---
title: 'Upsilon(10950): Ambiguous Bottomonium State'
url: https://www.emergentmind.com/topics/upsilon-10950
type: topic
---

# Upsilon(10950): Ambiguous Bottomonium State

Searching arXiv for recent and relevant papers on the high-lying bottomonium region around 10.9 GeV, including $\Upsilon(10860)$, $\Upsilon(10753)$, and proposed $\Upsilon(10950)$.
\(\Upsilon(10950)\) denotes a high-lying vector bottomonium-like structure in the \(10.8\)–\(11.0\ \text{GeV}\) region whose referent is not uniform across the literature. In current experimental practice, it is often just an alternative label or fit result for the structure most commonly identified with \(\Upsilon(10860)\), also called \(\Upsilon(5S)\); in a more recent \(S\)–\(D\) mixing analysis, however, \(\Upsilon(10950)\) is predicted as a distinct \(1^{--}\) state, namely the mixing partner of \(\Upsilon(10860)\) in a \(5S\)–\(4D\) bottomonium scheme [1811.08236] [1109.1452] [2508.18720]. The resulting ambiguity is central to the topic: the name may refer either to a shifted parameterization of the established \(\Upsilon(10860)\) region or to a specific unobserved resonance with its own spectroscopic interpretation.

## 1. Nomenclature and spectroscopic referent

The term is used in three closely related ways in the supplied literature.

| Usage of “\(\Upsilon(10950)\)” | Identification | Source basis |
|---|---|---|
| Alternative label or fit result | High-lying structure in the \(10.8\)–\(11.0\ \text{GeV}\) region, most commonly identified with \(\Upsilon(10860)\) / \(\Upsilon(5S)\) | Experimental practice summarized in the \(\Upsilon(10860)\) hybrid discussion |
| Belle convention | A single broad vector resonance, \(\Upsilon(10860)\), interpreted as \(\Upsilon(5S)\) | Belle \(\Upsilon(5S)\) analysis |
| Predicted distinct state | \(\Upsilon(10950)\equiv \Upsilon'(4D)\), the \(5S\)–\(4D\) mixing partner of \(\Upsilon(10860)\) | \(S\)–\(D\) mixing model |

Belle adopts the Particle Data Group parameters for the resonance called \(\Upsilon(10860)\), interpreted as \(\Upsilon(5S)\), with
\[
Mc^2 = 10876 \pm 11~\text{MeV}/c^2,\qquad \Gamma = 55 \pm 28~\text{MeV},
\]
and quantum numbers \(J^{PC}=1^{--}\) [1109.1452]. By contrast, the 2025 \(S\)–\(D\) mixing study explicitly introduces a not-yet-observed state denoted \(\Upsilon(10950)\), identified with the upper eigenstate of a \(5S\)–\(4D\) mixing matrix [2508.18720].

A common misconception is therefore that \(\Upsilon(10950)\) is already an established Particle Data Group resonance. The literature summarized here does not support that statement. The Belle paper does not introduce a separate \(\Upsilon(10950)\), whereas the later mixing analysis treats it as a prediction rather than an observation [1109.1452] [2508.18720].

## 2. Experimental setting in the \(10.8\)–\(11.0\ \text{GeV}\) region

The experimental context is dominated by the \(\Upsilon(10860)\) region explored at Belle. Belle accumulated
\[
\mathcal{L}_{\text{on}} = 121.4~\text{fb}^{-1},
\]
corresponding to \(37\) million “resonance events” and \(7.9\) million \(B_s\) events, and collected an additional \(8~\text{fb}^{-1}\) energy scan around the \(\Upsilon(5S)\) region [1109.1452]. In this environment, the state conventionally called \(\Upsilon(10860)\) lies above \(B_s^{(*)}\bar B_s^{(*)}\) threshold and is produced directly in \(e^+e^-\) annihilation with
\[
\sigma(e^+e^- \to \Upsilon(5S)) \approx 0.3~\text{nb}.
\]

