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Under the aegis of isospin conservation, the amplitudes in Born approximation, i.e., considering the only one-photon-exchange mechanism, of the decay    $$\psi \rightarrow \Lambda \overline{\Sigma }{}^0+\text {c.c.}$$  ψ → Λ Σ ¯ 0 + c.c. , where    $$\psi $$  ψ is a vector charmonium, and of the reaction    $$e^+e^-\rightarrow \Lambda \overline{\Sigma }{}^0+\text {c.c.}$$  e + e - → Λ Σ ¯ 0 + c.c. at the    $$\psi $$  ψ mass, are parametrized by the same electromagnetic coupling. It follows that, the modulus of such a coupling can be extracted from the data on the two observables: the decay branching fraction and the annihilation cross section. By considering the first two vector charmonia,    $$J/\psi $$  J / ψ and    $$\psi (2S)$$  ψ ( 2 S ) , it is found that, especially in the case of    $$\psi (2S)$$  ψ ( 2 S ) , there is a substantial discrepancy between the values of the modulus of the same electromagnetic coupling extracted from the branching ratio and the cross section. We propose, as a possible explanation for such a disagreement, the presence in the decay amplitude of isospin-violating contributions driven by two different mechanisms, that, however, appear to be more favored in the    $$\psi (2S)$$  ψ ( 2 S ) than in the    $$J/\psi $$  J / ψ decays.

european physical journal. c, particles and fields

The cross section of $$e^+e^-\rightarrow \Lambda \overline{\Sigma }{}^0+\text {c.c.}$$ as a litmus test of isospin violation in the decays of vector charmonia into $$\Lambda \overline{\Sigma }{}^0+\text {c.c.}$$