The observed enhancement of $pbar p$-production near the threshold in radiative decays of $J/psi$ and $e^+e^-$-annihilations can be explained with final state interactions among the produced $Nbar N$ system, where the enhancement is essentially determined by $Nbar N$ elastic scattering amplitudes. We propose to use an effective theory for interactions in a $Nbar N$ system near its threshold. The effective theory is similar to the well-known one for interactions in a $NN$ system but with distinctions. It is interesting to note that in the effective theory some corrections to scattering amplitudes at tree-level can systematically be summed into a simple form. These corrections are from rescattering processes. With these corrected amplitudes we are able to describe the enhancement near the threshold in radiative decays of $J/psi$ and $e^+e^-$-annihilations, and the $pbar p$ elastic scattering near the threshold.
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