The $D{\bar{D}}^{\ast }$ interaction with isospin zero in an extended hidden gauge symmetry approach

Abstract

The $D{\bar{D}}^{\ast }$ interaction via a $\rho$ or $\omega$ exchange is constructed within an extended hidden gauge symmetry approach, where the strange quark is replaced by the charm quark in the $SU(3)$ flavor space. With this $D{\bar{D}}^{\ast }$ interaction, a bound state slightly lower than the $D{\bar{D}}^{\ast }$ threshold is generated dynamically in the isospin zero sector by solving the Bethe-Salpeter equation in the coupled-channel approximation, which might correspond to the $X(3872)$ particle announced by many collaborations. This formulism is also used to study the $B{\bar{B}}^{\ast }$ interaction, and a $B{\bar{B}}^{\ast }$ bound state with isospin zero is generated dynamically, which has no counterpart listed in the review of the Particle Data Group. Furthermore, the one-pion exchange between the $D$ meson and the ${\bar{D}}^{\ast }$ is analyzed precisely, and we do not think the one-pion exchange potential need be considered when the Bethe-Salpeter equation is solved.

Comments: 15 pages, 4 figure, 2 tables