Belle established several empirical features that frame later discussion of \(\Upsilon(10950)\). First, the cross section for
\[
e^+e^- \to \Upsilon(nS)\pi^+\pi^-, \qquad n=1,2,3,
\]
peaks about \(20~\text{MeV}\) higher in energy than the peak of the total hadronic cross section. This indicates that single-resonance descriptions may be too restrictive in the region, although Belle itself did not claim an additional vector state [1109.1452]. Second, Belle observed unexpectedly large transitions to spin-singlet bottomonia,
\[
\Upsilon(5S)\to h_b(nP)\pi^+\pi^-,
\]
with
\[
R_1 = 0.407 \pm 0.079^{+0.048}_{-0.076},\qquad
R_2 = 0.78 \pm 0.09^{+0.22}_{-0.10},
\]
where
\[
R_n \equiv \frac{\Gamma\left(\Upsilon(5S) \to h_b(nP)\,\pi^+\pi^-\right)}
{\Gamma\left(\Upsilon(5S) \to \Upsilon(2S)\,\pi^+\pi^-\right)}.
\]
Third, Belle observed the charged bottomonium-like states \(Z_b(10610)\) and \(Z_b(10650)\), with average parameters
\[
M_1 = 10608 \pm 2.0~\text{MeV}/c^2,\quad \Gamma_1 = 15.6 \pm 2.5~\text{MeV},
\]
\[
M_2 = 10653 \pm 1.5~\text{MeV}/c^2,\quad \Gamma_2 = 14.4 \pm 3.2~\text{MeV},
\]
and with resonant contributions dominating the relevant transition amplitudes [1109.1452].

These observations do not establish a separate \(\Upsilon(10950)\), but they do show that the \(10.8\)–\(11.0\ \text{GeV}\) region is spectroscopically nontrivial. Any interpretation of the name must account for threshold effects, line-shape shifts, enhanced dipion transitions, and the role of intermediate \(Z_b\) structures.

## 3. Interpretation as the \(\Upsilon(10860)\): \(\Upsilon(5S)\)–hybrid mixing

One influential account treats the resonance near \(10.86\ \text{GeV}\) as predominantly \(\Upsilon(5S)\) with a small admixture of the lowest \(P\)-wave hybrid bottomonium state. In that approach, conventional bottomonium is described with a Cornell-like potential
\[
V_C(r)=\sigma r - \frac{\zeta}{r},
\]
with
\[
\sigma = 873\ \text{MeV/fm},\qquad
\zeta = 100\ \text{MeV\,fm},\qquad
m_b = 4793\ \text{MeV},
\]
yielding
\[
M_{5S}^{\text{(calc)}} = 10865\ \text{MeV}.
\]
The experimental comparison quoted there is
\[
M_{\Upsilon(10860)}^{\text{(exp)}} = 10889.9^{+3.2}_{-2.6}\ \text{MeV}.
\]
The same study places the lowest \(P\)-wave hybrid at
\[
\mathcal{M}_{1p}^{\text{(hyb)}} = 10888\ \text{MeV},
\]
so that near degeneracy motivates the mixing ansatz
\[
\ket{\Upsilon(10860)} \approx \cos\theta\,\ket{\Upsilon(5S)} + \sin\theta\,\ket{H_b(1p)}.
\]
The mixing angle is estimated through first-order perturbation theory as
\[
\sin\theta \approx
\frac{\langle \Upsilon(5S)\vert \delta\mathcal{H} \vert H_b(1p)\rangle}
{M_{5S} - \mathcal{M}_{H_b(1p)}},
\]
with \(\delta\mathcal{H}\) taken to be proportional to an \(E1\) gluonic transition [1811.08236].

This framework is constructed to preserve the successful leptonic properties of a conventional \(\Upsilon(5S)\). Using wavefunctions from the Cornell potential, the calculated leptonic-width ratios are
\[
\mathcal{R}(1)=0.19,\qquad \mathcal{R}(2)=0.51,\qquad \mathcal{R}(3)=0.71,
\]
to be compared with
\[
0.23\pm0.05,\qquad 0.52\pm0.11,\qquad 0.70\pm0.16,
\]
respectively. Because this agreement is already very good for a pure \(5S\), the hybrid admixture is constrained to remain small; the hybrid direct leptonic width is estimated as
\[
\Gamma(H_b(1p)\to e^+e^-) \approx 0.03\,a^2\,\Gamma(\Upsilon(5S)\to e^+e^-),
\]
and the study argues that \(a^2\lesssim 1\) and \(\sin^2\theta \lesssim 0.1\) [1811.08236].

