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

Abstract

$S$-wave bound-states composed of a nucleon($N$) and a heavy meson ($D$, $D^{\ast }$, $\bar{B}$ or ${\bar{B}}^{\ast }$) 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 $N{D}^{\ast }$ 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 $N{D}^{\ast }$ $S$-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 $\hat{I}{\pounds }_c(2800)$ 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 $\hat{I}{›}_c(2940{)}^{+}$ as an $S-$wave $N{D}^{\ast }$ state with $I=0$ and $J^P=3/2^{-}$. Further information on the $ND$ and $N{D}^{\ast }$ interactions in the (unbound) scattering kinematics are obtained from the corresponding $S$-wave phase shifts. The $N\bar{B}$ and $N{\bar{B}}^{\ast }$ 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.

11 pages, 4 figures