Upsilon(10753): Vector Bottomonium Candidate

• Upsilon(10753) is a vector bottomonium-like resonance observed in e+e- collisions near 10.75 GeV, with measured mass around 10756 MeV and a width near 30 MeV.
• It exhibits distinctive decay patterns into χbJω and π+π-Υ(nS), indicating complex coupled-channel dynamics and possible S–D mixing effects.
• Theoretical interpretations range from conventional 4S–3D mixed bottomonium to dynamical meson-meson resonance, hybrid, or tetraquark, fueling active debate in heavy-quark spectroscopy.

$\Upsilon(10753)$ is a vector bottomonium-like resonance observed in $e^+e^-$ annihilation near $10.75$ GeV in both $\pi^+\pi^-\Upsilon(nS)$ and $\omega\chi_{bJ}(1P)$ final states. It carries $J^{PC}=1^{--}$, and recent channel-dependent determinations place it at $(10756.3\pm2.7\pm0.6)$ MeV/$c^2$ with width $(29.7\pm8.5\pm1.1)$ MeV in $\pi^+\pi^-\Upsilon(nS)$, and at $e^+e^-$0 MeV/$e^+e^-$1 with width $e^+e^-$2 MeV in $e^+e^-$3 analyses (Collaboration et al., 2024, Belle et al., 29 Oct 2025). Its spectroscopic assignment remains unsettled. Proposed descriptions include a $e^+e^-$4–$e^+e^-$5 mixed conventional bottomonium, a pure $e^+e^-$6 level, a dressed hadronic resonance with large $e^+e^-$7 content, a hybrid bottomonium, and a compact tetraquark (Luo et al., 26 Aug 2025, Ortega et al., 2024, Castellà et al., 2021, Tan et al., 2022).

1. Experimental identification and resonance parameters

Belle first established the state as a resonant structure in $e^+e^-$8 with $e^+e^-$9, and Belle II later connected the same energy region to $10.75$0 with $10.75$1 (Liu et al., 2023, Collaboration et al., 2022). Production in $10.75$2 annihilation fixes the vector quantum numbers, and the Particle Data Group lists it as a $10.75$3 candidate.

Measurement channel	Mass and width	Source
Belle in $10.75$4	$10.75$5 MeV, $10.75$6 MeV	(Liu et al., 2023)
Belle + Belle II in $10.75$7	$10.75$8 MeV/$10.75$9, $\pi^+\pi^-\Upsilon(nS)$0 MeV	(Collaboration et al., 2024)
Belle + Belle II in $\pi^+\pi^-\Upsilon(nS)$1	$\pi^+\pi^-\Upsilon(nS)$2 MeV/$\pi^+\pi^-\Upsilon(nS)$3, $\pi^+\pi^-\Upsilon(nS)$4 MeV	(Belle et al., 29 Oct 2025)

The experimental picture is therefore internally consistent at the level of mass and total width. A notable feature is that $\pi^+\pi^-\Upsilon(nS)$5 sits between the established $\pi^+\pi^-\Upsilon(nS)$6 and $\pi^+\pi^-\Upsilon(nS)$7 regions, precisely where open-bottom thresholds and strong coupled-channel effects become unavoidable in spectroscopy.

2. Observed decay pattern and line-shape phenomenology

The state is experimentally distinguished not only by its mass but by an unusual channel pattern. Belle II observed $\pi^+\pi^-\Upsilon(nS)$8 at $\pi^+\pi^-\Upsilon(nS)$9 GeV with

$\omega\chi_{bJ}(1P)$0

and found the energy dependence consistent with a resonance centered near $\omega\chi_{bJ}(1P)$1 rather than $\omega\chi_{bJ}(1P)$2 (Collaboration et al., 2022). The later Belle–Belle II combined analysis sharpened this picture: at $\omega\chi_{bJ}(1P)$3 GeV it measured

$\omega\chi_{bJ}(1P)$4

$\omega\chi_{bJ}(1P)$5

with

$\omega\chi_{bJ}(1P)$6

(Belle et al., 29 Oct 2025).

The same combined fit extracted

$\omega\chi_{bJ}(1P)$7

$\omega\chi_{bJ}(1P)$8

and their ratio

$\omega\chi_{bJ}(1P)$9

(Belle et al., 29 Oct 2025). In the same study, $J^{PC}=1^{--}$0 was found to decay into $J^{PC}=1^{--}$1 but not into $J^{PC}=1^{--}$2, with upper limits

$J^{PC}=1^{--}$3

$J^{PC}=1^{--}$4

(Belle et al., 29 Oct 2025).