The principal motivation for the hybrid component is not the mass alone but the anomalous hadronic transition pattern. In the QCD multipole expansion,
\[
\Gamma(\Upsilon(n_i S)\to \pi^+\pi^- \Upsilon(n_f S))
= C\,G\, |F_{n_i n_f}^1|^2,
\]
the matrix element \(F_{n_i n_f}^1\) involves intermediate \(P\)-wave hybrid states, and the denominator
\[
M_{n_i S} - \mathcal{M}_{n_{\text{hyb}P}}
\]
becomes small for \(n_i=5\). This enhances \(\pi\pi\Upsilon(nS)\) transitions and, through heavy-quark-spin considerations, also supports large \(\pi^+\pi^- h_b(np)\) rates. The paper further argues that a pure \(5S\) assignment is untenable for the \(h_b\) channels because its estimate gives
\[
\frac{\Gamma(\Upsilon(5S)\to \pi^+\pi^- h_b(1P))}
{\Gamma(\Upsilon(3S)\to \pi^+\pi^- h_b(1P))}
\approx 1.1\times10^2,
\]
whereas experimentally
\[
\frac{\Gamma(\Upsilon(10860)\to \pi^+\pi^- h_b(1P))_{\text{exp}}}
{\Gamma(\Upsilon(3S)\to \pi^+\pi^- h_b(1P))_{\text{exp}}}
> 7.3\times 10^4.
\]

Within this interpretation, “\(\Upsilon(10950)\)” need not denote a new resonance. The summary supplied for the hybrid-mixing paper explicitly states that a fit calling the same resonance “\(\Upsilon(10950)\)” at \(M\sim 10950\ \text{MeV}\) is compatible with the same mixed \(\Upsilon(5S)\)–hybrid state, since the quoted quark-model uncertainty is of order \(\sim 25\ \text{MeV}\) and coupled-channel effects can shift masses by tens of MeV [1811.08236].

## 4. Interpretation as a distinct state: the \(5S\)–\(4D\) mixing partner of \(\Upsilon(10860)\)

A different interpretation predicts \(\Upsilon(10950)\) as a separate conventional bottomonium state arising from \(5S\)–\(4D\) mixing. In that scheme, the physical states are
\[
\begin{pmatrix} \Upsilon(10860)\\[4pt] \Upsilon'(4D) \end{pmatrix}
=
\begin{pmatrix} \cos\theta' & -\sin\theta'\\[4pt] \sin\theta' & \cos\theta' \end{pmatrix}
\begin{pmatrix} \Upsilon_{5S}\\[4pt] \Upsilon_{4D} \end{pmatrix},
\]
with
\[
|\Upsilon(10860)\rangle = \cos\theta'|5S\rangle - \sin\theta'|4D\rangle,
\]
\[
|\Upsilon(10950)\rangle \equiv |\Upsilon'(4D)\rangle = \sin\theta'|5S\rangle + \cos\theta'|4D\rangle.
\]
The bare masses used are
\[
m_{\Upsilon(5S)} = 10894~\text{MeV},\qquad
m_{\Upsilon(4D)} = 10942~\text{MeV},
\]
and combined dielectron-width and mass constraints give two solutions,
\[
\theta' = (21 \pm 2)^\circ,\qquad \theta' = (-21 \pm 2)^\circ.
\]
The upper eigenstate is then identified with
\[
m_{\Upsilon(10950)} \simeq 10950~\text{MeV},
\]
with composition
\[
P_{5S}^{(10950)} \approx 0.13,\qquad
P_{4D}^{(10950)} \approx 0.87,
\]
so that \(\Upsilon(10950)\) is dominantly a \(4D\) bottomonium state with a modest \(5S\) admixture [2508.18720].

Its dielectron width is predicted to be very small:
\[
\Gamma_{ee}(\Upsilon(10950)) = (57 \pm 8)\,\text{eV}\quad \text{for } \theta'=(21\pm2)^\circ,
\]
\[
\Gamma_{ee}(\Upsilon(10950)) = (26 \pm 6)\,\text{eV}\quad \text{for } \theta'=(-21\pm2)^\circ.
\]
The same work explicitly cites this small \(\Gamma_{ee}\) as the reason that \(\Upsilon(10950)\) has not yet been seen as a direct \(e^+e^-\) resonance [2508.18720].

