Mixture of $χ_{cJ}(2P)$ and Hadronic Molecules

Some hadrons are difficult to explain as normal hadrons made of quark-antiquark pairs or three quarks. These are called exotic hadrons. Since the Belle experiment discovered $X(3872)$ in 2003, more exotic hadrons containing charm quarks have been reported. Exotic hadrons likely have more complex structures than normal hadrons, but this is still uncertain. The $X(3872)$ is one of the most well-known exotic hadrons and has been observed in many experiments. It has the same quantum numbers as $\chi_{c1}(2P)$, but its mass differs from the quark model’s prediction. It is also very close in mass to the $D^{0}\bar{D}^{*0}$ threshold, with only a $0.04$ MeV difference. In this study, we analyze $\chi_{cJ}(2P)$ as a mixture of a hadronic molecule state, similar to a deuteron, and a bare $\chi_{cJ}(2P)$ core, comparing it to $X(3872)$ and others.