Bottomonia in an unquenched quark model

Jia-Jun Wu; Qian Deng; Ru-Hui Ni; Xian-Hui Zhong

REVIEW 3 major objections 6 minor 137 references

Bottomonia in an unquenched quark model

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read An unquenched quark model that lets bottomonium states mix with open-bottom meson pairs reproduces the observed spectrum and predicts that the $\Upsilon(10753)$ bump in $e^+e^-\to b\bar b$ is a threshold effect of the $\bar B^*B^*$…

desk verdict Solid systematic unquenched bottomonium calculation, but the headline Y(10753) threshold explanation is not actually computed in the reported cross-section formula. read the letter →

arxiv 2501.15110 v2 pith:FZMP6TV6 submitted 2025-01-25 hep-ph hep-ex

Ru-Hui Ni , Qian Deng , Jia-Jun Wu , Xian-Hui Zhong This is my paper · ORCID

classification hep-phhep-ex

keywords bottomoniumunquenchedquarkmodelcoupled-channeleffects3P0hadronicloopsthresholdY(10753)S-Dmixingdielectrondecaywidths

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

The paper tries to establish that the bottomonium spectrum, including the hard-to-classify resonances above the open-bottom threshold, can be described by an unquenched quark model: a conventional $b\bar b$ core that is allowed to mix with the two-meson continuum through $^3P_0$ quark-pair-creation loops. Using all OZI-allowed channels near each bare state and a once-subtracted self-energy for distant channels, the authors reproduce the masses and widths of the well-established states and give predictions for the $S$-, $P$-, and $D$-wave spectrum up to about 11.3 GeV. The outcome is a set of concrete claims: coupled-channel effects shift high-lying masses by tens of MeV, most high-lying resonances carry large non-$b\bar b$ components, hadronic loops induce $S$-$D$ mixing angles of roughly $-14^\circ$ to $-18^\circ$ for the D-wave vector states, and the non-$b\bar b$ components suppress dielectron widths. Their most striking claim is that $\Upsilon(10753)$ need not be a genuine state at all: the bump seen near 10.71 GeV in $e^+e^-\to b\bar b$ can arise as a threshold effect of the strong $\Upsilon(4S)$--$\bar B^*B^*$ coupling.

What carries the argument

The load-bearing object is the hadronic self-energy $g(M)=\sum_{BC} \int |\mathcal{M}_{A\to BC}(p)|^2/(M-E_{BC}+i\epsilon)\,p^2 dp$, built from $^3P_0$ model transition amplitudes between the bare bottomonium state and two-meson channels. Its real part, computed with a once-subtracted dispersion integral, gives the mass shift; its imaginary part gives each partial width. A momentum cutoff $\Lambda=0.78$ GeV damps unphysical high-momentum loop contributions. For resonances, the spectral density function $\omega_R(M)$ supplies the $\bar b\bar b$ core probability, and the off-diagonal self-energy between $n^3S_1$ and $m^3D_1$ states, computed from the same loops, produces the $S$-$D$ mixing angles without free mixing parameters.

What would settle it

A high-statistics measurement of $e^+e^-\to \bar B^*B^*$ across $\sqrt{s}=10.70$--$10.75$ GeV would settle it: if the enhancement at 10.71 GeV is a genuine Breit-Wigner resonance, its pole position and width will remain stable when the $B^*B^*$ threshold is treated with different final-state-interaction assumptions, whereas a threshold cusp will change shape and shift as those assumptions vary. A direct check of the $\Upsilon_1(3D)$ interpretation is the predicted $\Gamma_{ee}\simeq 0.028$ keV and $\sim 92\%$ $\bar B^*B^*$ branching; an experimental upper bound well below either would falsify the model's assignment.

