New insight into the exotic states strongly coupled with the $D{\bar{D}}^{\ast }$ from the $T_{cc}^{+}$

We have investigated the internal structure of the open- and hidden-charmed ($D{D}^{\ast }$/$\bar{D}{D}^{\ast }$) molecules in the unified framework. We first fit the experimental lineshape of the $T_{cc}^{+}$ state and extract the $D{D}^{\ast }$ interaction, from which the $T_{cc}^{+}$ is assumed to arise solely. Then we obtain the $D{\bar{D}}^{\ast }$ interaction by charge conjugation. Our results show that the $D{\bar{D}}^{\ast }$ interaction is attractive but insufficient to form $X(3872)$ as a bound state. Instead, its formation requires the crucial involvement of the coupled channel effect between the $D{\bar{D}}^{\ast }$ and $c\bar{c}$ components, although the $c\bar{c}$ accounts for approximately $1\mathrm{\%}$ only. Besides $X(3872)$, we have obtained a higher-energy state around $3957.9$ MeV with a width of $16.7$ MeV, which may be a potential candidate for the $X(3940)$. In $J^{PC}=1^{+-}$ sector, we have found two states related to the iso-scalar $\tilde{X}(3872)$ and $h_c(2P)$, respectively. Our combined study provides valuable insights into the nature of these $D{D}^{\ast }$/$D{\bar{D}}^{\ast }$ exotic states.