On possible $S$-wave bound states for a $N \bar N$ system within a constituent quark model

Abstract

We try to apply a constituent quark model (a variety chiral constituent quark model) and the resonating group approach for the multi-quark problems to compute the effective potential between the $N\bar{N}$ in $S$-wave (the quarks in the nucleons $N$ and $\bar{N}$, and the two nucleons relatively as well, are in $S$ wave) so as to see the possibility if there may be a tight bound state of six quarks as indicated by a strong enhancement at threshold of $p\bar{p}$ in $J/ψ$ and B decays. The effective potential which we obtain in terms of the model and approach shows if the experimental enhancement is really caused by a tight $S$-wave bound state of six quarks, then the quantum number of the bound state is very likely to be $I=1, J^{PC}=0^{-+}$.