$D^{\pm }{D}^{\ast \mp }$ Hadronic Atom as a Key to Revealing the $X(3872)$ Mystery

Abstract

The $X(3872)$, whose mass coincides with the $D^0{\bar{D}}^{\ast 0}$ threshold, is the most extended hadron object. Since its discovery in 2003, debates have never stopped regarding its internal structure. We propose a new object, the $X$ atom, which is the $D^{\pm }{D}^{\ast \mp }$ composite system with positive charge parity and a mass of $(3879.89\pm 0.07)$ MeV, formed mainly due to the Coulomb force. We show that a null signal of the $X$ atom can be used to put a lower limit on the binding energy of the $X(3872)$. From the current knowledge of the $X(3872)$ properties, the production rate for the $X$ atom relative to the $X(3872)$ in $B$ decays and at hadron colliders should be at least $1\times 10^{-3}$. New insights into the $X(3872)$ will be obtained through studying the $X$ atom.

6 pages, 3 figures