Possible $S$-wave $ND^{(*)}$ and $N\bar B^{(*)}$ bound states in a chiral quark model

Abstract

$S$-wave bound-states composed of a nucleon($N$) and a heavy meson ($D$, $D^*$, $\bar{B}$ or $\bar{B}^*$) are investigated in both the chiral SU(3) quark model and the extended chiral SU(3) quark model by solving the resonating group method equation. The results reveal that the $ND$ and $ND^*$ interactions in the corresponding relative $S$-wave states are attractive, arising mainly from one boson exchange processes between light quarks. It is shown that these attractions are strong enough to form six $ND$ and $ND^*$ $S$-wave bound states in the extended chiral SU(3) quark model with the binding energies in the range of $3-45$ MeV, and three $S$-wave bound states within the chiral SU(3) quark model with binding energies of $2-8$ MeV. In particular, the experimentally observed $\Sigma_c(2800)$ is interpreted to be most likely an $S-$wave $ND$ state with the total isopsin $I=0$ and spin-parity $J^P=1/2^-$, while $\Lambda_c(2940)^+$ as an $S-$wave $ND^*$ state with $I=0$ and $J^P=3/2^-$. Further information on the $ND$ and $ND^*$ interactions in the (unbound) scattering kinematics are obtained from the corresponding $S$-wave phase shifts. The $N\bar{B}$ and $N\bar{B}^*$ systems are also investigated within the present two models and some $S-$wave bound states with binding energies in the range of $1-60$ MeV are predicted in these systems: six (in total) within the extended chiral SU(3) quark model and, four, within the chiral SU(3) quark model.