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First measurement of J/ψ and ψ(3686) decay probabilities to a Σ0-hyperon pair plus an η meson refines the 12% rule.
An archaeologist carefully brushes away layer after layer, and each new stratum at the charmonium dig is a rare decay captured by the detector. Charmonium — a bound state of a charm quark and its antiquark — lives for mere fractions of a second, yet it manages to tell us about the forces that hold quarks together. This time, two new channels have been unearthed: J/ψ → Σ0Σ̄0η and ψ(3686) → Σ0Σ̄0η.
The probability of the first is 7.5 chances in 100,000, and of the second, 1.3 chances in 100,000. That sounds like finding one marked grain of sand in a handful of 13,000, but for physicists it's a goldmine. The ratio of these probabilities — 17.3% — is expected to follow the "12% rule" predicted by quantum chromodynamics. The rule states: if two particles decay into the same debris, the ratio of their probabilities should be 12%. Here we get 17.3% — within 3σ of the prediction. This is a moderate deviation, not as dramatic as the famous "ρπ puzzle," but it adds a new point to the map of violations.
The 12% rule is like expecting that two similar buildings made of identical bricks would collapse in the same way. But if one building has a hidden crack, the debris will fly differently. Deviations from the rule point to such "cracks" in our understanding of the strong interaction.
The BESIII detector at the BEPCII collider has accumulated record statistics: 10 billion J/ψ events and 2.7 billion ψ(3686) events. Σ0 hyperons were reconstructed via their decays to a photon and a Λ baryon, and the η meson via two photons. To separate signal from background, a kinematic fit with four constraints and a two-dimensional sideband method were used. The detection efficiency was determined by reweighting simulated events according to the observed Dalitz distribution — this is crucial because real events are distributed differently than predicted by simple phase space.
In the invariant mass spectra of Σ0η and Σ0Σ̄0, no significant intermediate resonances or threshold enhancements were found. This constrains hypotheses about baryonia and multiquark states, which are actively discussed for similar channels. The absence of enhancements is also a result: it indicates that the decay proceeds directly, without intermediate "stations."
Baryonium is a hypothetical bound state of a baryon and an antibaryon, which could manifest as a sharp rise in the number of events near the production threshold. Here, no such rise is seen.
This work adds a new point to the systematics of 12% rule violations for baryonic final states. For the first time, a channel with a Σ0 pair and an η meson has been measured, expanding the dataset for testing theoretical models. Accumulating more ψ(3686) statistics at BESIII and the future STCF will allow refining Q and determining whether the deviation from 12% is a statistical fluctuation or a real effect. The archaeologist keeps digging — each new layer brings us closer to understanding how quarks assemble into hadrons.