In $J^{PC}=1^{--}$5, Belle II reported the first observation of $J^{PC}=1^{--}$6 and $J^{PC}=1^{--}$7, but no evidence for $J^{PC}=1^{--}$8 (Collaboration et al., 2024). At $J^{PC}=1^{--}$9 GeV the measured Born cross sections were

$(10756.3\pm2.7\pm0.6)$0

for $(10756.3\pm2.7\pm0.6)$1,

$(10756.3\pm2.7\pm0.6)$2

for $(10756.3\pm2.7\pm0.6)$3, and

$(10756.3\pm2.7\pm0.6)$4

for $(10756.3\pm2.7\pm0.6)$5 (Collaboration et al., 2024). The resonance-peak ratios were reported as

$(10756.3\pm2.7\pm0.6)$6

showing a pronounced suppression of the $(10756.3\pm2.7\pm0.6)$7 channel (Collaboration et al., 2024).

Two further phenomenological features are already clear. First, no evidence was found for $(10756.3\pm2.7\pm0.6)$8 or $(10756.3\pm2.7\pm0.6)$9 intermediate states in $c^2$0 transitions (Collaboration et al., 2024). Second, the contrast with $c^2$1 is sharp: Belle and Belle II data indicate that the internal structures of $c^2$2 and $c^2$3 may differ, and the ratio

$c^2$4

whereas for $c^2$5

$c^2$6

(Belle et al., 29 Oct 2025).

3. Conventional bottomonium descriptions

A large fraction of the literature treats $c^2$7 as a conventional $c^2$8 state modified by strong threshold dynamics rather than as a manifest exotic. The most developed version is a $c^2$9–$(29.7\pm8.5\pm1.1)$0 mixing scheme in which the physical pair $(29.7\pm8.5\pm1.1)$1 and $(29.7\pm8.5\pm1.1)$2 arises from the basis $(29.7\pm8.5\pm1.1)$3 and $(29.7\pm8.5\pm1.1)$4: $(29.7\pm8.5\pm1.1)$5 so that

$(29.7\pm8.5\pm1.1)$6

(Luo et al., 26 Aug 2025). In one analysis the dielectron width of $(29.7\pm8.5\pm1.1)$7 yields two allowed angles,

$(29.7\pm8.5\pm1.1)$8

and predicts

$(29.7\pm8.5\pm1.1)$9

or

$\pi^+\pi^-\Upsilon(nS)$0

(Luo et al., 26 Aug 2025). A related study extracted

$\pi^+\pi^-\Upsilon(nS)$1

from $\pi^+\pi^-\Upsilon(nS)$2 and a mass-mixing interval

$\pi^+\pi^-\Upsilon(nS)$3

from a quadratic mass relation (Liu et al., 2023). Another hadronic-loop analysis using $\pi^+\pi^-\Upsilon(nS)$4 quoted

$\pi^+\pi^-\Upsilon(nS)$5

which indicates substantial model dependence in the electronic width (Bai et al., 2022).

The chief spectroscopic motivation for mixing is that pure $\pi^+\pi^-\Upsilon(nS)$6 quark-model masses tend to lie below the observed resonance. One S–D mixing analysis quotes $\pi^+\pi^-\Upsilon(nS)$7 MeV and $\pi^+\pi^-\Upsilon(nS)$8 MeV, with level repulsion shifting the physical states to $\pi^+\pi^-\Upsilon(nS)$9 and $e^+e^-$00 (Luo et al., 26 Aug 2025). A different mass-mixing study requires the pure $e^+e^-$01 mass in

$e^+e^-$02

and the pure $e^+e^-$03 mass around

$e^+e^-$04

(Liu et al., 2023).

Decay phenomenology is a more stringent test than mass alone. In the $e^+e^-$05 system, heavy-quark-spin-symmetry tree-level spin counting gives for a pure $e^+e^-$06-wave vector

$e^+e^-$07

while for a pure $e^+e^-$08-wave

$e^+e^-$09

After including open-bottom triangle loops for the $e^+e^-$10-wave component, one analysis finds at the $e^+e^-$11 mass

$e^+e^-$12

which is incompatible with the experimentally observed near equality of the $e^+e^-$13 and $e^+e^-$14 rates (Luo et al., 26 Aug 2025). The same work therefore concludes that $e^+e^-$15 cannot be a pure $e^+e^-$16-wave bottomonium and must involve S–D interference.