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Extended reading notes

Core claim

The central claim is that the unquenched coupled-channel mechanism simultaneously explains the masses and strong widths of the known $\Upsilon$ states and predicts the missing higher states. Mass shifts from hadronic loops are tens of MeV and non-monotonic: $\Upsilon(4S)$ and $\Upsilon(6S)$ shift down by about $-40$ and $-56$ MeV, bringing them close to $\Upsilon(10580)$ and $\Upsilon(11020)$, while $\Upsilon(5S)$ shifts by only about $-2$ MeV. The model yields $\bar b\bar b$ core fractions as low as roughly 30 percent for the lower $\Upsilon_3(3D)$ solution and about 37 percent for $\Upsilon(11020)$; gives hadronic-loop-induced mixing angles $\phi_D\simeq -(14\text{--}18)^\circ$ for $\Upsilon_1(3D,5D,6D)$; and produces two-pole structures for $\Upsilon_3(3D)$, $\Upsilon_3(5D)$, and $\eta_{b2}(5D)$ from strong coupling to $\bar B^*B^*$ and $\bar B^*B_2^*(5747)$. In the computed $e^+e^-\to b\bar b$ cross section, the $\bar BB^*$ and $\bar B^*B^*$ thresholds generate bumps near 10.63 and 10.71 GeV, and the 10.71 GeV bump is the paper's explanation for $\Upsilon(10753)$.

Load-bearing premise

The load-bearing premise is that the two mesons in the continuum do not interact after being created, so $H_c$ contains only kinetic energy; near the $\bar B^*B^*$ threshold, unmodeled meson-meson final-state interactions could alter the cusp that the paper identifies with $\Upsilon(10753)$ and could shift the mass integrals that generate the two-pole structures.

Editorial extensions

If this is right

If the model is right, $\Upsilon(10753)$ is a threshold bump rather than a quark-antiquark state, so its line shape should not follow a stable Breit-Wigner form.
The predicted $\Upsilon_1(3D)$ state at about 10.67 GeV, with $\Gamma_{ee}\simeq 0.028$ keV and about 92% branching to $\bar B^*B^*$, should appear as an enhancement in $e^+e^-\to \bar B^*B^*$ near threshold.
$\Upsilon(11020)$ should decay dominantly to $\bar B B(1P_1)$ (about 75%), making that mode the best place to search for the missing excited $B(1P_1)$ meson.
The higher D-wave vectors $\Upsilon_1(5D)$ and $\Upsilon_1(6D)$ get dielectron widths enhanced to about 0.019 and 0.023 keV by loop-induced $S$-$D$ mixing, while the S-wave states' dielectron widths are suppressed by their continuum components.
The predicted masses, widths, and dominant channels for the $7S$, $5P$, $6P$, $5D$, and $6D$ states give concrete search targets in open-bottom final states.

Reading between the lines

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

Neglect of continuum-continuum interactions is the main uncontrolled piece; including them could sharpen or shift the $\bar B^*B^*$ cusp, so the $\Upsilon(10753)$ line shape is also a probe of near-threshold meson-meson scattering.
The same once-subtracted loop machinery could be applied to other heavy-quark systems; if threshold artifacts explain $\Upsilon(10753)$, analogous 'states' in charmonium or bottom-strange spectra deserve re-examination before exotic interpretations are adopted.
A direct test: measure the phase of the $e^+e^-\to \bar B^*B^*$ amplitude across 10.71 GeV; a threshold cusp produces a different phase motion than a resonance pole, so the data can distinguish the two explanations without model dependence.

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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

You should know two things about arXiv:2501.15110. First, it is a serious, mostly self-consistent unquenched quark model calculation for bottomonium up to 11.3 GeV, including excited open-bottom channels. It produces useful predictions: mass shifts of tens of MeV, significant non-b bbar components, two-pole structures for 3D and 5D states, hadronic-loop S-D mixing angles around -14 to -18 degrees, and suppressed dielectron widths. The low-lying spectrum is described reasonably (chi2 = 61.5 for 14 states with 5 MeV scale errors), the Y(11020) width comes out 16.5 MeV versus 24(+8,-6) MeV, and the lower Y dielectron widths agree well. That part is worth taking seriously.\n\nNow the soft spots. The framework is not new—it was developed for charmonium and heavy-light mesons in refs [55,69]—and this application carries the same caveats: no propagated parameter uncertainties, hand-chosen cutoffs (Lambda = 0.78 GeV, rc = 0.101 fm), and neglect of continuum-continuum interactions. The Y(10860) width is a clear failure: predicted 8 MeV versus 37 +/- 4 MeV, and the paper resorts to speculative channels to patch it. Those are ordinary phenomenological limitations.\n\nThe real problem is the cross-section section. Equation (41) is an incoherent sum of constant-width Breit-Wigners. There are no energy-dependent widths and no explicit threshold singularities. A sum of Breit-Wigners cannot produce a cusp at the B*B* threshold. Yet the text says the bumps near 10.63 and 10.71 GeV are threshold effects and uses the latter to explain Y(10753) as not a genuine state. That conclusion is not a consequence of the reported calculation; the bump in Fig. 4 is just overlapping tails of the vector resonances. Threshold effects do appear in the self-energy mass-shift functions (the dips in Fig. 8), which generate the two-pole structures, but those are not what goes into Eq. (41). So the abstract's claim is stronger than what is computed. This is fixable—one should compute the cross section from the spectral densities with energy-dependent widths, or use a proper coupled-channel unitarized amplitude—but as written it is an internal inconsistency.\n\nWho is this for? Hadron spectroscopists, especially people working on bottomonium exotics and Belle II final states. There are concrete search predictions for 4P and 5D states and their decay channels that are worth having on the record. It deserves a serious referee because the spectroscopy is solid enough to be useful even if the Y(10753) interpretation needs reworking. I would send it to review and ask for a proper cross-section calculation and uncertainty estimates.

