$χ_{cJ}(2P)$ with hadronic molecules

Some hadrons are hard to explain as normal hadrons made of quarks and antiquarks, or three quarks. These are called exotic hadrons. Since the Belle experiment reported $X(3872)$ in 2003, more exotic hadrons containing charm quarks have been found. Exotic hadrons are believed to have more complex structures than normal hadrons, but no conclusion has been reached yet. The $X(3872)$ is one of the most famous exotic hadrons and has been seen in many experiments. It has the same quantum numbers as $χ_{c1}(2P)$, but its mass is different from what the quark model predicts. It is also very close in mass to the $D^{0}\bar{D}^{*0}$ threshold, with a difference of 0.04 MeV. In this study, we analyze $χ_{cJ}(2P)$ as a mixture of a hadronic molecule state, like a deuteron, and a bare $χ_{cJ}(2P)$ core, comparing it to $X(3872)$ and others. We consider one-boson-exchange and core-molecule mixture potentials.