Within the S–D mixing picture, the $e^+e^-$17 branching fractions inferred from Belle II data fall in the $e^+e^-$18–$e^+e^-$19 range. For example, with $e^+e^-$20 and the constructive solution,

$e^+e^-$21

$e^+e^-$22

while the destructive solution gives

$e^+e^-$23

and

$e^+e^-$24

respectively (Luo et al., 26 Aug 2025).

Other hidden-bottom transitions have been modeled in the same framework. For $e^+e^-$25, intermediate $e^+e^-$26 loops yield branching fractions that may reach the order of $e^+e^-$27–$e^+e^-$28 over $e^+e^-$29, with a preferred range $e^+e^-$30 giving partial widths

$e^+e^-$31

$e^+e^-$32

$e^+e^-$33

(Liu et al., 2023). For $e^+e^-$34, a separate loop calculation predicts that

$e^+e^-$35

and

$e^+e^-$36

can reach the order of magnitude of $e^+e^-$37–$e^+e^-$38, whereas

$e^+e^-$39

is around $e^+e^-$40–$e^+e^-$41 (Li et al., 2022). Hadronic-loop calculations for $e^+e^-$42 likewise obtain branching ratios of order $e^+e^-$43–$e^+e^-$44 and reproduce Belle $e^+e^-$45 values within the $e^+e^-$46–$e^+e^-$47 scenario (Bai et al., 2022).

A competing conventional assignment appears in a relativistic screened potential model, which identifies $e^+e^-$48 as a pure $e^+e^-$49 state with

$e^+e^-$50

and

$e^+e^-$51

together with a three-gluon width

$e^+e^-$52

(Bokade et al., 6 Jan 2025). That model treats $e^+e^-$53 as unmixed $e^+e^-$54, in contrast to the S–D mixing literature. The tension between these two conventional pictures is one of the central unresolved issues in the subject.

4. Coupled-channel and dynamical-resonance interpretations

A distinct line of work attributes $e^+e^-$55 primarily to threshold dynamics. In a lattice-QCD-based diabatic Born–Oppenheimer treatment using string-breaking potentials and an emergent-wave method, the state appears as a pole generated by mixing between a confined $e^+e^-$56 channel and open bottom channels (Bicudo et al., 2020). In the two-channel $e^+e^-$57 problem, the relevant pole lies near

$e^+e^-$58

with composition

$e^+e^-$59

After adding the $e^+e^-$60 channel, the pole becomes

$e^+e^-$61

with

$e^+e^-$62

(Bicudo et al., 2020). In that framework, $e^+e^-$63 is therefore a dynamical meson-meson resonance with dominant open-bottom content rather than a compact quarkonium.

A constituent-quark-model meson-meson coupled-channel calculation reaches a related but numerically different conclusion (Ortega et al., 2024). Including bare $e^+e^-$64, $e^+e^-$65, $e^+e^-$66, $e^+e^-$67 together with $e^+e^-$68, $e^+e^-$69, $e^+e^-$70, $e^+e^-$71, $e^+e^-$72, and $e^+e^-$73, it finds a pole at

$e^+e^-$74

whose wavefunction contains

$e^+e^-$75

with total quarkonium and meson-meson fractions close to equality (Ortega et al., 2024). The paper summarizes this as an equally mixture of a conventional $e^+e^-$76 state and $e^+e^-$77 molecule. It also stresses that poles obtained in the complex energy plane do not have to appear as simple peaks in the relevant cross sections, and that the $e^+e^-$78 candidate emerges as a dressed hadronic resonance.

An unquenched-quark-model study aimed at the $e^+e^-$79 question reaches a more conservative conclusion (Chen et al., 18 Jul 2025). Starting from a bare

$e^+e^-$80

and coupling to $e^+e^-$81 and $e^+e^-$82 channels, it obtains a total mass shift

$e^+e^-$83

and

$e^+e^-$84

very close to $e^+e^-$85 but far above $e^+e^-$86 (Chen et al., 18 Jul 2025). In that framework, coupled-channel effects are important but not large enough to identify $e^+e^-$87 with $e^+e^-$88, and $e^+e^-$89 and $e^+e^-$90 may be two different states.

These coupled-channel approaches share a common lesson: once explicit $e^+e^-$91 and $e^+e^-$92 thresholds are included, the vector bottomonium spectrum above open-bottom threshold is richer than the naïve quenched $e^+e^-$93 ladder. Whether $e^+e^-$94 should be regarded as predominantly dynamical or as a heavily dressed conventional state remains model-dependent.

