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 $$\Lambda \overline{\Sigma }{}^0+\text {c.c.}$$

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.