Referee Report

3 major / 6 minor

Summary. The paper develops an unquenched quark model for bottomonium in which bare quark-model states are coupled to two-body open-bottom meson channels via a 3P0 hadronic-loop vertex, with a once-subtracted self-energy and a Gaussian high-momentum cutoff. The model parameters are fitted to the low-lying bottomonium masses (chi2 = 61.5 for 14 states) and to the width of Upsilon(10580). Using this framework the authors compute mass shifts, bbbar-core probabilities, strong decay widths, hadronic-loop-induced S-D mixing, dielectron widths, and an e+e- -> bbbar cross section. They conclude that most high-lying states have large continuum components, that Upsilon1(3D,5D,6D) mix strongly with nearby S-wave states, and that the Upsilon(10753) bump may be a B*B* threshold effect rather than a genuine resonance.

Significance. If the calculations were fully substantiated, the paper would provide a broad, unified description of bottomonium above the open-bottom threshold, including masses, widths, mixing, and line shapes, with falsifiable predictions for missing 5P, 6P, 5D, and 6D states. The systematic inclusion of excited B-meson channels and the use of the same 3P0 vertex for both real and imaginary parts of the self-energy are valuable strengths, as is the effort to connect the model to Belle II observations of e+e- -> B(*)B(*) cross sections. However, the central interpretive claim about Upsilon(10753) is currently not a consequence of the reported cross-section calculation, and the absence of any propagated theoretical uncertainties makes it difficult to assess the precision of the many numerical predictions.

major comments (3)

[Sec. VII, Eq. (41)] The cross-section calculation in Eq. (41) is an incoherent sum of constant-width Breit-Wigner resonances and therefore cannot generate threshold cusps or threshold-induced bumps. No energy-dependent widths, no threshold phase-space factors, and no self-energy line shapes from Sec. III enter Eq. (41). The two structures near 10.63 and 10.71 GeV shown in Fig. 4 are merely overlapping tails of constant-width Lorentzians, yet the text attributes them to 'threshold effects' of the Bbar B* and B* B* channels and uses this to claim that Upsilon(10753) may arise from the B* B* threshold. As written, the abstract and Sec. VII conclusions are not supported by the computation. The authors should instead evaluate the cross section using the model's own energy-dependent spectral functions or coupled-channel amplitudes, for example by including the complex self-energy of Eq. (13)-(16) in the resonance propagators; otherwise the threshold-effect interpretation should be removed or explicitly labeled as an inference rather than a result of the calculation.
[Sec. II.B, Eq. (8)] The neglect of continuum-continuum interactions is acknowledged, but it is load-bearing for the threshold interpretation. Near the B* B* threshold, where the claimed Upsilon(10753) effect resides, meson-meson final-state interactions can alter the cusp shape, shift the apparent peak, and change the extracted widths. Since the manuscript uses the absence of a genuine Upsilon(10753) state as a conclusion, it needs at least an estimate of the FSI uncertainty (e.g., by comparing with unitarized or K-matrix approaches such as Ref. [68]) or a clear statement that the threshold interpretation is model-dependent and could be modified by FSI. This issue is separate from the missing energy dependence in Eq. (41), but both must be addressed before the central claim can be accepted.
[Sec. III, Tables II-XI] No theoretical uncertainties are propagated, although the model has seven parameters (alpha_s, sigma, C0, rc, gamma, Lambda, alpha'_s) and several procedural choices (the once-subtracted zero point, the 100 MeV virtual-channel window, the integration interval Delta in Eq. (25)). Many predictions are quoted to the MeV or sub-keV level, and comparisons such as the 30 MeV discrepancy for Upsilon(10860) or the claimed agreement for Upsilon(11020) cannot be evaluated without an error estimate. At minimum, the authors should quantify the sensitivity of the central results to variations of Lambda and rc within their stated ranges (0.8 +/- 0.2 GeV and the fitted rc) and to the choice of M0; otherwise the precision implied by the tables is not justified.

