Revisiting the proton-antiproton scattering using a constituent-quark-model based coupled-channels calculation

Motivated by the last experimental and theoretical advances in the analysis of possible baryonium resonances, the $X(1835)$ and their partners, we perform a constituent-quark-model based coupled-channels calculation of the proton-antiproton scattering in order to analyze the possible existence of bound states or near-threshold structures. The used $N\overline N$ potential is derived from a $G$-parity transformation of the quark-model-based $NN$ interaction which has described well deuteron properties, $NN$ phase shifts, and even hadron-hadron phenomenology. The additional $N\overline N$ annihilation is taken into account by a complex phenomenological potential whose real part is generated by one-pion and one-gluon exchange annihilation potentials and its imaginary part is an energy-independent potential of Gaussian form. Then, all the parameters of the interaction are constrained by the $NN$ sector except those determining the imaginary part of the annihilation potential. Our study concludes that the nucleon-antinucleon dynamics is complex and rich in scattering singularities near the proton-antiproton and neutron-antineutron thresholds.