Study of $T_{cc}$ and X(3872)

In this study, we utilize experimental data for the $T_{cc}$ to determine the interactions within the $DD^*$ system. By applying the one boson exchange model and heavy quark effective field theory, we derive extend this interaction to the $D\bar{D}^*+\bar{D}D^*$ based on charge conjugation symmetry. Subsequently, we employ the decay width of $\psi(3770) \to D\bar{D}$ to constrain the parameters of the $^3P_0$ model. Without introducing free parameters, we identify the pole position of $X(3872)$ by considering the coupling between the $c\bar{c}$ bare state predicted by the conventional quark model and the $D\bar{D}^*+\bar{D}D^*$ channel, and calculate its wave function. Our findings reveal that the long-range part of $X(3872)$ is dominated by $D\bar{D}^{*}+\bar{D}D^*$, whereas the $c\bar{c}$ component plays a significant role at short-range. Additionally, we predict the existence of a higher-energy $\chi_{c1}$ particle, predominantly composed of $c\bar{c}$, with its main decay channel being $D\bar{D}^{*}+\bar{D}D^*$.