minor comments (6)

[Sec. II.C, Table I] The fit yields chi2 = 61.5 for 14 states with Merr = 5 MeV, but the paper does not discuss the quality of this fit or the number of degrees of freedom; a sentence stating the corresponding rms deviation would help readers calibrate the model uncertainty.
[Sec. III.C, Table II] Entries such as '33D3 1-- 10702 -52/+16 10650/10718 30/60' are ambiguous; the caption should explicitly state that the two numbers correspond to the two physical solutions and which quantity (mass shift, width, or core probability) is being split.
[Sec. V, Eq. (32)] The off-diagonal terms are written as DeltaM_SD(M) and DeltaM_DS(M) but the text immediately below writes 'DeltaMSD(M) and DeltaMSD(M)'; please use consistent notation and state whether the matrix is symmetric.
[Sec. VI, Eqs. (37) and (39)] Equation (37) uses alpha'_s for the QCD radiative correction while Eqs. (39) and (40) use alpha_s; clarify whether these are the same quantity or intended to be different, and define both.
[Sec. VII] The phrase 'The interpolations of Upsilon(10753) as a hybrid or a tetraquark state are also possible' should read 'interpretations' or 'explanations'.
[Captions of Figs. 5-8] In the manuscript version provided, the figure captions and axis labels contain unreadable encoded text (e.g., '/s57/s46/s52'); the figures must be regenerated with properly rendered labels and captions before publication.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation found; the coupled-channel predictions are genuinely computed from fitted inputs, but the abstract's Y(10753) threshold-effect claim is not actually obtained from the reported Breit-Wigner cross-section formula.

full rationale

The paper's derivation chain is not circular. The potential parameters αs, σ, C0 and rc are fitted to low-lying bottomonium masses and splittings, and the 3P0 strength γ is fitted to the single Υ(10580) width; the high-lying masses, widths, S-D mixing angles, and dielectron widths are then obtained by solving the coupled-channel equation M = M_A + ΔM(M) with the once-subtracted self-energy, and they are not refit to their own targets. The use of Λ=0.78 GeV and of B/Bs wave functions from the authors' prior papers [55,69] is an input choice from separate fits to charmonium and heavy-light spectra; it does not make the high-state predictions equivalent to those inputs by construction. The paper honestly states the neglect of continuum-continuum interactions in Sec. II.B ('Hc here only includes the kinetic energy term'), which is a model limitation, not circularity. The one notable defect is that the abstract and Sec. VII attribute the 10.71 GeV bump to B*B* threshold effects, but the only reported cross-section calculation, Eq. (41), is an incoherent sum of constant-width Breit-Wigners with no energy-dependent widths, interference, or threshold singularities. That conclusion is therefore unsupported by the reported computation; this is an internal-consistency/correctness problem, not a case of the derivation reducing to its inputs. Accordingly, the circularity score is 2, reflecting only the minor, non-load-bearing reliance on the authors' own previous model papers.

Assumptions & free parameters 7 free parameters · 7 assumptions · 2 invented entities

The paper relies on a standard potential model plus coupled-channel machinery. The free parameters are the usual quark-model and 3P0 fitted constants; the axioms are modeling choices about the continuum Hamiltonian, the subtraction procedure, the cutoff, and the channel-selection window. The invented entities are predicted hadronic states rather than ad hoc forces or mediators, and they carry testable signatures.

free parameters (7)

alpha_s = 0.372
Strong coupling in the Cornell potential; fitted via chi2 to low-lying bottomonium masses (Sec. II.C).
sigma = 2.42 GeV
Width of the Gaussian spin-spin hyperfine potential; primarily constrained by the Y(1S)-eta_b(1S) splitting and fitted in the chi2 (Sec. II.C).
C0 = -35.0 MeV
Zero-point energy in the Cornell potential; fitted to the overall mass scale of low-lying states (Sec. II.C).
rc = 0.101 fm
Cutoff for the 1/r^3 singularity in spin-orbit and tensor potentials; fitted to the chi_b1(1P)-chi_b0(1P) fine splitting (Sec. II.C).
gamma = 0.482
3P0 quark pair-creation strength; fitted to the width Gamma[Y(10580) -> B Bbar] = 20.5 MeV (Sec. II.C).
Lambda = 0.78 GeV
Gaussian cutoff suppressing high-momentum coupled-channel contributions; adopted from the authors' previous charmonium and heavy-light studies, not fitted here (Sec. II.B).
alpha'_s = 0.18
Strong coupling in the QCD radiative correction to dielectron widths; adopted from Refs [30,39,45] (Sec. VI).

