Study of the $J/ψ o ΛarΣ^0η$ reaction

We study the isospin violating $J/ψ\to Λ\bar Σ^0 η$ reaction, recently measured by the BESIII collaboration, by looking at the dominant terms with $\bar Σ^0$ and a pair of pseudoscalar-baryon particles that form together an SU(3) singlet and can thus couple to the $J/ψ$. Next we allow these pairs to undergo final state interaction to produce the final $ηΛ$. We find that the relevant original channels are $\bar K N$ and $K Ξ$, and the non cancelation of terms involving charged and neutral particles, because of their different masses, is responsible for the reaction. With that mechanism we find a good agreement with the three experimental mass distributions.

💡 Research Summary

The paper presents a theoretical study of the isospin‑violating decay J/ψ → Λ ¯Σ⁰ η, a channel recently measured by the BESIII collaboration. In the BESIII data a clear Λ(1670) signal appears in the η Λ invariant‑mass spectrum, accounting for essentially the whole strength of the distribution. The authors aim to explain this observation by exploiting the fact that Λ(1670) is dynamically generated from coupled meson‑baryon channels within the chiral unitary approach.

First, the authors treat the J/ψ as an SU(3) singlet in the light‑quark sector. They construct the possible SU(3) singlet structures involving an antibaryon (¯Σ⁰), a baryon (B) and a pseudoscalar meson (P) from the octet matrices. By evaluating the traces ⟨¯B B P⟩ and ⟨¯B P B⟩ and discarding contributions that couple only weakly to Λ(1670) (π Σ, π Λ, η Σ⁰), they isolate two dominant combinations that can be produced at the primary J/ψ decay:

1. ½ ¯Σ⁰ (p K⁻ − n ¯K⁰) (originating from the ¯B B P trace)
2. ½ ¯Σ⁰ (K⁺ Ξ⁻ − K⁰ Ξ⁰) (originating from the ¯B P B trace)

Both combinations have overall isospin I = 0, matching the J/ψ quantum numbers. However, because the charged and neutral members of each isospin doublet have different masses, the loop contributions involving these pairs do not cancel, providing a source of isospin violation.

The final‑state interaction (FSI) that converts the intermediate meson‑baryon pair into the observed η Λ is treated with the coupled‑channel Bethe‑Salpeter equation

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