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

Abstract

Under the aegis of isospin conservation, the amplitudes in Born approximation, i.e., considering the only one-photon-exchange mechanism, of the decay $\psi \to \Lambda \overline{\Sigma }{}^0+c.c.$, where $\psi$ is a vector charmonium, and of the reaction $e^{+}{e}^{-}\to \Lambda \overline{\Sigma }{}^0+c.c.$ 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 $J/\psi$.

Comments: 8 pages, 4 figures