M. Badalian, B. L. G. Bakker, and I. V. Danilkin, Possi bility to observe higher n3D1 bottomonium states in the e+e− processes, Phys. Rev. D 79, 037505 (2009)

2009
[84]

Segovia, P

J. Segovia, P. G. Ortega, D. R. Entem, and F. Fern´ andez, Bottomonium spectrum revisited, Phys. Rev. D 93, 074027 (2016)

2016
[85]

A. K. Grant and J. L. Rosner, Dipole transition matrix el ements for systems with power-law potentials, Phys. Rev. D 46, 3862 (1992)

1992
[86]

Eichten, S

E. Eichten, S. Godfrey, H. Mahlke, and J. L. Rosner, Quar konia and their transitions, Rev. Mod. Phys. 80, 1161 (2008)

2008
[87]

A. M. Badalian and B. L. G. Bakker, Dominant spin-orbit e ﬀects in radiative decays Υ(3 S) → γ + χbJ (1P ), Phys. Rev. D 86, 074001 (2012)

2012
[88]

Abdesselam, I

A. Abdesselam, I. Adachi, K. Adamczyk, H. Aihara, S. A. S aid, et al. , Study of χ{ bJ}(1P ) Properties in the Radiative Υ(2 S) Decays, arXiv 10.48550/arXiv.1606.01276 (2016), 1606.0 1276

2016 doi arXiv
[89]

Cawlﬁeld, B

C. Cawlﬁeld, B. I. Eisenstein, I. Karliner, D. Kim, N. Lo wrey, et al. , Experimental study of χb(2P ) → ππχ b(1P ), Phys. Rev. D 73, 012003 (2006)

2006

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [61]

S. F. Radford and W. W. Repko, Potential model calculati ons and predictions for heavy quarkonium, Phys. Rev. D 75, 074031 (2007). 22

work page 2007

[2] [1]

F.-K. Guo, H. Peng, J.-J. Xie, and X. Zhou, Hadron spectro scopy at STCF, arXiv 10.48550/arXiv.2203.07141 (2022), 2203.07141

arXiv doi:10.48550/arxiv.2203.07141 2022

[3] [2]

D. M. Asner, H. Atmacan, S. Banerjee, J. V. Bennett, M. Ber temes, et al. , Belle II Executive Summary, arXiv 10.48550/arXiv.2203.10203 (2022), 2203.10203

work page Pith review arXiv doi:10.48550/arxiv.2203.10203 2022

[4] [3]

Brambilla, S

N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P . Shen, et al. , The XYZ states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020)

2020

[5] [4]

S. W. Herb, D. C. Hom, L. M. Lederman, J. C. Sens, H. D. Snyde r, et al. , Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-Nucleus Collisions, Phys. Rev. Lett. 39, 252 (1977)

1977

[6] [5]

W. R. Innes, J. A. Appel, B. C. Brown, C. N. Brown, K. Ueno, et al. , Observation of Structure in the Υ Region, Phys. Rev. Lett. 39, 1240 (1977)

1977

[7] [6]

K. Han, T. B¨ ohringer, P. Franzini, G. Mageras, D. Peters on, et al. , Observation of P -Wave b¯b Bound States, Phys. Rev. Lett. 49, 1612 (1982)

1982

[8] [7]

Eigen, G

G. Eigen, G. Blanar, H. Dietl, E. Lorenz, F. Pauss, et al. , Evidence for χ ′ b Production in the Exclusive Reaction Υ ′′ → γχ ′ b → (γγ Υ ′ or γγ Υ), Phys. Rev. Lett. 49, 1616 (1982)

1982