  After investigating the decays of a charmonium $\psi = J/\psi, \psi(2S)$ into
a spin-1/2 baryon-antibaryon $B \bar{B}$ pair, with the determination of the
only parameter that gives the EM amplitude for neutral final states, in this
work we focus our attention on the decays into charged baryons, whose EM
amplitudes can be expressed in terms of a further parameter. By considering the
BESIII data on the $e^+e^- \to p \overline p$ cross section we obtain a full
parametrization for the EM amplitudes and make predictions on the cross section
of the decays $e^+ e^- \to \Sigma^+ \overline \Sigma{}^-$, $e^+ e^- \to
\Sigma^- \overline \Sigma{}^+$ and $e^+ e^- \to \Xi^- \overline \Xi{}^+$ at the
$J/\psi$ and $\psi(2S)$ masses.
