Amplitudes separation and strong-electromagnetic relative phase in the $\psi(2S)$ decays into baryons

The strong, electromagnetic and mixed strong-electromagnetic amplitudes of the $\psi(2S)$ decays into baryon-anti-baryon pairs have been obtained by exploiting all available data sets in the framework of an effective Lagrangian model. We observed that at the $\psi(2S)$ mass the QCD regime is not completely perturbative, as can be inferred by the relative strength of the strong and the mixed strong-electromagnetic amplitudes. Recently a similar conclusion has been reached also for the $J/\psi$ decays. The relative phase between the strong and the electromagnetic amplitudes is $\varphi = (58\pm 8)^\circ$, to be compared with $\varphi = (73\pm 8)^\circ$ obtained for the $J/\psi$. On the other hand, in the case of the $\psi(2S)$ meson, different values of the ratio between strong and mixed strong-electromagnetic amplitudes are phenomenologically required, while for the $J/\psi$ meson only one ratio was enough to describe the data. Finally, we also observed a peculiar behavior of the mixed strong-electromagnetic amplitudes of the decays $\psi(2S)\to\Sigma^+ \overline \Sigma{}^-$ and $\psi(2S)\to\Sigma^- \overline \Sigma{}^+$.