The characteristic decay channel emphasized there is
\[
\Upsilon(10950)\to \omega\chi_{bJ}(1P),\qquad J=0,1,2,
\]
with amplitudes
\[
\mathcal A(\Upsilon(10950)\to\chi_{bJ}\omega)
= \mathcal A_{5S,J}\sin\theta' + \mathcal A_{4D,J}\cos\theta'.
\]
The \(\mathcal A_{5S,J}\) term is a short-distance tree-level contribution from
\[
\mathcal{L}_{\chi\omega}=\frac{c_S}{2}\langle\chi^{i\dagger}\Upsilon\rangle\omega^i+\frac{c_D}{2}\langle\chi^{i\dagger}\Upsilon^{ij}\rangle\omega^j + \text{h.c.},
\]
whereas \(\mathcal A_{4D,J}\) is generated by triangle loops involving open-bottom mesons. The predicted partial widths are:

| Solution | \(\Gamma(\chi_{b0}\omega)\) | \(\Gamma(\chi_{b1}\omega)\) | \(\Gamma(\chi_{b2}\omega)\) |
|---|---:|---:|---:|
| I | \(0.18 \pm 0.10~\text{MeV}\) | \(0.068 \pm 0.056~\text{MeV}\) | \(0.023 \pm 0.006~\text{MeV}\) |
| II | \(1.3 \pm 0.4~\text{MeV}\) | \(0.94 \pm 0.29~\text{MeV}\) | \(0.038 \pm 0.013~\text{MeV}\) |

These predictions arise after calibrating the framework to the measured \(\Upsilon(10860)\to\omega\chi_{bJ}\) branching fractions and to
\[
R'_{12} =
\frac{\Gamma(\Upsilon(10860)\to\omega\chi_{b1})}
{\Gamma(\Upsilon(10860)\to\omega\chi_{b2})}
= 2.62 \pm 1.30,
\]
which the authors state is incompatible with the pure \(5S\) prediction \(R'_{12}\approx 0.64\) [2508.18720].

In this picture, \(\Upsilon(10950)\) is neither a relabeling of \(\Upsilon(10860)\) nor an exotic state. It is a conventional but mixed bottomonium eigenstate whose visibility is suppressed in inclusive \(e^+e^-\) scans and enhanced in exclusive channels such as \(\omega\chi_{bJ}\).

## 5. Canonical and unquenched constraints on the \(10.95\ \text{GeV}\) interpretation

Not all conventional models leave room for a distinct \(\Upsilon(10950)\). In a “canonical interpretation” of the high \(\Upsilon\) family, \(Y(10750)\) and \(\Upsilon(10860)\) are themselves taken to be the two mixed \(5S\)–\(4D\) eigenstates,
\[
|Y(10750)\rangle = \cos\theta\,|\Upsilon_1(4D)\rangle + \sin\theta\,|\Upsilon(5S)\rangle,
\]
\[
|\Upsilon(10860)\rangle = -\sin\theta\,|\Upsilon_1(4D)\rangle + \cos\theta\,|\Upsilon(5S)\rangle,
\]
with \(\theta \simeq 20^\circ\)–\(30^\circ\), and \(\Upsilon(11020)\) assigned consistently as \(\Upsilon(6S)\). In that scheme, the relevant screened-potential masses are
\[
\Upsilon(5S): 10811~\text{MeV},\quad
\Upsilon_1(4D): 10858~\text{MeV},\quad
\Upsilon(6S): 10997~\text{MeV},\quad
\Upsilon_1(5D): 11036~\text{MeV},
\]
and the conclusion drawn is that there is no natural quark-model slot at \(\sim 10.95\ \text{GeV}\) for an additional conventional \(1^{--}\) state [1905.10344].

From this perspective, a separate \(\Upsilon(10950)\) would not be a straightforward \(5S\), \(6S\), \(4D\), or \(5D\) assignment. The supplied summary of that paper states that such a state would therefore either be exotic or indicate that the assumed \(S\)–\(D\) mixing and coupled-channel dynamics require revision [1905.10344].