assumptions (7)

domain assumption The 3P0 model describes the bare-to-continuum transition operator with a universal pair-creation strength gamma.
Invoked in Eq. (9) to compute all transition amplitudes M_A->BC(p); the same gamma is used for all channels.
domain assumption Continuum-continuum interactions between the two final mesons are negligible; H_c contains only kinetic energy.
Stated in Sec. II.B; the authors note that such interactions involve many unknown parameters and cannot be constrained by current data.
domain assumption Contributions of channels with thresholds far above the bare state can be absorbed into a constant redefinition of the bare mass via a once-subtracted dispersion relation.
Used in Eq. (16) with subtraction point M0 = M[Y(1S)]; high-lying channels are numerous and assumed to vary slowly.
ad hoc to paper A Gaussian factor e^{-p^2/(2 Lambda^2)} suppresses unphysical high-momentum contributions.
Eq. (18); the cutoff is taken from previous studies and has no independent derivation in this paper.
ad hoc to paper Only OZI-allowed two-body channels with thresholds below the bare mass, plus virtual channels within 100 MeV above it, need to be included.
Sec. II.B; the 100 MeV window is motivated by potential-model uncertainties but is a hand-chosen limit.
domain assumption The spectral density function can be integrated over an interval Delta chosen by line shape to estimate the bbar component of resonances.
Eqs. (22)-(25); for distorted line shapes the integration interval is chosen by inspection, introducing subjectivity.
domain assumption The Van Royen-Weisskopf formula with QCD radiative corrections describes dielectron widths.
Eqs. (37)-(38); a standard formula, but its applicability to high excited states is assumed.

invented entities (2)

Y'1(3D) mixed vector state near 10676 MeV independent evidence
purpose: Explains the rapid rise in e+e- -> B*B* cross section near the B*B* threshold; it is the physical state formed by Y(4S)-Y1(3D) mixing with phi_D about -16 degrees, a dielectron width near 0.028 keV, and dominant B*B* decay.
The state is a standard 3D1 bottomonium predicted by the model, but its mixing angle, width, and dielectron width are model-dependent predictions; Belle II data provide a current hint.
Continuum-dominated two-pole partners, e.g., Y3(10650) from the bare 3D3 state independent evidence
purpose: New physical states generated by coupled-channel dynamics near the B*B* threshold; the lower pole is narrow and B*B*-dominant, the higher one is broad and bbar-dominant.
The states have predicted masses, widths of about 19 and 63 MeV, and decay channels that have not yet been observed, providing falsifiable handles.

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Cite this review

Pith. "Pith review of Bottomonia in an unquenched quark model." pith.science (2026). https://pith.science/paper/FZMP6TV6

@misc{pith2026250115110,
  author       = {Pith},
  title        = {Pith review of: Bottomonia in an unquenched quark model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FZMP6TV6}},
  note         = {Machine review of arXiv:2501.15110}
}

abstract

The bottomonium spectrum is systematically studied within an unquenched quark model. Based on a good description of both the masses and widths for the well-established states, we further give predictions for the higher $S$-, $P$-, and $D$-wave bottomonium states up to a mass region of $\sim 11.3$ GeV. For the vector states, the $S$-$D$ mixing and dielectron decays are studied. Additionally, to understand the role of the higher vector resonances in the $e^{+}e^{-}$ annihilation reaction, we evaluate the cross section by combining our quark model predictions for the mass, dielectron and strong decay properties. It is found that (i) The mass shifts of the high $b\bar{b}$ states due to the coupled-channel effects are the order of a few tens MeV, most of the high-lying resonances contain significant non-$b\bar{b}$ components. (ii) The $\Upsilon_1(3D,5D,6D)$ states significantly mix with $\Upsilon(4S,6S,7S)$, respectively, which is mainly induced by the intermediate hadronic loops. (iii) The non-$b\bar{b}$ components will lead a significant suppression for the dielectron decay widths of some vector resonances.(iv) The threshold effects of open-bottom meson pairs can cause rich bump structures in the cross section of $e^{+}e^{-}\to b\bar{b}$. Our model shows that the $\Upsilon(10753)$ may arise from threshold effects due to the strong coupling between $\Upsilon(4S)$ and $\bar{B}^*B^*$.

