X(2370): BESIII constrains a decay forbidden for a flavour singlet

The BESIII collaboration searched for a very specific decay path of the X(2370), a hadronic candidate observed in radiative J/ψ decays. In its preprint, it finds no significant signal for $X(2370)\to K^*(892)^0\bar K^0+\text{c.c.}$X(2370)→K∗(892)0Kˉ0+c.c.—the channel and its charge conjugate: the fit gives $0.1\,\sigma$0.1σ. This quantitative absence is compatible with a selection rule expected for a pseudoscalar flavour-singlet state. The authors present the analysis as the first determination of this property for the X(2370). It strengthens a body of evidence in favour of a glueball, without establishing on its own that the X(2370) consists solely of gluons.

Source: arxiv.org

In plain language

Quantum chromodynamics allows gluons—the mediators of the strong interaction—to interact with one another. They could therefore form bound states called glueballs. Identifying them is difficult because such a state can mix with mesons made of quarks and share the same mass and quantum numbers.

BESIII uses an indirect test here. A flavour-singlet $0^{-+}$0−+ state should not follow the $K^*(892)^0\bar K^0$K∗(892)0Kˉ0 path if generalised G-parity is conserved. Among more than ten billion J/ψ, the sought signal remains compatible with zero. This is a clear constraint on that channel, not a picture of the X(2370)'s internal composition.

The caveat is decisive: the text is a preprint, and the step “flavour singlet → glueball dominated” combines this new limit with several earlier observations and theoretical expectations. This analysis alone does not exclude other hadronic structures or mixtures.

The measurement

Technical explanation

1. The test concerns an intermediate path, not the entire final state. The $J/\psi\to\gamma K_S^0K_S^0\pi^0$J/ψ→γKS0​KS0​π0 channel contains an X(2370) signal in the earlier analyses cited by the collaboration. The new question is narrower: what fraction of these events passes through a recognisable $K^*(892)^0$K∗(892)0 in a $K_S^0\pi^0$KS0​π0 pair? Each candidate must contain at least one combination lying within $50 \text{MeV}/c^2$50MeV/c2 of the $K^*(892)^0$K∗(892)0 mass. An absence in this substructure therefore does not mean that the X(2370) or the $K_S^0K_S^0\pi^0$KS0​KS0​π0 final state is absent.

2. The fit turns a visual absence into a statistical limit. The $K_S^0K_S^0\pi^0$KS0​KS0​π0 mass spectrum is fitted without binning. For the signal, the X(2370)'s mass and width are fixed at $2359 \text{MeV}/c^2$2359MeV/c2 and $170 \text{MeV}$170MeV; the shape is then efficiency corrected, weighted by phase space and convolved with the resolution obtained from simulation. The central result,
   $(0.1\pm1.2_{\rm stat}\pm1.1_{\rm syst})\times10^{-6},$(0.1±1.2stat​±1.1syst​)×10−6,
   is much smaller than its uncertainties. The significance of $0.1\,\sigma$0.1σ is neither an observation nor evidence that the physical rate is exactly zero; it motivates an upper limit of $2.7\times10^{-6}$2.7×10−6 at 90% confidence.

3. Normalisation isolates the relative suppression. The authors also form a ratio $R$R with the inclusive X(2370) mode to the same final state. They obtain
   $R=0.003\pm0.040_{\rm stat}\pm0.026_{\rm syst}, \qquad R<0.081$R=0.003±0.040stat​±0.026syst​,R<0.081
   The bound is quoted at 90% confidence.
   The common production factor $\mathcal B[J/\psi\to\gamma X(2370)]$B[J/ψ→γX(2370)] does not appear in $R$R. The numerator and denominator nevertheless come from two fits whose efficiency curves and phase-space weightings are tailored separately. Under the conditions of these fits, $R<0.081$R<0.081 means that less than 8.1% of the inclusive mode can pass through this intermediate path at the chosen confidence level.

4. The selection rule probes flavour. According to the theoretical argument used in the preprint, conservation of generalised G-parity forbids a flavour-singlet $0^{-+}$0−+ meson from decaying into $K^*(892)^0\bar K^0$K∗(892)0Kˉ0. The observed suppression is therefore a test of the “flavour singlet” property. It measures no gluonic fraction and is not sufficient, in isolation, to establish the composition of the X(2370); the authors' glueball interpretation combines this limit with several other properties.

5. The systematics test the robustness of the limit. BESIII varies, in particular, the X(2370) parameterisation, the phase-space model, the background description and the possible addition of resonances. For the absolute product branching fraction, reconstruction efficiency also enters the budget. These variations are incorporated into the reported limit; they do not eliminate dependence on the assumed signal shape, since the mass and width remain fixed in the nominal fit.

