Uncovering the mystery of $X(3872)$ with the coupled-channel dynamics

Abstract

The $X(3872)$, as the first and the most crucial member in the exotic charmoniumlike $XYZ$ family, has been studied for a long time. However, its dynamical origin, whether stemming from a $D\bar{D}^*$ hadronic molecule or the first excited $P$-wave charmonium $χ_{c1}(2P)$, remains controversial. In this Letter, we demonstrate that the $X(3872)$ definitely does not result from the mass shift of the higher bare $χ_{c1}(2P)$ resonance pole in the coupled-channel dynamics involving a short-distance $c\bar{c}$ core and the long-distance $D\bar{D}^*$ channels. Instead, it originates from either the $D\bar{D}^*$ molecular pole or the shadow pole associated with the anti-resonance of the $P$-wave charmonium, depending on the weak or strong coupling mode, respectively. To differentiate these origins and fully exploit the nature of $X(3872)$, we conduct a comprehensive analysis in a couple-channel dynamics framework, including the isospin violation, the three-body $D\bar{D}π$ effect, the dynamical width of $D^*$, and non-open-charm decays of the bare $χ_{c1}(2P)$. Our findings highlight the pivotal role of the coupled-channel dynamics in explaining the disparity between the pole widths of $X(3872)$ and $T_{cc}^+$, while also predicting a new resonance with $J^{PC}=1^{++}$ around 4.0 GeV. By matching the newly observed $χ_{c1}(4010)$ by the LHCb Collaboration to our predicted resonance, we conclude that the $X(3872)$ most likely originates from the $D\bar{D}^*$ pole with a confidence level exceeding $99.7\%$.