The bound state problem of S-wave heavy quark meson-aitimeson systems

Abstract

We investigated systematically whether the S-wave ($\bar{Q}q$) meson and the ($Q\bar{q}$) meson may form S-wave bound states in a chiral SU(3) quark model by solving the resonating group method equation. Here $Q=c$ or $b$ and $q=u$, $d$ or $s$. Our preliminary calculation disfavors the existence of $I=\frac{1}{2}$ ($\bar{Q}l$)-($Q\bar{s}$) molecules ($l=u,d$) while favors the existence of isoscalar $B\bar{B}$, $B^{\ast }{\bar{B}}^{\ast }$ (J=2) and $B{\bar{B}}^{\ast }$ (C=+) molecules. The existence of isovector (charm-anticharm) and (charm-bottom) molecules is also disfavored. Therefore the resonance-like structure $Z^{+}(4051)$ is unlikely to be an S-wave $D^{\ast }{\bar{D}}^{\ast }$ molecule.

Comments: 8 pages, 7 tables, accepted by Phys. Rev. C