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

TL;DR

This paper models the $Dar{D}^*$ interaction using an extended hidden gauge symmetry approach, predicting bound states that may correspond to the $X(3872)$ and a new $Bar{B}^*$ state, with implications for understanding exotic mesons.

Contribution

It introduces an extended hidden gauge symmetry framework for $Dar{D}^*$ interactions, dynamically generating bound states associated with exotic mesons like $X(3872)$.

Findings

A $Dar{D}^*$ bound state near threshold is generated, potentially matching $X(3872)$.

A novel $Bar{B}^*$ bound state is predicted without PDG counterpart.

One-pion exchange is deemed negligible in the Bethe-Salpeter equation analysis.

Abstract

The $D \bar{D}^*$ 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 $D \bar{D}^*$ interaction, a bound state slightly lower than the $D \bar{D}^*$ 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 $B \bar{B}^*$ interaction, and a $B \bar{B}^*$ 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 $\bar{D}^*$ is analyzed precisely, and we do not think the one-pion exchange potential need be considered when the Bethe-Salpeter equation is solved.