5. Hybrid and tetraquark proposals

The hybrid interpretation identifies $e^+e^-$95 with the lowest $e^+e^-$96 bottomonium hybrid supported by the $e^+e^-$97 static-energy multiplet in Born–Oppenheimer EFT (Castellà, 2022). In that formulation the state is written as a spin-singlet hybrid,

$e^+e^-$98

and is paired with $e^+e^-$99 as the first excited $10.75$00 hybrid (Castellà, 2022, Castellà et al., 2021). The transition formalism employs weakly coupled pNRQCD with singlet–octet chromoelectric and chromomagnetic operators,

$10.75$01

and

$10.75$02

which enforce characteristic spin-selection rules (Castellà, 2022).

Under this hypothesis, $10.75$03 has specific exclusive and semi-inclusive decay patterns. The predicted widths include

$10.75$04

$10.75$05

$10.75$06

$10.75$07

as well as a semi-inclusive width

$10.75$08

(Castellà, 2022). The hybrid papers treat these channels as discriminants of explicit gluonic excitation rather than of ordinary quarkonium.

The tetraquark interpretation has also been developed quantitatively in a chiral quark model with scalar nonet exchange (Tan et al., 2022). In that study conventional $10.75$09 is calculated near $10.75$10 GeV and found unsuitable for the $10.75$11 GeV resonance, while a full-channel-coupling calculation over molecular $10.75$12, molecular $10.75$13, and diquark–antidiquark configurations produces a stable resonance

$10.75$14

with width

$10.75$15

(Tan et al., 2022). Its internal composition is dominated by about $10.75$16 diquark–antidiquark and about $10.75$17 hidden-color octet–octet components, with compact rms distances, and it is proposed as a candidate for the experimental $10.75$18 (Tan et al., 2022).

These proposals differ sharply in ontology. The hybrid picture emphasizes a $10.75$19 pair bound to excited glue on $10.75$20 and $10.75$21 adiabatic surfaces, whereas the tetraquark calculation emphasizes a compact $10.75$22 resonance with large diquark–antidiquark content. Both are motivated by the difficulty of accommodating all observed properties in a single simple $10.75$23 assignment.

6. Present status, tensions, and decisive observables

Several misconceptions can already be excluded. The first is that $10.75$24 is straightforwardly the same state as $10.75$25. Belle II’s exclusive-channel program shows the opposite: $10.75$26 decays into $10.75$27 but not into $10.75$28, whereas $10.75$29 decays into $10.75$30 but not into $10.75$31 (Belle et al., 29 Oct 2025). The second is that a pure $10.75$32 interpretation automatically explains the $10.75$33 data. It does not: Belle II measured

$10.75$34

at $10.75$35 GeV (Collaboration et al., 2022), and the later $10.75$36 ratio

$10.75$37

is very far from the pure $10.75$38-wave expectation of $10.75$39 and only consistent with the quoted S–D-mixed expectation $10.75$40 at the $10.75$41 level (Belle et al., 29 Oct 2025).

The most important unresolved quantity is the electronic width. A pure $10.75$42 model gives

$10.75$43

(Bokade et al., 6 Jan 2025); one S–D mixing analysis gives

$10.75$44

(Luo et al., 26 Aug 2025); another mixed-state loop treatment quotes

$10.75$45

(Bai et al., 2022). This wide spread indicates that $10.75$46 is currently one of the clearest theory discriminants. A precise direct determination would immediately constrain the allowed wave-function composition.

Open-bottom and radiative channels are equally decisive. In the coupled-channel picture of (Ortega et al., 2024), the $10.75$47 candidate should decay predominantly to $10.75$48, with $10.75$49. In the pure-$10.75$50 screened-potential picture, the characteristic signatures are a very small $10.75$51, a three-gluon width near $10.75$52 keV, and sizable E1 transitions to $10.75$53 with widths of order $10.75$54–$10.75$55 keV (Bokade et al., 6 Jan 2025). In the $10.75$56–$10.75$57 mixing literature, promising tests include $10.75$58, $10.75$59, $10.75$60, $10.75$61, and $10.75$62, the last with a predicted branching fraction of $10.75$63 in one loop model (Liu et al., 2023, Li et al., 2022, Liu et al., 2024).

The present evidence therefore supports a narrower conclusion than a definitive assignment. $10.75$64 is a well-established vector resonance with a distinctive $10.75$65 signature, suppressed non-$10.75$66 three-pion modes, observed $10.75$67 decays, and no evidence so far for $10.75$68-dominated dipion substructure (Collaboration et al., 2024, Belle et al., 29 Oct 2025). These facts disfavor a simple pure-$10.75$69-wave description and indicate that threshold dynamics are essential. Whether the dominant language should be mixed bottomonium, dressed hadronic resonance, hybrid, or tetraquark remains an active problem in heavy-quark spectroscopy.