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Under the aegis of isospin conservation, the amplitudes in Bornapproximation, i.e., considering the only one-photon-exchange mechanism, of thedecay $\psi\to \Lambda \overline \Sigma{}^0+{\rm c.c.}$, where $\psi$ is avector charmonium, and of the reaction $e^+e^- \to \Lambda \overline\Sigma{}^0+{\rm c.c.}$ at the $\psi$ mass, are parametrized by the sameelectromagnetic coupling. It follows that, the modulus of such a coupling canbe extracted the data on the two observables: the decay branching fraction andthe annihilation cross section. By considering the first two vector charmonia,$J/\psi$ and $\psi(2S)$, it is found that, especially in the case of$\psi(2S)$, there is a substantial discrepancy between the values of themodulus of the same electromagnetic coupling extracted from the branching ratioand the cross section. We propose, as a possible explanation for such adisagreement, the presence in the decay amplitude of an isospin-violatingcontribution driven by a mechanism based on physical (on-shell) intermediatestates, that, due to their own nature, should be more effective in the$\psi(2S)$ decay than in that of the $J/\psi$.

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