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 $Lambda overline Sigma{}^0+{rm c.c.}$

Under the aegis of isospin conservation, the amplitudes in Born approximation, i.e., considering the only one-photon-exchange mechanism, of the decay $psito Lambda overline Sigma{}^0+{rm c.c.}$, where $psi$ is a vector charmonium, and of the reaction $e^+e^- to Lambda overline Sigma{}^0+{rm c.c.}$ at the $psi$ mass, are parametrized by the same electromagnetic coupling. It follows that, the modulus of such a coupling can be extracted the data on the two observables: the decay branching fraction and the 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 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 an isospin-violating contribution driven by a mechanism based on physical (on-shell) intermediate states, that, due to their own nature, should be more effective in the $psi(2S)$ decay than in that of the $J/psi$.