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

TL;DR

This paper investigates isospin violation in vector charmonia decays into Lambda and Sigma0 states by comparing electromagnetic coupling extractions from decay and production data, revealing significant discrepancies especially for psi(2S).

Contribution

It introduces a novel analysis of isospin violation effects in charmonium decays, highlighting the role of on-shell intermediate states in causing observed discrepancies.

Findings

Discrepancy between coupling values from decay and cross section data, especially for psi(2S).

Isospin-violating contributions are more significant in psi(2S) decays.

On-shell intermediate states may explain the observed differences.

Abstract

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