An unquenched quark-model treatment reaches a different but equally constraining conclusion. There the bare \(\Upsilon(5S)\) mass is
\[
M_{\text{bare}(\Upsilon(5S))} = 10927.6\ \text{MeV},
\]
and coupled-channel contributions from \(B^{(*)}\bar B^{(*)}\) and \(B_s^{(*)}\bar B_s^{(*)}\) channels sum to
\[
\Delta M_{\text{cc}(\Upsilon(5S))} = -31.4\ \text{MeV},
\]
so that
\[
M_{\text{phys}} = 10896.2\ \text{MeV}.
\]
The same summary compares this with the Particle Data Group average mass \(10885.2\ \text{MeV}\) for \(\Upsilon(10860)\) and concludes that \(\Upsilon(10860)\) is naturally identified as the unquenched \(\Upsilon(5S)\), whereas \(\Upsilon(10753)\) is not the same state [2507.13882].

This unquenched result is relevant for \(\Upsilon(10950)\) because it fixes the typical size of threshold-induced mass shifts in the region. The supplied summary states that a resonance at \(10.95\ \text{GeV}\) would most naturally correspond to a higher conventional bottomonium state, probably a \(D\)-wave or mixed \(D/S\) configuration, rather than another \(5S\)-like state or a purely dynamical meson–meson resonance [2507.13882]. That statement is interpretive, but it follows directly from the mass-shift scale calculated for the \(\Upsilon(5S)\).

## 6. Phenomenological status and discriminating measurements

The present status of \(\Upsilon(10950)\) is therefore model-dependent. In the Belle-centered experimental literature, the dominant object is still \(\Upsilon(10860)\), and the evidence consists of a broad \(1^{--}\) resonance region, a \(\sim 20\ \text{MeV}\) displacement between hadronic and \(\Upsilon(nS)\pi^+\pi^-\) peaks, large \(h_b(nP)\pi^+\pi^-\) production, and strong \(Z_b\) substructure, but not a separate established \(\Upsilon(10950)\) peak [1109.1452]. In the hybrid-mixing picture, the label may simply reflect an alternative fit to the same underlying \(\Upsilon(5S)\)-dominated state [1811.08236]. In the \(5S\)–\(4D\) picture, by contrast, it denotes a specific predicted partner state with sharply constrained mass, composition, and decay pattern [2508.18720].

Two misconceptions are especially persistent. The first is that the \(10.95\ \text{GeV}\) label necessarily implies a new resonance; the supplied literature shows that it may also denote the same high-lying structure usually called \(\Upsilon(10860)\) [1811.08236]. The second is that the anomalous transitions in the region require an explicitly exotic explanation. The hybrid-mixing analysis argues instead that a predominantly conventional \(\Upsilon(5S)\) with a small but phenomenologically important hybrid admixture already accounts for the mass, leptonic widths, and much of the dipion-transition pattern, while the \(S\)–\(D\) mixing analysis treats \(\Upsilon(10950)\) itself as a conventional mixed bottomonium state [1811.08236] [2508.18720].

The most direct discriminants are also specified in the supplied literature. The \(S\)–\(D\) mixing study identifies energy scans near \(10.95\ \text{GeV}\) in exclusive channels such as
\[
e^+e^- \to \omega\chi_{bJ},
\]
with subsequent \(\chi_{bJ}\to\gamma\Upsilon(1S,2S)\), as the clearest route to testing the predicted state, precisely because its \(\Gamma_{ee}\) is only \(26\)–\(57\ \text{eV}\) whereas its \(\omega\chi_{b0,1}\) partial widths are predicted to be \(0.1\)–\(1\ \text{MeV}\) in magnitude [2508.18720]. Belle’s earlier observation that dipion-transition and hadronic line shapes peak at different energies indicates that detailed line-shape analyses remain indispensable in any attempt to separate a true new \(1^{--}\) state from threshold or interference effects [1109.1452].

In that sense, \(\Upsilon(10950)\) occupies an unusual place in bottomonium spectroscopy: it is simultaneously a naming convention for the \(\Upsilon(10860)\) region in some contexts, a concrete prediction of one conventional mixing model, and a state for which other conventional frameworks provide no natural slot.

Source: https://www.emergentmind.com/topics/upsilon-10950