The measurements of the $J/\psi \rightarrow \gamma p \overline{p}$ decays by the BES Collaboration indicate an enhancement at the $p \overline{p}$ threshold which, however, is not present in the J/$\psi$ decays into $\omega p \overline{p}$ and into $\pi p \overline{p}$. Here, two processes for describing the decays $J/\psi \rightarrow \mathcal{B} p \overline{p}$ where $\mathcal{B} = \gamma, \omega$ are presented in some detail and the cases $\mathcal{B} =\phi, \pi $ are briefly touched on... The first one, applied not only to the radiative decay to reproduce the threshold peak but also to the $\omega p \overline{p}$ decay channel to improve the description of the spectrum, postulates a direct emission of the boson before the baryon pair is formed. The second process assumes that the boson $\mathcal{B}$ is emitted from the baryon pair following the $J/\psi$ decay and includes for the decays into $\gamma p \overline{p}$ a final state nucleon-antinucleon interaction based on the Paris $N \overline{N}$ potential. The reproduction of the $p \overline{p}$ distribution in the $J/\psi \rightarrow \omega p \overline{p}$ decays needs a final state interaction involving a $N(2050)\ 3/2^-$ resonance. The photon- and meson-emission rates are reproduced in a semi-quantitative way. (read more)