Charmonium decays into proton-antiproton and a quark-diquark model for the nucleon

A quark-diquark model of the nucleon is applied to a perturbative QCD description of several decays of the charmonium family: ${\eta }_c, {\chi }_{c0,c1,c2,} f_{c2\mathrm{}}\to p\overline{p}$. Both experimental data and theoretical considerations are used to fix the parameters of the model. The decay rates for the $\chi \text{'}\mathrm{s}$ and for the ${\eta }_c$ cannot be made to simultaneously agree with the experimental results: we can obtain a good agreement with the existing data on the $\chi \text{'}\mathrm{s}$, but the values for the decay of the ${\eta }_c$ are then found to be much smaller than the data. The available experimental information is also discussed. Our formalism provides a general framework for the computation of the decay amplitudes of any ${}_{}{}^{2S+1}{}_{}{}^{}L_J^{}{}_{}{}^{}$, $C=+1\mathrm{}$, heavy-quarkonium state into a hadron-antihadron pair. The explicit expression for the decay into two photons is also given.