Why it worked

The strategy replaces a general comparison among numerous decay rates—which is vulnerable to modelling uncertainties and hadronic mixing—with a targeted question based on a selection rule. The statistical power comes from the sample of $(10\,087\pm44)\times10^6$(10087±44)×106 J/ψ and a fully reconstructible final state. The result can be read at two scales: the absolute product is below $2.7\times10^{-6}$2.7×10−6, and the normalised fraction is below $0.081$, in both cases at 90% confidence.

This precision does not turn a non-observation into ontological proof. The measurement directly supports suppression of a channel and, through the authors' symmetry argument, the flavour-singlet classification. The next step—regarding the X(2370) as dominated by the lightest pseudoscalar glueball—rests on the combination of its mass, its $0^{-+}$0−+ quantum numbers, its radiative production, its other modes and comparisons with lattice QCD. The preprint provides no single global significance for this identification.

The authors also illustrate the dependence on an external assumption: if $\mathcal B(J/\psi\to\gamma X(2370))>10^{-3}$B(J/ψ→γX(2370))>10−3, their limit implies $\mathcal B(X(2370)\to K^*\bar K)<1.6\,\%$B(X(2370)→K∗Kˉ)<1.6% and a partial width below $2 \text{MeV}$2MeV. This limit is at least 7.5 times lower than the bottom of the $15$–$200 \text{MeV}$200MeV range cited by the preprint for an $\eta$η–$\eta^\prime$η′ excitation. These numbers remain conditional on the production floor and the models being compared; they are not independent measurements of composition.

Causal chain

Gluon self-interaction in QCD → prediction of gluonic bound states → search for the pseudoscalar in radiative J/ψ decays → earlier observations of the X(2370) and assignment of $J^{PC}=0^{-+}$JPC=0−+ → selection of the $K^*(892)^0\bar K^0$K∗(892)0Kˉ0 submode → signal compatible with zero and $R<0.081$R<0.081 at 90% confidence → more stringent test of the flavour-singlet hypothesis → need for independent analyses to distinguish a pure glueball, mixing and other hadronic structures.

An anecdote

BESIII observed the X(2370) in 2011 in $J/\psi\to\gamma\pi^+\pi^-\eta^\prime$J/ψ→γπ+π−η′, with 225 million J/ψ and a significance above $6.4\,\sigma$6.4σ. The present search uses $(10\,087\pm44)\times10^6$(10087±44)×106 events to ask a different question: no longer whether the inclusive peak can be found, but whether it passes through the $K^*(892)\bar K$K∗(892)Kˉ substructure.

Legacy and current evidence

This analysis adds a flavour constraint to the evidence already assembled around the X(2370), but it does not close the search for glueballs. Robust confirmation would require other forbidden or allowed channels to follow the same pattern, branching fractions to be measured with alternative models, and the composition to be quantitatively confronted with lattice-QCD calculations and mixing scenarios. As of the preprint, the collaboration presents a cumulative interpretation, not the direct observation of a gluonic constituent.

The researcher's view — open questions

(Interpretation, not results from the authors.)

• Does the limit remain stable if the X(2370)'s mass and width are profiled rather than fixed, or if several amplitudes interfere?
• Do other channels governed by the same selection rule show suppression consistent with a single flavour composition?
• Can a global fit of observed and unobserved modes quantify a glueball–quarkonium mixing angle, with uncertainty intervals?
• Can an independent experiment reproduce the $R<0.081$R<0.081 constraint with a different production mechanism and different systematics?

Sources

Primary reference verified during the August 2026 fact-checking audit.

1. BESIII Collaboration — Lightest 0⁻⁺ Glueball as Dominant Constituent of X(2370) — arXiv:2607.20366v1 preprint, submitted July 22, 2026.

Background references

1. C. J. Morningstar and M. J. Peardon — The Glueball Spectrum from an Anisotropic Lattice Study — lattice-QCD prediction of the glueball spectrum.
2. H. J. Lipkin — Glueballs versus quarkonium—flavor symmetry signatures — flavour-symmetry signatures used by BESIII.
3. BESIII Collaboration — Confirmation of the X(1835) and observation of the resonances X(2120) and X(2370) — first observation of the X(2370), reviewed in the preprint's history.

Confidence statement

High confidence in the reproduced sample, fit, product branching fraction, significance and limit values, checked in the primary preprint. Medium confidence in the interpretation of the X(2370) as a dominant glueball: it is the authors' cumulative conclusion, not yet peer reviewed and not accompanied by a single global significance. Uniqueness check: no A001–A018 entry shares arXiv:2607.20366, the X(2370) or this central result; verdict UNIQUE. This bulletin's own contribution is to distinguish the non-observation of the submode, the flavour-singlet property inferred by the authors and the glueball interpretation, which requires their complete body of evidence.