Figures

Figures reproduced from arXiv: 2501.15110 by the authors.

**Figure 2.** FIG. 2: Bottomonium spectrum compared with the observation [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** FIG. 3: The total and partial decay widths of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4: Estimation of the cross section of the [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]

**Figure 5.** Figure 5: FIG. 5: The line shapes of the mass shift function [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]

**Figure 6.** Figure 6: FIG. 6: The line shapes of the mass shift function [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]

**Figure 7.** Figure 7: FIG. 7: The line shapes of the mass shift function [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

**Figure 8.** Figure 8: FIG. 8: The line shapes of the mass shift function [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Υ(11020) Firstly, we give some discussions about a well-established resonance Υ(11020). It is often assigned to the Υ(6S ) state classiﬁed in the quark model. In the present work, it is found that the Υ(11020) resonance may have signiﬁcant hadron con- tinuum components, while the b¯b-core component is only ∼ 40 %. The decay width is predicted to be Γ≃ 16....
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This solution does not correspond to any resonance structure in the spectral function, as evidenced by the lowe r panel of Fig. 8. Then we focus on the Υ3(5D) and ηb2(5D) states. Both Υ3(5D) and ηb2(5D) couple strongly to the ¯B∗B∗ 2(5747) chan- nel, the strong coupled-channel...
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It is often assigned to the Υ(6S ) state classiﬁed in the quark model

Υ(11020) Firstly, we give some discussions about a well-established resonance Υ(11020). It is often assigned to the Υ(6S ) state classiﬁed in the quark model. In the present work, it is found that the Υ(11020) resonance may have signiﬁcant hadron con- tinuum components, while the b¯b-core component is only ∼ 40 %. The decay width is predicted to be Γ≃ 16....

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If taking the measured mass Mexp = 10885 MeV , the width is predicted to be Γ≃ 8 MeV, (28) which is notably narrower than the observed one Γexp ≃ 37 ±4 MeV [ 7]

Υ(10860) For the Υ(10860) resonance, as the Υ(5S ) assignment, the decay properties cannot be well explained in theory, althou gh the observed mass is consistent with the quark model predic- tions. If taking the measured mass Mexp = 10885 MeV , the width is predicted to be Γ≃ 8 MeV, (28) which is notably narrower than the observed one Γexp ≃ 37 ±4 MeV [ 7...

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If ta k- ingβe f f = 0.500 GeV , the ¯B∗B∗ and ¯BB∗ are the main decay channels of the Υ(5S ), which seems to favor the observation

It is seen that the partial widths of ¯B∗B∗, ¯BB∗, ¯B∗ s B∗ s, and ¯BsB∗ s are rater sensitive to the details of the wave function. If ta k- ingβe f f = 0.500 GeV , the ¯B∗B∗ and ¯BB∗ are the main decay channels of the Υ(5S ), which seems to favor the observation. However, in this case the decay rates of Υ(5S ) → ¯B∗ s B∗ s, ¯BsB∗ s are too small to be co...

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It should be mentioned that similar analysis was car- ried out recently by Ortega et al. [113]. In Fig. 4, one can see four prominent peak structures, which contributed by fo ur S -wave states Υ(4S ), Υ(5S ), Υ(6S ), and Υ(7S ), respectively. The Υ(4S ), Υ(5S ), and Υ(6S ) have been established in exper- iments, which should correspond to the Υ(10580), Υ(...

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3: The total and partial decay widths of Υ(5S ) as a function of its wave function size parameterβe f f

higher S -wave states For the other missing S -wave states, n1S 0 (n = 5, 6, 7) and 73S 1, our predicted decay properties have been given in Ta- /s48/s46/s52/s53 /s48/s46/s53/s48 /s48/s46/s53/s53 /s48/s46/s54/s48 /s48/s46/s54/s53 /s48 /s49/s53 /s51/s48 /s52/s53 /s54/s48 /s71 /s32/s40/s77/s101/s86/s41 /s98 /s101/s102/s102 /s32/s40/s71/s101/s86/s41 /s98 /s1...