Study on $N\bar{N}$ $S$-wave Elastic Cross Section and Possible Bound States Within a Constituent Quark Model

In the framework of a chiral constituent quark model, considering the contributions of $\pi$ annihilation and one-gluon annihilation, the proton-antiproton $S$-wave elastic scattering cross section experimental data can be reproduced by adjusting properly one-gluon annihilation coupling constant. Meanwhile, using the fixed model parameter, we do a dynamical calculation for all possible $S$-wave nucleon-antinucleon states, the results show that, there is no $S$-wave bound state as indicated by a strong enhancement at threshold of $p\bar{p}$ in $J/\psi$ and $B$ decays.